II III lliillili iiliiii III i III ifill II
NBSIR 75-763^
Thermodynamic and Transport
Properties of Ethylene and Propylene
D. M. Vashchenko, Yu. F, Voinov, B. V. Voityuk, E. K. Dregulyas, A. Ya. Kolomiets, S. D. Labinov,
A, A. Morozov, I. A» Neduzhii (Principal Author),
V. P. Provotar, Yu, A. Soldatenko, E. I. Storozhenko,
Yu. I. Khmara
State Office of Standards and Reference Data U.S.S.R.
June 1972
Final
\
I
Prepared for
Office of Standard Reference Data, NBS
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75"- 7^3 I
NBSIR 75-763
THERMODYNAMIC AND TRANSPORT PROPERTIES OF ETHYLENE AND PROPYLENE
D. M, Vashchenko, Yu. F. Voinov, B. V. Voityuk, E. K. Dregulyas, A. Ya. Kolomiets, S. D. Labinov,
A. A. Morozov, I. A. Neduzhii (Principal Author),
V. P. Provotar, Yu, A. Soldatenko, E, I. Storozhenko,
Yu. I. Khmara
State Office of Standards and Reference Data U,S.S.R.
June 1972
Final
Prepared for Office of Standard Reference Data, NBS
/ V ^ * 1—i,'^ f
' •"•c.u o«
U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary
James A. Baker, III, Under Secretary Dr. Betsy Ancker-Johnson. Assistant Secretary for Science and Technology
NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director
Foreword
The thermophysical properties of ethylene and proplylene are of considerable interest because of the widespread use of these compounds as starting materials in chemical syntheses. The Office of Standard Reference Data of the National Bureau of Standards, with support from a number of industrial firms, has undertaken a program to establish definitive values for the equation of state and thermodynamic properties of ethylene. As one of inputs to this program, the book, "Thermodynamic and Transport Properties of Ethylene and Propylene," has been translated from the Russian. This translation is being made available to interested parties by issuing it as an NBS Internal Report.
For further information on the ethylene program, please contact:
Dr. H. J. White, Jr. Office of Standard Reference Data National Bureau of Standards Washington, D. C. 20234
THERMODYNAMIC AND TRANSPORT PROPERTIES OF ETHYLENE AND PROPYLENE
[Book; Moscow, Termodinamicheskiye i Transportnyye Svoystva Etilena i
Propilena , Russian, 1971, Standards Publishing House, signed to press 23 June 1971, 182 pages]
Table of Contents Page
Preface 1 Symbols Employed in Manual 3
PART I. REVIEW AND ANALYSIS OF EXISTING DATA ON THERMOPHYSICAL PROPERTIES OF ETHYLENE AND PROPYLENE
Chapter I. Thermal Properties of Gaseous Ethylene and Propylene 5 Review of Experimental Data on Density of Gaseous Ethylene and Propylene 5 Analysis of Thermal Equations of State for Gaseous Ethylene and Propylene 7 Thermal Equations of State of Gaseous Ethylene and Propylene 12 Review of Data on Second Virial Coefficient 25 Determination of Second Virial Coefficient of Ethylene and
Propylene According to Experimental Data on Speed of Sound . . 29 Determination of Second Virial Coefficients of Ethylene and Propylene According to Compressibility Data. Recommended Values 32 Recommended Values of Specific Volume, Enthalpy, Entropy, Isobaric Heat Capacity of Gaseous Ethylene and Propylene ... 37
Chapter II. Specific Volume of Liquid Ethylene and Propylene
Review of Experimental Data 39 Recommended Specific Volumes of Liquid Ethylene and Propylene. 45
Chapter III. Properties of Ethylene and Propylene on Saturation Curve 47 Pressure and Density of Saturated Vapor and Liquid 47 Heat of Evaporation 55
-a- Critical Parameters 57
Chapter IV. Thermodynamic Functions of Ethylene and Propylene in Perfect-Cas State 61 Review of Data 61 Recommended Isobaric Heat Capacity, Entropy and Enthalpy of Ethylene and Propylene in Perfect-Gas State 67
Chapter V. Speed of Sound and Heat Capacities of Gaseous Ethylene and Propylene 69 Review of Data on Heat Capacities of Gaseous Ethylene and Propylene 69 Review of Experimental Data on Speed of Sound in Gaseous Ethylene and Propylene 71 Recommended Thermodynamic Speeds of Sound, Adiabatics Index, Heat Capacity Ratios and Isobaric Heat Capacity of Gaseous Ethylene and Propylene 80
Chapter VI. Caloric Properties of Ethylene and Propylene in Condensed State 85
Review of Experimental Data 85 Recommended Caloric Properties of Ethylene and Propylene in Condensed State 95
Chapter VII. Viscosity of Ethylene and Propylene 99
Viscosity of Gaseous Ethylene and Propylene at Atmospheric Pressure 99 Viscosity of Gaseous Ethylene and Propylene at High Pressures. 105
Viscosity of Ethylene and Propylene on Saturation Curve. . . . 109
Viscosity of Liquid Ethylene and Propylene at High Pressures . 115
Chapter VIII. Thermal Conductivity of Ethylene and Propylene 116
Thermal Conductivity of Ethylene and Propylene at Atmospheric Pressure 116 Thermal Conductivity of Ethylene and Propylene at High Pressures 123 Thermal Conductivity of Liquid Ethylene 129
PART II. TABLES OF THERMODYNAMIC AND TRANSPORT PROPERTIES OF ETHYLENE AND PROPYLENE 130 Units of Measurements Used in Tables 130 Table I. Thermodynamic Properties p, v, i, r, s, C of
Ethylene on Saturation Line as Functions of Temperature. . . . 131
Table II. Thermodynamic Properties v, i, s, C of Ethylene . . 132 Table III. Specific Volume of Liquid Ethylene? 155 Table IV. Velocity of Sound w. Index of Adiabatics k^, Ratio of Heat Capacities k of Gaseous Ethylene 155
-b- Table V. Thermodynamic Properties p, v, i, r, s, of
Propylene on Saturation Line as Functions of Temperature. . , 160
Table VI. Thermodynamic Properties v, i, s, of Propylene . 161
Table VII. Specific Volume of Liquid Propylene 181
Table VIII. Velocity of Sound w. Index of Adiabatics k , Ratio of Heat Capacities of Gaseous Propylene k.. 182 Table IX. Viscosity n'lO^ and Thermoconductivity X'lO^ of Ethylene and Propylene on Saturation Line as Functions of Temperature 185 Table X. Viscosity of Gaseous Ethylene ri^'lO^ and Propylene ri2*10® at Atmospheric Pressure 186 Table XI. Viscosity n'lO^ and Thermoconductivity A«10^ of Ethylene 187 Table XII. Viscosity n'lO^ and Thermoconductivity A'lO^ of Propylene 189
BIBLIOGRAPHY 191
-c- 3
UDC 536. 7:547. 313. 2/. ANNOTATION
This reference monograph contains tables of density, enthalpy, entropy, isobaric heat capacity, heat capacity ratios, velocity of sound, index of adiabatics, viscosity and thermal conductivity of ethylene and propylene in the temperature and pressure ranges encompassed by the experiment. The tables are preceded by a review and analysis of experimental data appearing in the literature.
The book is intended for a large community of engineers, working on problems of calculation, planning and operation of petrochemical industries. It may also be of use to scientists investigating the thermophysical properties of compounds and allied problems.
The monograph contains 76 tables, 227 bibliographic references and 23 illustrations.
Staff of authors: D. M. Vashchenko, Yu. F. Voynov, B. V. Voytyuk, E. K. Dregulyas, A. Ya. Kolomiyets, S. D. Labinov, A. A. Morozov, I. A. Neduzhiy (supervisor of the author staff), V. P. Provotar, Yu. A. Soldatenko, Ye. I. Storozhenko, and Yu. I. Khmara.
-d- PREFACE
This book is dedicated to the founder of the problem laboratory of engineering thermophysics of KTILP [Kiyevskiy
tekhnologicheskiy institut legkoy promyshlennosti ; Kiev Technological Institute of Light Industry] professor N. V. Pavlovich.
The use of ethylene and propylene in the organic synthesis industry and the high rates of expansion of the capacities of planned mass production gas fractionation plants for ethylene and propylene production stimulated a need for the development of detailed tables of the thermodynamic and trans- port properties of these compounds, essential for technological calculations in the planning of equipment and apparatus.
Previously published manuals contained thermodynamical ly contradictory data on the various properties of ethylene and propylene for a narrow range of temperatures and pressures, and often in a form unsuitable for use in engineering practice.
An attempt is made in this work to systematize existing experimental data on the thermodynamic and transport properties of ethylene and propylene and to create thermodynamical ly concordant tables of these properties in the temperature and pressure ranges that are of interest in technological applications. The solution of this problem required the organization of additional experimental and theoretical investigations of the properties of ethylene and propylene, which were carried out by the authors in the problems laboratory of engineering thermophysics of the Kiev Technological Institute of Light Industry from 1963-1968.
The properties measured included the density of the liquid phase, density of the vapor and of the liquid on the saturation line, isobaric heat capacity of the liquid, velocity of sound in gaseous ethylene and propylene, viscosity and thermal conductivity of ethylene and propylene, and thermal equations of state of gaseous ethylene and propylene were derived on the basis of more reliable data on compressibility.
-1- Part One of the book contains a review and analysis of existing data on thermodynamic and transport properties of ethylene and propylene, as well as the results of investigations performed by the authors; the method of processing data on the various properties and the method by which the tables were compiled^ are described in detail.
Part Two contains tables of the thermophysical properties of ethylene and propylene. The tables of the thermodynamic properties contain: properties on the liquid-vapor equilibrium line in the temperature range from 160°K to the critical point; specific volume, enthalpy, entropy and isobaric heat capacity of the liquid at pressures up to 60 bar, of the heated vapor up to 2,000 bar and 450°K; data on the density of liquid propylene at pressures of 65-600 bar and at temperatures of 270-360°K; data on the density of liquid ethylene at pressures of 70-500 bar and at temperatures of 180-270°K.
Tables of speed of sound, heat capacity ratio and adiabatics index are given for gaseous ethylene and propylene in the 210-470° K temperature range at pressures up to 100 bar.
The tables of the transfer coefficients contain: data on viscosity and thermal conductivity of ethylene in the 170-450°K temperature range at pressures up to 1,000 bar (viscosity) and 3,000 bar (thermal conductivity); data on viscosity and thermal conductivity of propylene at 270-450°K at pressures up to 1,000 bar (viscosity) and 50 bar (thermal conductivity), and also data on these properties of ethylene and propylene on the liquid-vapor equilibrium line.
Chapter I was written by V. P. Provotar, S. D. Labinov and Ye. 1. Storozhenko; section 1.5 of this chapter was written by Yu. A. Soldatenko and E. K. Dregulyas; Chapter II was written by B. V. Voytyuk and S. D. Labinov; Chapter III by Yu. F. Voynov and S. D. Labinov; Chapters IV-VI by Yu. A. Soldatenko, A. A. Morozov, E. K. Dregulyas and D. M. Vashchenko; Chapter VII by I. A. Neduzhiy and Yu. I. Khmara, and Chapter VIII by I. A. Neduzhiy and A. Ya. Kolomiyets.
Yu. I. Khmara and Yu. A. Soldatenko contributed greatly to the preparation of the manuscript.
The authors gratefully acknowledge N. A. Khanmurzinaya , M. E. Aerov and V. A. Kulikova for their cooperation in the investigations and also doctor of technical sciences professor V. A. Zagoruchenko for his review and esteemed advice.
The authors invite the critical comments and requests pertaining to the material in the monograph, and request that they be mailed to: Moscow,
K-1, ul . Shchuseva, d. 4, Standards Publishing House.
^The authors used literature data published prior to 1969.
-2- ;
I
SYMBOLS EMPLOYED IN MANUAL
B(T) -- second Virial coefficient in expansion in terms of density;
-- C , C isobaric and isochoric heat capacities;r ' p V f -- vibration frequency;
H°-H° -- change of enthalpy of compound in standard state from 0 to T 0 ^ o^.
i -- enthalpy;
i^ -- enthalpy in perfect-gas state at temperature T, measured from the crystalline state at 0°K;
I -- electric current;
k -- Boltzmann constant;
-- adiabatics index of real gas in equation; M -- molecular weight;
p -- pressure;
Q, q -- heat; R -- gas constant;
-- universal gas constant, equal to 8.3143 kJ/ (kmole'deg)
r -- heat of vaporization, linear distances;
S -- entropy;
S° entropy in perfect -gas state at temperature T °K;
T -- absolute temperature, °K; kT T* = reduced temperature;
t -- temperature on Celcius scale;
U -- voltage of electric current;
V, V -- mole and specific volumes; w -- speed of sound;
-3- 1
Z = ^ -- compressibility coefficient; A -- finite change of property, absolute error;
6 -- relative error;
£ -- depth of potential well;
ri -- dynamic viscosity coefficient;
a -- effective diameter of molecular interaction;
X -- thermal conductivity coefficient, heat of fusion;
7T = E reduced pressure; Pk p -- density; T T = — reduced temperature; ^k T -- time;
cj)(r) -- potential function of molecular interaction;
C K = ^ -- heat capacity ratio; v -- reduced density.
-4- . .
PART I. REVIEW AND ANALYSIS OF EXISTING DATA ON THERMOPHYSICAL PROPERTIES OF ETHYLENE AND PROPYLENE
CHAPTER I. THERMAL PROPERTIES OF GASEOUS ETHYLENE AND PROPYLENE
Review of Experimental Data on Density of Gaseous Ethylene and Propylene
The works cited in Table 1 pertain to experimental analysis of p, v, T-dependence of gaseous ethylene.
Systematic analysis of the density of ethylene was first done by
Amagat [1] . His work is now of historical importance only, despite the rather high accuracy of 0.2-0.3% of the results, since more recent data are now available [4, 5], distinguished by the maximum accuracy for the contemporary level of investigations.
The experimental results [2, 3, 6, 12, 13] are fragmentary. The most
noteworthy among them are the data of Walters and coworkers [6] . Agreement of the data of Walters and Michels falls within the range of error of 0.5-0.3%, as stated in [6].
Data on the density of gaseous ethylene and propylene at low pressures are found in [11, 13]. The data of both works coincide, since they were obtained on the same experimental apparatus. These works are of importance in determining the second Virial coefficient.
In [7, 8, 9, 10] are found p, v, T-data obtained by means of grapho- analytical processing of experimental data. Dick and Hedley [8] did correct smoothing of Michels' data [5].
Presented in Table 2 is a list and brief description of investigations of the p, V, T-properties of propylene.
The compressibility of propylene was first subjected to systematic analysis by Vaughan and Graves [17]
The pressure range was expanded to 700 bar by Farrington and Sage [18] The accuracy of the experiment, according to the authors, is 0.3%. Data of
-5- Table 1. List of Works Containing Data on the p, v, T-Function of Ethylene
^1 1) 2) |3)n„:. iian.T30ii ICTOxa HC- ABTOpU UdD,ie>HU'\ ,1, I .orpruiiPCTb CJieAOBSllHOl '> T. C 6ap ra3a, %
AMara [1] 1P03 0-190 -100 [li MeccoH 11 Ro.i.iH 132o 24,95 -125 |2] (2]
/laiiiKviL II Cto.1l- ly29 21—202 [3] AT ^ 0,PC 97.8 ueiiocpr 1 3] Av 0,5% Ap T--. 0,1 Cap MHxe.-.bc II JIhc- 19J6 0—150 20-70 [li] 0.01% ceii [4]
Miixe.ibc II Feji- 1942 0—150 16—3000 |14J 0.01 % AepMiJiic [5] 11) 4-: Ba;ib repc ii ;;p. [6] 1954 !(_7)— ( 3—40 0.5% N,-0,2; Apy- rue raau 0,2 KpaMep 1955 [7) i i ) 06pa6oTKa ,aaiiubix linK 11 Xo;i.nii (8] 1956 0-150 1—2500 >Ke Saropv'it-HKo 1959 (-lOOj - 0,5—20u0 ni):'C''ler no } (9. '10] (4 300) y]?aBiieHHio COCTOMKIiq Typ.lHHrTOII, 19G1 (--^.:0)- 0,5—1.5 [15] 0.1 ?6 MauKeiTa [11] (-1-301 ToMai: H UaiiAcp 19G6 0-50 0— 2i [16] |12J 1957 32,2; 48,8; 1—2 [15] 0.1% 99.9 Keira [13] (18,9
KEY: 1. Authors 2. Year Amagat [1] 3. Temperature range T, °C Mas son and Dolly [2] 4. Pressure range p, bar Dannell and Stolzenberg [3] 5. Method Michels and Niesen [4] 6. Error Michels and Geldermans [5] 7. Purity of investigated gas, % Walters, et al [6] 8. Data processing
Cramer [7] 9 . Same Dick and Hedley [8] 10. Calculation by equation of state Zagoruchenko [9, 10] 11. N -- 0.2; other gases 0.2 Turlington and McKetta [11] Thomas and Zander [12] Pfennig and McKetta [13]
Marchman, Prengle and Motard [19] coincide with an accuracy of 0.3% with data of Farrington and Sage. Results of Vaughn and Graves for low pressures agree satisfactorily with Marchman 's data. At high pressures, however, deviations reach 1-2.7%.
Michels and coworkers [21] published data in the 0-150°C temperature range and 6-2,800 bar pressure range. The error is 0.03%. They investi- gated high-purity propylene.
Data [17, 18, 19] at pressures to 20-30 bar coincide with Michels' results within 0.3-0.5%. At higher pressures the discrepancies reach 3-3.5%.
-6- Table 2. List of Works Containing Data on the p, v, T-Function of Propylene
1) 3; 5) icTora 1 o.; cny- A\i'To;; ;i-,cne- pcLU-
AuTOpbl ii'Mii'.p-'ryp .'13 ll.^i 'M .1 i liOCTb, Baiiiioro b:iii>i II /. -(.; oaf) u. rasa. %
Boyrc-ii h Ficw: 17j :!0 0—300 -SO 1 j [17] 0)- ffcappHHrxoii II Cci'f.iiiv \\S] \WJ I 4—?82 -689 118] 0,3 npiiMecefi 0,11 '>\ap4Maii, [Ijx'Kr.'ib, A\oinp;t 30—2o0 0—215 (24) 0,25 99,7 (19] Kam.-'^p, fo,'i;iMcin. Alaji'i- 19; (—10) - 1—200 ^) Po^iier no Mair(201 (+200) ypabiiciiiiio C0CTO;ililIH Miix-'^.ii.c ii roTpyjiiiiKii [21 3—150 6—2830 | 1 15) 0,03 n4)t'HllHr, AiaKKCTTJ (]3| 32,2; 48,.'!; 1—2 |23j 0,1 99.7
KaHbnp H coipyvmnKi; f22J I0i;3 — ^ ) OupafxjTKa
ilHir.iap 11 Cly;ibu 1962 100,110,120, GO— 1000 — i 130.140 I
KEY: 1. Authors 2 . Year published Vaughan and Graves [17] 3. Temperature range T, °C Farrington and Sage [18] 4. Pressure range p, bar Marchman, Prengle, Motard [19] 5. Experimental method Michels, et al [21] 6. Error, % Pfennig and McKetta [13] 7. Purity of investigated gas, % Canjar, et al [22] 8. Calculation by equation of state Ditmar and Schultz 9. Data processing 10. Impurities
Published in [20] are data obtained by calculation according to the Benedict-Webb-Rubin equation, the constants of which were determined by Marchman on the basis of experimental data.
It follows from the above review that highly accurate experimental data exist for gaseous ethylene and propylene in a rather wide pressure range, but in a narrow temperature range of 0-150°C. Experimental data [6, 11, 13] for ethylene can also be recommended as reference material. The range of the gas adjacent to the right boundary of the curve is not experimentally investigated.
Analysis of Thermal Equations of State for Gaseous Ethylene and Propylene
Numerous equations of state, derived on the basis of existing experimental p, v, T-data for ethylene and propylene, have been published in Soviet and foreign literature.
The constants of the Benedict-Webb-Rubin (B-W-R) equation are given in [23, 25, 26]. In addition, Michels' equations of experimental isotherms are given in [5, 21]. Most recent are V. A. Zagoruchenko ' s equations of
-7- state [9, 27] and those o£ Ya. Z. Kazavchinskiy and V. A. Zagoruchenko [28]. The Martin-Hou [29] and Bentzler [30] equations are used to a lesser extent.
The equations of state describe the p, v, T-surface of ethylene and propylene with various accuracy, depending on the pressures and temperatures Tables of reference data were compiled on the basis of the experimental data of Michels [5, 21] and Walters [6] for analysis of these equations, and were later used for checking the equations with the computer. Calculation results are presented in the form of nomograms in Figure 1.
The region encompassed by the experiment is cross hatched in the nomograms. The area of the nomograms is divided into regions by pressures, in which they are given with a constant step. The mean and maximum devia- tions of the experimental and calculated data are stated on the isotherms for each region, as are the average deviations for the entire region. The measure of deviation is the relation
" ^^^^^ 6 = ^^^P . 100%. p^exp
The B-W-R equation (Figure la) can be used with confidence with a mean error not exceeding 0.1% for interpolation of the p, v, T-properties of ethylene to a pressure of the order of 20 bar at temperatures of 270-440°K. Here the maximum deviation does not exceed 0.2%. The maximum deviations occur in the region next to the saturation line.
The B-W-R equation describes the p, v, T-properties of propylene (Figure lb) with lesser accuracy, but at pressures up to 10 bar the maximum deviations are 0.3-0.4% and the mean deviation for the given region of parameters is 0.19%. In the 10-100 bar pressure range the accuracy decreases the mean deviation for the given region is 0.74%, whereas the maximum devia- tion near the saturation line is 5.5%.
Zagoruchenko ' s equation [9] for ethylene quite accurately describes the p, V, T-data (Figure Ic) in the 1-200 bar pressure range and 270-400°K temperature range, where the mean error does not exceed 0.2%. Here the maximum deviations up to a pressure of 20 bar fall within the limits of 0.2%. At higher pressures (300-1,800 and 1,500-3,000 bar) the mean deviation for the region is 2-3%, i.e., substantially exceeds the experimental error. The equation may be used for calculations in the 1-200 bar pressure range and 270-400°K temperature range.
The Kazavchinskiy-Zagoruchenko equation [28] (Figure Id) should be considered unsuitable for describing the p, v, T-function of propylene, since it gives deviations exceeding the error of experimental determination of the p, V, T-data in the entire range of parameters (p = 1-3,000 bar and T = 270-440°K).
-8- —
KEY: 1) Mean deviation 2) Maximum deviation 1)
','/ .' • ^ , /\ ^ 0.035 / ^ / / r, °K
1 51 2) ' —[
'\ '1 -1 -.^ 1 1) 1)
0 —y—7—7
2) _ / / / // 2)
1) llllij-irMSiiiMIlIli w 1)
2)
1)
2) 2^ 1)
Z/////y//////, //
/ ///// //.// // . /. 2)
1)
2) 2) ICO 1) 1} y///y/y////7///. '//// -e.^ ^/// 2) 2) 1) 1 ) loon
2) 2) JOOO
Figure 1. Field of errors of thermal equations of state for ethylene and propylene: a -- field of errors of the Benedict- Webb-Rubin equation for ethylene [23, 25, 26]; b -- field of errors of Benedict-Webb-Rubin equation for propylene [23, 25, 26]; c -- field of errors of Zagoruchenko' s equation for ethylene [9]; d -- field of errors of the Kazavchinskiy-Zagoruchenko equation -- for propylene [28]; e field of errors of Zagoruchenko ' s equation for propylene [27]; f field of errors of Zagoruchenko' s equation
for liquid propylene [27] ; density and equation of state of gaseous phase. [Continued on next page].
-9- .
r,°K
Figure 1 [Continued on next page]
-10- .
Figure 1.
The Zagoruchenko equation [27] (Figure le) should be considered most accurate for propylene. Its maximum deviation in the near-critical region, however, reaches 3.8%. Here the path of the isotherm in p, v-coordinates does not correspond to the path of the experimental isotherms in the super- critical region. Equation [27] describes the range of the liquid state of propylene (Figure If)
-11- It can be concluded on the basis of analysis of the existing equations j of state of ethylene and propylene that none of the examined equations i describes the experimental data in the entire, rather wide pressure range. The authors of this reference manual, therefore, attempted to derive equa-
tions of state for the entire gaseous range, for which experimental informa- i tion exists for the p, v, T-data of ethylene and propylene.
Thermal Equations of State of Gaseous Ethylene and Propylene j
Several methods are now being used [31, 32, 33] for formulating the equation of state on the basis of experimental data using polynomial theories. Approximation of the p, v, T-plane with the aid of orthogonal polynomials, as shown in the work of Pings and Sage [31], has certain advantages over other methods.
In the usual method of least squares the matrix of the linear equation system is usually poorly defined. The situation gets worse as the degree of approximation of the polynomial and the number of experimental points used for the approximation increase. In view of this the matrix inversion opera- tion leads to considerable difficulties in the calculations.
When orthogonal polynomials are used the matrix becomes diagonal and the inversion operation is obviated.
The use of orthogonal polynomials increases the power of the approximating polynomial without repeated calculation of the coefficients, which were determined earlier for a lower power. However, the use of first and second order Chebyshev polynomials [31] for the given problem involves certain inconveniences. Specifically, the experimental data must be repre- sented as a special matrix, where the roots of the stated polynomials are taken as the nodes of approximation, and this entails graphic processing of the data, which inevitably leads to loss of accuracy.
The essence of the proposed method of approximation consists in application of the Forsythe algorithm [34] to the case of the function of two variables. The advantage here is that it is not necessary to use a special lattice for representing the experimental data. If f(x, y) is integrable with weight R(x, y) in rectangle a<_x<_b, c<_y<_d, then to it can be compared the Fourier series
fix. y) = EQfcO),fe(.v. y), (1)
, i.k where
oXkix, ij) - fPi(x)Mf^ (ij), ^2)
< < d, and (j). (x) , ^, (y) are the orthogonals in the intervals a x b and c <_ y <_ 1 K respectively.
-12- '
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I I I
XiOCOI-OCMT — -OOXrrCDOCvtrOO — t-~OTr lO oo o o o r^cc^ic-joc^oco — xoo m o o -3 - pc o I o Xi X o '"2 c-i o; X- I-- CM OO CO — lO 1 - ^ C^' CJ ' o X 1-: V. M X o O C^J TO CJ o -T CO — 1^ ~. •-0 cr. - rC -.-1 1" 1 l.- 1 - lO CM O 1 X lt; o i-O 1- cr -o CO 1 lT [ - l'^ 1 CJ rc c; t - 1.^ X X X X X o o O o o T --• c^ — o I- — o X -T IC rr lo r~- X 'w' o x o o o o o o o o — CM CJ O o o o o o o o o o o o o o o o o o c- o c o o o_ o o o o o o o O O o OOOOOOCT O CMOOCir-xxc^ioo-•n CJ O '-3 O lO CC O C^ O cr "T O CO CO O O (T; o o o o — I'l — -,- t -T- M O Xj CI - O X O o c o cc X 1 o o - — -r c^] /D cr> X — • o 1 ~ ' --: ~^ lT' _~ CM c^l r- — o — — — o : — — r ^ o c i o c-^ o ^- "^r o O O " O X -C I— 'O O — C-> O ~ •>! C~i ^- Ol :^ X C^ — i.O C3 cr> C; C^ CM ir. CM o ci t-- iC' o I': ^ o o c: C' o o — -m . t -o o ri c- --o t~- x ci — n lO x co cm XcCiO-rcoc^i — — —.r^o--c; — — — '?r^ — cmxo — oocMr^CMCi-ror. o-n* ' -'•^ . . ^- . -- -T- i-O — — — — — — — o o o o o o cr — — J 'M CM cn — — lo t-- ~ --5 cr o o o o o c, o o c o o o o o cr: -.r c; o o o "o o o o o o o o o o OO O^OOO ooooo CJOOOOZCT): . ^ '-l^.'^ ^ o" o' o" o' o" o" o" o' c' o' o" o" o" o' o" o" o" o' o" o' o" o o' o' o" o" o" o' o' o' o' o' o" o" I I I I I I I I J I I I I I I "-^ CO r~ o lO o r: r -•• x cT/ c-i x ci -r c; n » oo — ^ to — co o o ci — o o co oocr>C)Oc-:.~-ri— ox — o — x-c^rcMiTi^'MCMor^iO'Ocix-ox-rro — CO -?• J I I >ir CM CO o — X CT) c r. c~. — t~- c-1 CI I ~ - J -r cr. — 'O — X -r -o — 00 lO -.- -- ~, — 00 — r » XX :~ — 'C o X If: o O — — ~r cm i o x_ cm cj x_ -^r -c cm ~ t~- a>_ ' "* — — r-." oo"h-~ 'J? r" i i o" ^ i i'.' iJ " "c r^' cm" x" cm" c~)" " x" i—" o' lo o' o' o o' cm' o cd" co" •>*• lO o X c > c. c^ cr c: Cn r -r i.o w t-- c~> o — r i ci -r o m >o i^ oo ctj o cm ro CO c^j CO CO CO rc C-"; ^ *r T' vr ^ ^ ^ ^ to 1^./ lO lO lO lO uO LO lO lO U3 O <0 -14- : The system of orthogonal functions 0^(x) is constructed in the examined range of change of the argument by means of orthogonalization of the system of power functions 1, x, x'^, ... with unit weight. The polynomials (})^(x) satisfy the recurrent relations (Pi = a; -f a? (P2 = 4- rti) (pi 4- G2(po (3) where the coefficients a* and a° are determined from the conditions of orthogonality ((()., 4).) = 0, if i (4) The condition of orthogonality of polynomials The coefficients a^ and a° of the polynomials (J)^(x) and ^j^Cy) are thus defined by the equations: 1=1 A' The coefficients C^j^ in equation (1) are determined from the condition of the minimum mean square deviation of series (1) from the function f(x, y) M.N Vx2 Si.p ^ mill, (7) m,n . = - S C oo., (x are of where 6 f(x , y.) , yo) ; m, n the maximum powers 0(, , p Ot p .1 IK IK Ot p 1 ,K -15- the expansions in terms of the variables x and y, respectively; M, N are the numbers of values of the arguments x and y, respectively, according to which the orthogonal functions cj>- (x) and \ (y) are constructed. — 2 {Xa, IJ?^) — V C,,a),; (Xa, ^Tp) O', V [/ [Xa, (Oj-fc = f'.h' Af.A' a,P a.H — (8) o/t = M.N 2 a.P In our work the variables were selected as follows: = y T fix, y) {-^f-\]v (9) The program that executed the described algorithm was written in the command system of the BESM-3M computer^. To calculate the coefficients of the polynomials and C^^^ we used experimental data of Michels [5, 21], presented in Tables 3 and 4. Table 4. Michels' [21] Experimental Data on Propylene f(x, y) -(•If-')';''" Date for T, °K p. li£,lM' ..l.''..i6 323,15 348,15 12,4233 —0.008 1-: 2040 —0,007059020 -0.006824940 —0,005757110 ;'i05 —0,005761340 15,9476 —o.oo'ii 1 — 0.0070 U'lOO —0,006795350 19,4701 — 0,0nM}s7200 — o,cu;o;)0,:90 —0.006762940 —0,005733210 23,1491 —0.00805: 670 — 0,006':'6kI)50 —0,006727450 —0,005698640 37,5319 —0,no.>022750 —0.00u-.'29450 —0,006683050 —0,005657940 31,0289 — 0.0(!7'J871()0 — 0,006.s:'0240 —0.006638430 —0,005616470 35,0957 —0,00: 954700 —C.0078o20IO —0,006612500 —0,005585090 37,3n27 —0.007943500 —0.00'i8 12220 —0.006581410 —0,005561000 43,9004 —0.007888800 —0,006/82570 —0.006524020 —0.005492450 [Continued on next page] The authors gratefully acknowledge the cooperation of S. A. Mednikova of the NIIASS [Nauchno-issledovatel • skiy institut avtomatizatsii sistem planirovaniya i upravleniya stroitel 'stvom; Scientific-Research Institute of Automation of Construction Planning and Control Systems] , Gosstroy [Gosudarstvennyy komitet po delam stroitel ' stva ; State Committee for Construction] Ukrainian SSR in the writing of the program. -16- 1 Table 4 (Continued) Data for T . °K p. Ki/.ll-' JV3.15 423.15 12,4233 —0,001962120 —0,004290550 —0,003732490 15,9-'. 76 —0,004940160 —0.004270200 —0,003711970 i9,;701 —0,004915570 —0,004247620 —0,003688400 23,1-191 —0,004885230 —0,004220770 —0,003663540 27,5319 —0,004847380 —0,004186510 —0,003632940 31,0289 —0,001809250 —0.004154600 —0,003600700 35,0957 —0,004779940 —0,004124790 —0.003574840 37,3027 —0.004760250 —0,004106960 —o!o03558860 43,9904 —0,004694800 —0,004047790 —0!003506590 52,8920 —0,004610220 —0,003971950 —o!0O3438I98 61,5180 —0,004527-1 :50 —0,003898150 —o!o03371820 70,6220 —0,004439900 —0,003819860 —0i003302120 79,6525 —0!004353160 —0,003743200 —o!o03233700 81,0886 —0.004339190 —0,003730270 — 0^003223200 88,3320 —0,004269306 —0,003669145 —0!o03 167406 90,4061 —0.004248 <70 —0,003650646 —o!o03 152033 97,4213 —0,004180899 —0,003591424 — o!o0.3098313 100,6545 — 0,004149677 —0,003563372 — 0'003074903 110,4019 — 0!004055528 —0,003480733 —o!c0.30 13851 120,88G9 —0.003954789 —0.003392546 —0,092923342 126,7396 — o!oC3898SG7 —0.003344120 —0,002879851 130,4939 — 0.00386.-!2 ".4 —0.003313040 - -0.002852312 140,6308 —0.00.4/67124 —0.003230031 —0,002778148 141,3968 —0,003 759! 130 —0,00322.(810 —0,092772800 150,8833 —0,003671041 —0,003147013 —0,002704459 157.32C2 —0,00361 1516 —0.003095750 —0.002658556 172,5556 —0,003472976 —0.002976295 —0,002551512 183,1000 — 0.003379121 — 0.0028'. K'..} 4 8 —0,002478264 188,9419 —0.003327957 —0,00-.'851226 —0.002437862 203,9584 —0.OU3199102 —0,002739256 —0,002335080 204,2748 —o!o03196U,6 —0,0027:;6923 - 0,002332858 2)9,8116 —o!oO306S]Ol — 0!c02f'i2.i556 —0,002274196 227,2808 —o!o030C0793 —0.00256903S —0.002176840 235,fc269 —0,002940571 -0,00250.Vi7l —0,0021 19053 2-.' 9,2921 —0!0028.372:'6 - -0!o024 13168 —0,002027679 272.9678 — o!o026626i6. —0,0022-16114 — 0,001864452 277,1274 —0,0026325-19 —0,002217066 —0,001835143 291,6654 —0,00250727 — 0.002091 136 —0,001708965 309,1 ?09 —o!oo2--02.- -:2 — 0.001981736 —0,001599899 311,3877 — 0',0023e69.'-'« -0,001968078 —0,0015830.50 317,5738 —0,00234 19._ 9 --0,001 92 O.SOO —0,001534271 340,7207 —0[002 166257 —0,001734836 — 0,001341329 3-14,0120 — 0.002 13f)S',)4 —0,00170714.1 — 0,001312372 347,41 15 — o!o02l 12652 0 001677987 - 0,001281994 3'^15'^06 377,3512 —0.001847991 0 00 1 —o!o00986096 - 386,5670 —0,001 7566' i9 —0 001297730 —0,000885584 17*^88 402,2800 —0 001586016 0 001 1 —0.000698908 0009.^'0'^0'> 4 1 3,2332 —0,001455716 —0 —-o!o0055666! 424,0634 — 0,00!31627(j 0 000iS3427'> — o!o004071 16 446,1533 —0 000993O'^7 —0 00049^69'? — 0 000064«50 448,9080 —0 00094 Ol io 0 00015.1476 0 coo 196579 464,4563 —O.O0OG82212 —0,000181321 —0,0002.57318 480.9735 —0,000363010 —0,00914230:.! —0,000583.351 499,7097 —0.000048175 -0,000555590 —0,000998587 501.5707 —0.0000921 14 —0,000599570 —0,001041855 516,2530 —0.0C0459127 —0,000965308 —0.001404222 540,9137 —0,001181318 —0,001661405 -0,002031397 548,5700 —0,001401^07 —0 0018"S789 —0,002324141 580,9129 — 0.002558v!(i --0,003027422 —0.003427535 601.5930 —0,00341870! —0,003863837 —0,004238065 650,9040 —0,005905562 —0,006264682 —0,006556777 -17- . The equation of state is written in the form from which it is easy to convert to the Virial form by reduction of like terms The conversion to the Virial form is provided for by the program and is executed after calculation of the coefficients of the polynomials (j)^ , ip^^ and coefficients C, . ik In the theory of approximation of the functions of two variables there is no explicit criterion for determining the optimum number of powers of the expansion with respect to each of the variables. Therefore the optimum power of the expansion in terms of 1/v and 1/T was found as a set of powers. Here the deviations at the points and the minimum sum of squares of deviations were the criterion. Equation (10) is written in Virial form as ri , ;j -w-^'^'lvl'^^'yTj' (11) This method requires a rectangular network of experimental data. For this reason the field of p, v, T-data of propylene is broken down into two regions, for each of which is constructed an equation of the form (11). The constants determined by the above-described method for the equa- tions are presented below. - —450° Ethylene iP = I — 3000 bar. T 250 K) 10-' + 0,760072429 C02 — 0,548705429 • • 10'- Cu — 0,134563818 • 10^ C12 -\- 0,972058755 • 10=^ c„ + 0,9500G:)6 IG • 10" C22 — 0,686258650 • 10* — 0,331667515 • lO'' C32 -i- 0,2 11393035 10'" 10" • C41 + 0,587269730 . C42 — 0,423108315 10'^ • 10'= C51 — 0,410898360 . C52 -1- 0,295678870 10-^ • 10"" Co3 + 0,132142978 . Coi — 0,144380734 10-' C,3 — 0,233803377 10' Cu + 0,255267906 • 10" . 10^ C23 + 0,164875060 . C24 — 0.179881158 C33 — 0,579326847 10' C34 + 0,631603632 • 10" [Continued on next page] -18- • 10' C43 + 0,101441262 C44 — 0.110517516 . 10' 10'° c„ — 0,708228885 • C54 = + 0.771067345 • 10^ • 10-' 10-' — -1- 0,831940857 = — 0,269842664 • . 10~^ 10-^ Cl5 = — 0,147018406 = + 0.476717255 • C25 + 0,103550508 C26 — 0.335666604 • 10"^ C35 — 0,303412433 • 10' C36 + 0,117765335 • 10^ 10'^ Q5 + 0,63558120,0 C46 — 0,2055894276 • Cos = — 0,443212965 • 10' C56 + 0,143526876 • 10^ 10-'^ 10-'^ + 0,494436598 • Cos — 0,476946020 • 10-' 10-'^ C,7 — 0.873357290 C18 + 0,842422128 • 10-' 10-' C27 + 0,614844932 • C2S — 0,593032017 • 10-"^ 10-^ C37 — 0.215673041 C3S + 0,208007008 • 10-' 10-^ C47 + 0.376996322 • C48 — 0,363565579 • 10"^ C57 — 0.262743658 10' + 0,253357565 • 10""* Co9 = + 0,188031735 • 10"'^ ^19 = — 0,332130351 • C29 == + 0,233813590-10-'^ 10"'° = — 0.820120622 • 10"^ C40 = + 0,143345912 • r C59 = — 0.998924485 • lO""*' Propylene. (T = 270 — 450° K, p - I — 30 bar) Coi = —0,396637152 10' C02 + 0.860745715 Cn - + 0.678436327 10^ C12 — 0,147721665 • 10^ Cn, = — 0,463021591 10^ C22 + 0,101 148055 10^ 10'° C31 = +0,157557275 C32 — 0,345410258 • 10' C41 - —0,207451170 10'^ C43 + 0,588277177 10" 10'^ • 10'^ Cc,, = +0,181147750 C52 — 0,399749543 10-' • 10- Co3 = —0.634256919 Co4 + 0,189023628 Ci3 = +0,109085668 10^ Cm — 0,325404985 • 10' C23 = —0,748515689 10^ C24 + 0,223489403 • 10" C33 = +0,256142088 10^ C34 — 0,765471148 10^ [Continued on next page] -19- 10 '43 0.437127355 • 10 CiA = -[- 0.130749631 • 10 !0 Cr,-. - 4- 0,297025345 • lo'^ C51 - n.891 006876- 10 < „r. — (I, I ') in I / I ill 10 Ci5 - -1- 0.3342;:G852 • nr C25 = —0,229744935 • 10^ C35 = + 0,787500243 • 10^ C45 = —0,134615528 • 10^ C55 - + 0,918055308 • 10^ 450=^ Propylene {T = 370 — K, p 1 — 3000 bar) 10"-3 -4 • • 10" Coi = 0,65985925 ^02 ~ -f- 0,440437102 -1 Cii —0 1076759'^7 — n 3-13n'^77'^7 . 012Co 1 u —0,761754943 • 10' ^22 — + 0,758758270 • 10' -6 10- ~ 10"-8 Cos = — 0.7078394G2 Co4 + 0,199772917 • 10" -3 -5 c, - -f 0.586824620 • Cm- — 0,202807342 10" -3 — 0,1 14054261 C24 - 4- 0,433482162 • 10" ~ 10"-11- -12 Cos + 0,238533263 Cog — 0,169756637 • 10" -7 9 — 0,166153171 10" ClG -= + 0,129786612 10~ 10"-5 -7 Ct.^ -1- 0,309699415 C2r, — 0,255484795 • 10" -IF) -IS 10" • 10" Co7 - -t- 0,434039867 Cos = — 0,500738055 1? -15 • 10^ • C,7- — 0,340025191 C18 — -f 0.396632938 10" 10"-10 13 C27 + 0,680235151 C2S — 0,799576203 • 10" 10-^' Co J — + 0,2 1S934207 • -18 Co9- —0/174502194 10" -IG C29 - -h 0,3532Gi;277 • 10 The deviations at the points, i.e., the differences between the experimental values of f(x, y) and those calculated according to the equa- tions, are listed in Tables 5 and 6. The. mean pressure deviations on the isotherm calc 6 = 100% exp in the entire region of states covered by the experiment on ethylene [5] and propylene [21], are found within the limits of 0.1-0.2%. The proposed method of writing the interpolation equations of state is suitable for the description of the p, v, T-data in wide temperature and -20- I 1 ^ ' I I I I I I I 1 i I I I I 1 I I I I I I I i II I I 111 ]oooc-ooooooooooooooooooooooooooo 1-^ r- r--. lo CO t-^ I I i i I I I 1 I i I I I I I + 1 + 1 I I + 1 + 1 + 1 +++ 1 I I I I I I I I I I I I I I I I I I II I I I I I I I II oooc:oo.'z>ooooooooocooc:>oooooooooooI 1 rCi lO 1 I - i.o CM to _ CO — 0 o CO o T oo CM o to CM — CI to o —• CO o cr. • OD CO lO lo to r-- a; c-j o c i o to ^ -o t~ o cm —. cm ^ o CMCOI-CTvCOCOOOOC-irOO-i-XlOt^ r-rCl"^«irOCOCOiOC0 04tO — —.— CM . ! ^ to J_ CM_ _ C CO TJ< — C CM C^J — CI CM C '0_ CM — — — ^. —1 °^ — 1_ — — ~ CM CS O O O O o" O O O" O o" o" o' O' o" O o" o' o" O C; O o" O O O CD o o o" o I H-+ ++^-++ I I I -I-+++++ I + 4-> UJ <4-l o 0 !-> I I I I I I I I I I I I I I I I I I I .... nJ o OOOOOOOOTiOOOOOOCOOOOOOOCDOOOOOOOcL: +-> c/5 C0l'^OX;00c'lC0«^:^CMC-lC0 — C~Cin--COcl — C)COCOOOCOCM~-»• CO • - uo +-> i.o to o — to ic I— "o -o 'O —^ o I I I I I I I I I ! 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Field of Errors of Equations of State of Propylene A = f(x, y) - ffx, y) ^ Field of errors at T°K 1 298,15 318.15 323,15 348,15 -5 -5 12,4233 —0.1228- 10 0,1646- 10 —0,16i9- 10 0,1639- 10-^ -6 -6 15.9476 —0,2798- 10~^ —0,3097.10" -0.8453-10' —0,1853- 10'-^ 10"" 10"-G -6 1Q-.6 19,470! —0,1861 - —0.5650- 0,1120-10- 0,9076 10""^ -0 -6 23,1491 —0 2773- —0,8692 -10' 0,8404-10' 0,7853- 10~^ -5 —5 27,5319 -0,6705-10"'^ —0,2363- 10" 0,3370-10' —0,1737- 10-5 5 -5 31,8333 —0.8757.10-'^ —0.3182- 10" 0,7404-10" —0,3007 10-5 - -5 35.C9j7 —0,4300-10"'^ —0,5021-10" 5 -0,3086-10" —0,3934 10-5 37,3027 10"^ 10"-5 — —0,2065- —0,5360 • —0.1336-10" —0,1790- lo-"^ 43,9904 10"-5 -5 —0,4020- lO'-'^ —0.4503- 0,5282-10' —0,3010- 10-5 Field of errors at T°K p. kz/m' 373.15 398,15 423.15 • — i 1 - 0,6272-10-5 1-2,4233 0.79 1 10 0,2813 - lO-'' 15,9476 0,1294 10-5 0.9871-10-^ —0.4811-10-^ 10-5 19,4701 —0,2884 U,ZijU/ • lU — —U.oo/0- I (J 23 1491 —0,3525 10-5 -- 0.3374-10-5 —0,1328. 10-5 27.53)9 - 0,3401 10-5 —0,3160.10-5 —0,2598. 10-5 31,8333 —0,3070 10' "5 —0,2392- 10-5 -0.1714-10-5 35.0r'57 —0.2886 10-5 —0,1900-10-5 0.4553- 10-^ 37.3027 -0.3101- 10-5 -0,2057- 10-5 -0,4118-10-5 43,9901 0,1126 10-5 0.1826- 10-5 0,4506-10-5 52,8926 0,2479 10-5 0,2643- 10-5 0.1903-10-5 61,5480 0,2901 10-5 0.2433- 10-5 0,1737-10-5 70,6220 0,2996 10-5 0,2490-10-5 0.1434-10-5 79,6525 0.2006 10-5 0.104 1-10-5 0.3246- 10"-° 81,08,<::C- 0.1982- 10-5 0 1549-10-5 —0.2028-10-5 88,3320 10-5 10-' 0.1082- 0.9312- 0,1 135 -10-5 90.4661 0,1274- 10-5 0,1894-10-^' —0,7566-10-'^ 97,4213 0,8191- 10-'' —0,3980- 10-*^ 0,1583-10-"^ 100,6545 10-*^ 0,4894- —0,4531 -10"-^ —0.8486- lO-*^ 110.4019 10"-^ —0,2582- — 0,1114 10-'' —0,1286- 10-^ 120.8863 —0.9827- 10-5 —0,5099- 10-'^ -0.1370- 10-' i:'G,73fj6 -0,1326- 10-5 —0,8635-10-'' —0.6104-10-"'^ 130.4938 10-5 -0,1G09. — 0,3029. lO'-*' —0,8057-10-5 140,6366 —0,1764- 10-5 —0.9755.10-'^ —0.1737-10-5 141,3965 —0,1733- —0,9309-10-'' 0.1655-10-5 IU-5 . [Continued on next page] -23- —^ —^67^S6 ^O^ Table 6 (Continued) Field of errors at T °K 373, 15 398.15 423. 15 1 OOO 1 I ft— loO.oooI A AO^Q 0,2362-10 1 — l5/,3202 — u,iDiy- JU —u,ouoy-A AAOO JUA 0,2805-10 ^ — A TOAO 1 ft " 1 1 2,555o —u, J o^y • lu 0,3470-10 A — 183,1002 —u.cDDo- JU o^ni 1 ft 0,3958-10 — j8o,y419 —U, 219,81 14 u.i^oy • JU U,0-i-t / - 1 U 0,4187-10 n — A o I — A 1 AC7 1 fit in 227,2805 U,Iuo/ • JU 0,4859- lO""^ ^ ft fiQft^ 1 ft 235,8269 U, (\ 01 4/1 1ft— ft 874Q. in~'' 249,29.'?4 U,zl4fl-JU 0,4100- IQ—^ — A 1 272,9678 000 1 ft ft =iS77. in~''^ 0,25/6-10 10""^ 277,1274 ft 1 1 fij . 1 ri~^ 0 37'18- 0,2441-10 — A OOC^l 1 ft A f^f^OO I A*"--* 294,6654 U,401 U * I u U.UDZj- lu 0~^ 10"^ A OA*?! 1 A— 309,1809 —0,1 140-1 —0,7522- 0,2071-10 —0,1411-10-^ —0,7704-10-* —0,1153-10-^ 311,3877 ]0~'' —0,7825-10"'' —0,1796-10-^ 317,5738 - 0,1860- —0,2633- 10--' —0,1147.10-^ - 0.9285-10-^ 340.7294 10"^'' 10~^ — 0,24S5- —0,1423- —0,1152-10-^ o4-i,UlZ>J "'" 10""' —0,2595- lO' -0,160-!- —0,1100- 10—' 10^^ 10~" —0,1209- — 9,101 ?- -0.9384-20-'' 10~* — (),77l)9- 10"^ — 0,7607- - 0,8559-10-^ 10""'' —0,1006- 10"- 0,8753- —0,5512-10-^ 10""'' 0 1G70- '0~^ 0 3783- 0.2490-10"^ 0"'' 4 9.1 n'i3-1 0 1943- 1 0,5329- 10 — 0,9963-10-' » ^ 44G 1533 0,2698- 1.0" 0,1291 - IQ— 0,9934-10—^ 10""^ 132- 10""^ 148 9C80 0 2373- 0,1 0,4231 - IQ— ft ]0~^ 10~^ ''64 4563 1504- 0 I l.jjj- 0 3018-10—^ 2317-10"''' 480,9735 —0 0 5790- lO"*^ 0 3882- 10—' 10~'^ —0,2829- ft 3955- 499,7094 0 1 190- IQ— 501,5701 —0,3039-10"-^ -0,3187-10-'^ 0 6349- IQ- / 10-^ 515,2524 —U,4 1 y i U —0,bJ2J- 10 —0,7662- fiiD 0 1 97 —0,1281-10—' —0,5311-10-" —0,2803-10 —0,6549-10-^ 548,5700 — 0.1031-10-^ —0, 1196- 10-^ 10-^ 580,9)29 — 0,2958-10-'' —0,5599- 0,5977-10-' 10-^ 001,5949 0,2528-10-^ 0.1579- 0,5894-10-^ 650,9030 —0,3294-10-* —0,309-1-10-^ —0,9953-10-^ -24- . . pressure ranges with an accuracy close to the error of the experimental data, and can be used for the construction of tables of the thermodynamic proper- ties . The high accuracy of description of these data by the equations derived ensures the required accuracy of calculated caloric values. Review of Data on Second Virial Coefficient The Virial form of equation of state is now considered theoretically founded. Despite the difficulties encountered in the extraction of the Virial coefficients of the equation of state from various types of experi- mental data, several methods have been worked out in recent years for derivation of the equation of state in Virial form. Data on the second Virial coefficient of ethylene, published by various investigators, are presented in Table 7 and Figure 2. As seen in Figure 2, the existing data display considerable scattering. Data of Roper [35], Turlington and McKetta [11], Pfennig [13], Ratzsh and Bittrich [36] , were obtained from measurements of compressibility at low pressures (to 2 bar) Figure 2. Second Virial coefficient of ethylene according to the following data: 1 -- authors of present book (from data -- -- on compressibility) and of Michels [5] ; 2 Roper [35] ; 3 Walters and coworkers [6]; 4 -- Thomas and Zander [12]; 5 -- Pfennig and McKetta [13] ; 6 -- calculated according to the Leonard-Jones potential [25]; 7 -- Turlington and McKetta [11]; 8 -- Pfennig [13]; 9 -- Ratzsh and Bittrich [36]; 10 -- -- calculated according to the Corner potential [38] ; 11 David and Hamman [39] ; 12 -- authors of present work (from data on -- -- speed of sound) ; 13 Butcher and Dadson [37] ; 14 calcu- lated by equation [33] -25- I Table 7. Second Virial Coefficient of Ethylene According to Various Data Ponep i 1 35] 6) RSBHA XCMMCH (39) 250,00 200.00 1,10029 0,5846 290,00 210.00 1,00752 0,5490 300,00 220,00 0,925809 0,5098 310,00 230,00 0,853511 0,4741 320,00 240,00 0,789237 0,4420 330,00 250,00 0,731862 0,4099 340,00 260,00 0,C80H3 0,3779 350,00 270,00 0,634182 0,3518 400,00 298,15 0,526397 0,2524 323,15 0,451925 7) MHxcnbc [5] 273,15 2) TypjiHHfTOH II MaKKCTTa [11] 0,5985 298,15 243,15 0,6672 0,5004 323,15 258,15 0,6358 0,4207 348,15 273,15 0,5984 0,3557 373,15 288,15 0,5019 0,3028 398,15 0,2579 303,15 0,5019 423,15 0,2221 3) n(f)CH!inr [13] 305,35 0,5002 8) n(f>eHHHr H Ma.KKCTTa (13] 310,95 0,4775 305,37 0,50201 316,55 0,4630 322,04 0.45028 321,95 0,4473 338.71 0,40820 327,55 0,4312 9 ) ToMac H Ua'wep [13] 333,15 0,4190 273,15 0,575744 338,65 0,4081 283,15 0,533836 293,15 4) Perm ii 5nTTpnx (36) 0,503694 303,15 0,473599 293,15 0,5205 313,15 0,444738 303,15 0,4812 323,15 0,418603 313,15 0,4492 Damep 10) H Zla;icoH (37 J 323,15 0,4070 263,15 0,615999 273,15 0,575360 5) Ba.ibTepc h ,ip- [6] 283,15 0,537930 299,10 0,480536 244,26 0,7830 313,15 0,439:<41 249,82 0,7481 323,15 0,410309 255,37 0,7 i 18 333,15 0,384999 260,93 0,6836 343,15 • 0,360758 265,43 0,65-10 353,15 0,33f;657 272,01 0,6269 363,15 0,315842 277,59 0,6013 373,15 0,296592 283,15 0,5770 423,15 0,213176 473,15 0,152930 KEY: 1. Roper [35] 6. David and Hamman [39] 2. Turlington and McKetta [11] 7. Michels [5] 3. Pfennig [13] 8. Pfennig and McKetta [13] 4. Ratzsh and Bittrich [36] 9. Tliomas and Zander [12] 5. Walters, et al [6] 10. Butcher and Dadson [37] The data of Turlington and McKetta agree with those of Pfennig, but the temperature dependence B given in these works differs from the temperature dependence according to other authors. The data of Thomas and Zander [12], and those of Butcher and Dadson [37], were obtained from -26- measurements of compressibility by the Burnett method in the pressure range up to 20 bar. Their values of B agree, but are somewhat higher than the values of B obtained by other authors. The data of Roper [35], Ratzsh and Bittrich [36] and Michels and Geldermans [5] , who obtained values of B by expanding the compressibility at low densities into a series by powers of 1/v, the coefficients of which were determined by the method of least squares, agree quite satisfactorily. David and Hamman [39] found that the values of B for many compounds can be described by a third-power polynomial in terms of reduced temperature i3-.a+i- (12) + -J- + ^, where • [kp=cr] fKp ' V'^,, v^^ = 129 cm^/mole; T^^ = 282. 4°K is the critical temperature. The constants for ethylene have the following values: a = -4.912, 3 = 18.575, Y = -23.892, 5 = 8.975. Walters and coworkers [6] represented the results of their experi- mental investigations at low pressures up to 45 bar as polynomials by powers of 1/v. The values of the coefficients for 1/v are somewhat lower than the data of Roper and Michels. It is noteworthy that when compressibility is expanded into the series 7 - 1 J V MJ) the coefficient for 1/v can be equated to the second Virial coefficient under completely determined conditions, as shown in [40]. Roper's values [35] of the second Virial coefficient for ethylene are described by a polynomial of the third power of the inverse temperature in the 199-343°K range 16,036 9^3.58 10^ • 10' D 12 — ^3,3855 Roper's data for temperatures below 270° K fall on a smooth continuation of the curve plotted according to the data of Michels, Ratzsh and Bittrich. At temperatures above 270°K the deviation of Roper's data increases with temperature. This is apparently caused by the fact that the error of Roper's determination of the specific volume of ethylene increases as the temperature increases. -27- Table 8. Second Virial Coefficient of Propylene According to Data of Different Investigators - li- 10". -«-lo«. — S•lo^ — fl-IO'. !j T -\ K r^ K M*/K2 M*/Ke 298,15 0,825304 Porlep 320 0,7163 323,15 0,6942 1) |35] 318,15 0,721790 330 0.6702 348,15 0,5887 323,15 0,699533 n C07J. 220 340 UiO-i' "I 0,oUot) 348,15 0,603162 230 1,4687 1 350 0,5894 398,15 0,4374 240 1,33050 2 XeMMCK [39] 400 0,4349 423,15 0,3811 0,9240 450 0,3280 250 1,212031 280 .^<})cniiiir n MaKKCTva 290 0.8722 260 1,070198 [13] 270 1,020919 300 0,8270 c H jp. |21j 305,37 0,76819 280 1,943270 310 0,7629 298,15 0,8241 322,04 0,674490 318,15 0,7175 338,71 0,599090 KEY: 1. Roper [35] 3. Micliels, et al 2. David and Hamman [39] 4. Pfennig and McKetta [13] The values of B calculated according to tlie Leonard- Jones potential [6-12] with the parameters: e/k = 199. 2°K, = 116.7 cmVmole [25] and according to the Corner potential for long molecules [38] with the para- ' meters : l/a = 0.21, e = 192°K, = 4.1 A, are presented in Figure 2 c The values of B calculated by the Leonard- Jones potential agree with ' Michels • data. Such agreement is quite understandable, considering that the stated constants were determined from values of B obtained in Michels' work [5]. The Corner potential with the stated parameters, which he himself obtained [38] , does not yield the correct values for the second Virial coefficient of ethylene. Published data on the second Virial coefficient of propylene are presented in Table 8 and Figure 3. It is clear from the table and figure that there is good agreement of data obtained by the various authors. The exceptions are the data of Pfennig and McKetta [13], which are higher than the others. Roper [35] proposes a polynomial that describes the dependence of B of propylene on temperature: 6,81 J^CP _ 31,35 • 10^ CM^lMOAb. 7 (15) The deviations of Roper's data from those of the other authors are analogous to the deviations in the case of ethylene. Presented in Figure 3 are the values of B calculated according to the Leonard- Jones potential. The parameters of the potential are deter- mined from the critical data are: e/k = 0.77 • T = 281°K: cr -28- ; . = = cm 18.4, T /p 147.95 /mole and for the Corner fpotential theyJ are: 0 cr ^cr < ^ l/a = 0.26, e = 220°K; a = 4.9 A. c c The values of B determined according to the Corner potential are considerably closer to the actual values than in the case of ethylene. The Corner potential model is apparently more valid for propylene than it is for ethylene. 8, 1 ^ -0.05 o ; A 2 r o -0,09 • J «> if o A 5 -Oil o 6 » 7 e 8 ~0J5. -r 0^ Figure 3. Second Virial coefficient of propylene according to the following data: 1 -- authors of present book (from results on compressibility); 2 -- David and Hamman [39]; -- -- 3 Michels [21] ; 4 calculated according to the Leonard- Jones potential (6-12) . a and e/k determined by critical parameters; 5 -- Roper [35]; 6 -- calculated according to -- the Corner potential [38] ; 7 Pfennig and McKetta [13] 8 -- authors of present book (from data on speed of sound) Determination of Second Virial Coefficients of Ethylene and Propylene According to Experimental Data on the Speed of Sound In the range of low pressures, in which the volumetric behavior of gas is described with sufficient accuracy by the equation of state with the second Virial coefficient (16) the thermodynamic speed of sound is determined through the equation 1)-' dB (>'-o- d '-B \ 1 +2p!5 + (Xo (17) dT 'Tn j It follows from this equation that the isotherms of the square of the speed of sound in coordinates w^ - p are straight lines in the above-mentioned range of states, and the angle of inclination of these lines is determined by the second Virial coefficient and its temperature derivatives. Differentiation with respect to pressure and passage to the limit for p ^ 0 gives equation (17) the form -29- . (18) The analogous equations are described in the literature and are used for calculating the second Virial coefficients of gases according to acoustical data. The dependence of the second Virial coefficient is quite well trans- mitted in a sufficiently broad temperature range by an equation of the type B A.-i- A, (19) From expressions (18) and (19) we have d (20) For a given slope of the isotherm of the square of the speed of sound equation (20) contains the unknowns A^, A^, A^, The accuracy of calculation of the second Virial coefficient by the examined method depends on the accuracy of determination of the angle of inclination of the isotherms of the square of the speed of sound and on the number of experimental isotherms in the investigated temperature range. The accuracy of determination of the angle of inclination, in turn, depends on the accuracy of the initial experimental data on the speed of sound, number of experimental points on each isotherm of the investigated pressure range and method of determining the angle of inclination of the isotherms on the basis of experimental data. The analytical method in which the isotherms of the speed of sound are approximated, yields the best accuracy in determination of the angle of inclination of the isotherms. Used for calculating the second Virial coefficients is an approximating function of the form w~ = Wo + ap hp^, (21) where w^ = /RTk^ is the perfect-gas speed of sound. As indicated by analysis of experimental data, function (21) is most suitable for approximating the speed of sound in a rather broad pressure range The essence of the method used for calculating the second Virial coefficient on the basis of acoustical data consists in the following. The experimental isotherms for the speed of sound in gas are approximated by the method of least squares by polynomials (21) , with the result that the slope is determined for each isotherm: -30- 'dp \ Tif^) T. p-'C wfiere a is the coefficient of polynomial (24) at the pressure in the first power. The unknowns , A^, A^ are found from the condition of the minimum sum of squares of relative deviations of the experimentally determined angles of inclination of the isotherms from the calculated according to the equation i = tnin, where (22) is the absolute error of set Y. . 1 Data on the speed of sound, obtained by Yu. A. Soldatenko and E. I. Dregulyas (see Chapter V) in the 190-480°K temperature range on 18 isotherms by acoustical interferometry , the accuracy of which is characterized by the maximum possible error of ±0.15%, were used for calculating the second Virial coefficient for ethylene and propylene. The pressure range for each isotherm, in which the experimental data are described within the limits of accuracy of the experiment by a polynomial of type (21) , were determined by trial and error. Data (Chapter IV) on the perfect-gas heat capacities of ethylene and propylene, and values of w^ determined on the basis of measurements of the speed of sound, were used in the calculations. The following analytical dependences B(T) were obtained for ethylene in the 230-470° K temperature range: nnn/inn-^ ^/Go 38.172 2.S5i.io« ISR-^ 0,00400o — - -t- ; (23) for propylene in the 190-170°K range: 2 519 9 266 -10* B = 0,003256 - . (24) The scattering of the angles of inclination of the isotherms of the square of the speed of sound relative to the smooth curves, calculated according to formula (20) using expressions (22) and (24) , does not -31- . . exceed ±3.5%. This indicates that the dependence of the second Virial coefficient of ethylene and propylene is satisfactorily transmitted in the investigated temperature range by these equations. The theoretical values (jf the second Virial coefficient of ethylene and propylene agree with most of the published values within the limits of 0.0005 m^/kg. Determination of Second Virial Coefficients of Ethylene and Propylene According to Compressibility Data. Recommended Values There are several methods of finding the Virial coefficients from experimental compressibility data. The method most commonly used is calculation of the Virial coefficients according to low pressure data. Since {Z-\)v ^B-\--^+ (25) the second Virial coefficient can be determined by means of limit transition lim (Z— l)y Z?. ("25^ The contribution of the third and subsequent Virial coefficients to the compressibility of a gas is presumably negligible at low pressures up to 2-3 bar, since at low pressures Z ^ 1, the small error in the experi- mental determination of Z leads to large errors in the determination of B. Limit (26) is usually found graphically in coordinates (Z - l)v, 1/v. This method is discussed in detail in [25] and [41] . The Virial coefficients are found, as a rule, to be somewhat higher than in the case of other methods (see Figures 2 and 3) Methods of extracting the Virial coefficients from experimental data on compressibility in a wide range of densities [40, 42, 43] have been worked out in recent years. A method is proposed in [42] based on repre- sentation of compressibility as a series by powers of 1/v or p. The coefficients of this series are calculated by the method of least squares using the experimental data at moderate pressures. Since the solution obtained by the method of least squares is not unique, the authors examined such polynomials, the slope (-^ or and curvature gj^y^) 8 (1/v) of which correspond to the slope and curvature of the compressibility isotherms in the corresponding coordinates. The coefficients of such a polynomial are taken as the Virial coefficients. The stated conditions are by no means sufficient. This is convincingly shown in the works of Michels and coworkers [40] , Hall and Canfield [43] Michels, Abels and Ten Seldam [40] studied in detail the feasibility of extracting the Virial coefficients from the experimental data p, v, T in a wide density range. The essence of the method of Michels and coworkers -32- consists in the following. The compressibility factor Z is represented as a polynomial by powers of density. The investigated density range is broken down into subranges, for each of which is found, by the method of least squares, a polynomial that approximates the experimental data. It is shown that some of the first coefficients of the polynomials constructed for the various subranges with the corresponding density powers-, coincide within the limits of accuracy of their determination, which is, in turn, a function of the experimental error. This confirms the feasibility of unique representation of Z as a series by powers of density. Suppose the experimental data, contain an error, which is random in character and obeys the Gauss distribution. This means that the set of experimental points obtained is one of a number of possible sets, for each of which can be found an approximating polynomial by the method of least squares. The coefficients of the polynomials thus obtained display scattering, which is a function of the error of the experiment. It is further shown that the coefficients of the polynomial (of the model func- tion) will be close to the coefficients of the true Virial series. For the proof a criterion is introduced, the essence of which consists in the fact that if the sum of squares of deviations [40] is small compared with the experimental error, the deviations of the polynomial coefficients from the coefficients of the true series will be small compared with the scattering of polynomial coefficients. In the work are presented relations that permit the relation between the error of the experimental data and errors of the "model" polynomial coefficients to be established. The proposed method [40] is suitable for calculating several of the first Virial coefficients of carbon dioxide on the 49.712°C isotherm. It can be concluded from the results obtained that this method makes it possible to calculate with acceptable accuracy only the second and third Virial coefficients. The error in the calculation of the fourth coefficient is comparable with the magnitude of the coefficient itself. It is noteworthy here that the Virial coefficients obtained by means of the above-described very complex and laborious computational procedure are close to the coefficients presented in [44] . The Virial coefficients were calculated in the cited work for carbon dioxide in a narrow density range by the method of least squares. Hall and Canfield [43] proposed a somewhat different approach to the problem of determining the Virial coefficients on the basis of compressibility data. Hall and Canfield used the method of least squares for calculating the coefficients of the polynomials. This method employs orthogonal systems of functions and has considerable advantages over the method of least squares in the usual form. -33- . . A more stringent criterion was developed for identification of the coefficients of the approximating polynomial with the true Virial coefficients. They call it the series cut-off criterion, which takes into account the fact that an infinite Virial series is approximated by a finite polynomial. The method of optimal determination of the Virial coefficients is illustrated by Hall and Canfield in two examples. As the first example they calculate the coefficients of some function, selected as an infinite series with known coefficients. Using this function they simulate the path of compressibility isotherms. The computed coefficients of the poly- nomial, approximating the selected function, are found to agree satis- factorily with the true coefficients. \ ^ Also, the Virial coefficients of carbon dioxide were calculated [43] on the 49.712°C isotherm, for which there are the coefficients computed by Michels and coworkers. The Virial coefficients and their errors, obtained by Hall and Canfield and by Michels, practically coincide. This is evidence of equal effectiveness of both methods. The Hall-Canfield method requires considerably fewer computational operations. The method of extracting the second Virial coefficients employed by the authors of the present work is a compromise between Michels and the Hall-Canfield methods in the sense that the coefficients of the approxi- mating polynomial were calculated using orthogonal polynomials, and the errors of the calculated coefficients are determined by a method which is somewhat similar to the proposed by Michels. The Forsythe algorithm [34] is used for approximation of the isotherms for the case of one variable. The function f = - l)v was approximated as 1 a function of density p = — ' V The Virial form of the isotherm equation was found by reducing similar terms for identical powers of The program for approximation was written in the command system of the BESM-3M computer. The program finds 10 powers of the expansion. The deviations at points 6^, sum of squares of deviations Z6? and coefficients of the Virial form of the isotherm equation are read out on the printout system of the computer The program was written as a standard program that can be used for approximating any tabulated function. -34- . Table 9. Values of Second Virial Coefficient B, Calculated for Various Density Ranges and Various Expansion Powers on 348.15°K Isotherm of Ethylene -zi-io'. mVkg for n, equal to I,: 12 30 43 64 0 0,3079 0,2397 0,1872 0,1026 1 0,3555 0,3557 • 0,3630 0,4174 0,4609 2 0,3555 0,:543 0.3452 0,3130 0,2941 0,3547* 0,35G5 0,3025 0,3763 0,3802 A 0,'-555 * 0,3504 * 0,3534 0,3574 0,3613 5 0,3510 0.35G2 * 0,3555 * 0,3519 0,3513 6 0,3430 0,3563 * 0,3559 * 0,3546* 0,3536 * 7 0.3328 0.3620 0,3503 0,3594 * 0,3585 * 8 0,3221 0,3671 0,3445 0,3039 0,3630 9 0,3113 0,3720 0,3385 0.3G83 0,3073 10 0,3001 0,3769 0,3.324 0,3725 0,3714 *The asterisk denotes the region in which B acquires approxi- matel,y constant values and is shifted toward higher powers as the number of experimental points used for the approxima- tion is increased. The coefficients of a series for the experimental isotherms of ethylene and propylene were computed with the program for various density ranges Listed in Table 9 by way of example are the calculations of the second Virial coefficient of ethylene on the 348.15°K isotherm. The number denotes the number of experimental points, read from the beginning of the isotherm. The initial experimental data for ethylene and propylene are presented in Tables 3 and 4. As seen in the table, the second Virial coefficient, starting at some power, does not depend on the number of expansion powers m. For the purpose of identifying the values of B obtained for the various powers of the expansion and various density ranges with "true" values, the results obtained were statistically processed to enable evaluation of the error (confidence interval) of the calculated second Virial coefficients. Using Michels' experimental data they calculated the error A' where n. = f - f , ; (28) 1 exp calc -35- . m is the power of the approximating polynomial; N is the number of experi- mental points. Twelve samplings were made with the aid of random numbers tables and in consideration of the values o:^ a obtained, for each isotherm, each of which, within the limits of error, is an experimental set of data. The approximating polynomial was formulated for each sampling. The final values of the coefficient were obtained as the most probable values on the stability segment. The values of B and AB, given in Table 10, were obtained by statistical evaluation of the parameters of the normal law (confidence interval) A/? ==..1.088 5a; . (29) where n is the number of samplings. The significance of the band AB is that the probability of the calculated AB falling within this band is 70%. Table 10. Virial Coefficients of Ethylene and Propylene According to Data of the Authors T.'K r. °K h, M'/Ke AS. m'/kz Ethylene Propylene 208,15 —0,005014 ±0,000023 298.15 —0,008242 ±0,000010 323.15 —0,00120? ±0,000054 318.15 —0,007183 ±0,000091 348,15 —0,003551 ±0,000012 323.15 —0,006903 ±0,000052 373.15 —0,003032 ±0,000018 .348.15 —0,005901 ±0,000074 398,15 —0,002584 ±0,000021 375.15 —0,005027 ±0,000095 423,15 —0,002224 ±0,000037 398.15 —0,004328 ±0.000083 423,15 —0,003829 ±0,000093 On the basis of the above review of analysis of published data and of calculations done by the authors on compressibility and the speed of sound, the most reliable data were selected, and were then approximated by the polynomials: B (T) =^ 0,02OS4G81 - 0,3325105 ~ ^ - 0,2079736 — 0,6639566 + (for -fOJ003753~-— 0,5853397 — ethylene) ; (30) b m - _ 0,08480S03 + 0,128800 ~- — 0,7710073 ~ + 0,22 1 5 1 4^' 92 4-r - 0,31 -12363 + 0, 1 7366099 (for propylene) -36- 1 1 The recommended second Virial coefficients and their first derivatives, calculated on the basis of polynomials (30) and (31), are listed in Table 11. Table 11. Recommended Values of Second Virial Coefficients and Their First Derivatives for Ethylene and Propylene 7', K dBldT dBldT Ethylene Propylene 200 0,01 101 0,0037776 200 0,020.0 19 0,0219912 210 0,010054 0,0031971 210 0,018292 0,0168845 220 CoC'^riG 0,0030131 220 0,016321 0,0130191 230 O.OOJS'^'P 0,0023545 230 0,0146.39 0,01020bo 2-10 O,n07'i'2''' 0,0020177 240 0,013224 0,0080745 25(^ 0,007.< J6 0,0017950 250 0,012031 0,0064572 260 0,00ij7iii< 0,0015869 260 0,01 1018 0,00521 10 270 O,00G2Ni 0,0014125 270 0,010147 0,0042432 280 0,0058 0,001265 280 0,009389 0,0034826 2S0 0,0053; '3 0,001 1411 290 0,008720 0,0028798 300 0,005003 0,0010345 300 0,008120 0,0023982 310 0,001016 0,0009607 310 t), 007577 0,0020104 320 0,001321 0,0008632 320 0,007082 0,0016956 330 0 fin -(074 0 0007937 330 0 0066''^G 0 0014383 340 0,003704 0,0007330 340 0,006364 0,0012266 350 0,003509 0,0006788 350 0,005819 0,0010512 360 0,0032^s-1 0,0006309 300 0,00.5461 0,0009051 370 0,003079 0,000.5881 370 0,005132 0,000782 380 0.002891 0,0005498 380 0,004829 0,0006730 390 0,002718 0,0005153 3Ju 0,004552 0,0005918 400 0,001558 0.;)001840 !00 0,004.302 0,000517 410 0,002409 0.0001557 410 0,004076 0,0004535 420 0,00227! 0,0004299 420 0,003874 0,0003961 430 0.0021 12 0,0004062 430 0,003697 0,000351 440 0,002090 0,0003841 410 0,003.542 0,0002809 1 0,0002743 450 0,00 1 90G 0,000..;646 450 0,0034 i: 41.0 0,0002441 460 0,00 1 7! 0,000,>162 0,003.302 G'' i 0.00.3214 '0,0002156 470 0,00 1 0,!;C03292 470 "0,0ij0.<135 0,00 1 4MJ 0,003148 0,0001914 80 im 1 •J 490 0,001 4fiL. 0.000290S 490 0,003102 0,0001701 500 O.OOMO:; 0.0002852 500 0,003075 0.0001511 Recommended Values of Specific Volume, Enthalpy, Entropy, Isobaric Heat Capacity of Gaseous Ethylene and Propylene The recommended specific volumes of ethylene and propylene were calculated using equations of state of the form (11), the coefficients of which are given on page 18. The roots of the equation were determined by methods of iterations and half division using the BESM-3M computer^. The specific volumes in the 200-270°K temperature range and 0.5-20 bar pressure range were computed by an equation with the true second Virial coefficient: The authors gratefully acknowledge the cooperation of N. S. Levchuk and K. A. Lensyurovskaya of NIIASS Gosstroy Ukrainian SSR in the writing of the programs and execution of the calculations in the computer. -37- : The second Virial coefficients of ethylene and propylene are listed in Table 11. The enthalpy, entropy and heat capacity were calculated on the same computer in accordance with equations derived on the basis of thermal equations of state. The enthalpy was measured from the 0°K crystalline state A/ - RT S = St~ A5; AS= R C, = C,+ R 1 + = Cl — R In these equations are the "Virial coefficients" of the equations of state of ethylene and propylene. •V ' 1 /!=0 ' ^ dAi _ V r' d^Ai _ V r' Given in Tables II and VI are the i'sobaric heat capacities C of P ethylene and propylene, calculated by the above-mentioned method, for pressures above 100 bar. The isobaric heat capacities in the range of parameters of state near the saturation curve and in the supercritical region to a pressure of 100 bar were calculated on the basis of experimental data on the speed of sound. These data agree well (deviation up to 3% in the region of peak heat capacity C^) with data calculated by the equations of state. This fact and the high accuracy of description of the p, V, T- data confirm the reliability of the computed caloric properties of gaseous ethylene and propylene with the aid of the thermal equations of state offered on pp. 18-20. -38- . CHAPTER II. SPECIFIC VOLUME OF LIQUID ETHYLENE AND PROPYLENE Review of Experimental Data Three works have been published to date on experimental determination of the specific volume of liquid ethylene. Michels and Gelderman [1] did investigations on the 273.15°K isotherm at pressures up to 2,696 bar. The accuracy of these data is 0.01%. The specific volumes obtained in [1] are listed below: p , bar p , bar V, CM^/e 43..'^7 2,8738 330,81 2.1138 2,7919 353.11 2,0961 54,52 2,7187 494.72 2,0072 61.52 2.6582 527.24 1,9908 69,27 2.6055 729,04 1,9076 77,8G 2,5584 774,79 1,8922 86.33 2.5195 1053.43 1,8152 87.24 2.5157 1116,12 1,8010 . 91.78 2,4975 1130,42 1,7977 335.57 2.3690 1450,80 1,7365 144,82 2,3486 1532.15 1,7231 215.57 2.2320 '769,7? 1,6883 230.53 2.2130 2695.80 1,5878 N. V. Boyko and B. V. Voytyuk [2] investigated the specific volume of liquid ethylene at temperatures from 180 to 273°K and pressures up to 60 bar by the method of hydrostatic weighing using strain gauges. The error of the data, according to the authors, was 0.5%. Considering the low purity of the investigated compound (99.7%), these data should be considered preliminary. Later on, after improvement of experimental method, the specific volume of liquid ethylene with the same parameters was investigated by B. V. Voytyuk for a specimen containing 99.99% ethylene. The data obtained, the accuracy of which is 0.15%, are presented in Table 12. The main procedural element of this work is consideration of the correction for heat transfer in the weighing head. Since high-density current (55 A/mm^) passes through the strain gauge, the latter is a heating element. The conditions of heat exchange between the strain gauge and the investigated gas are governed, assuming other conditions to be equal, by the nature and density of the gas, which varies as the pressure in the system changes -39- Table 12. Experimental Data on Specific Volume of Liquid Ethylene (Ethylene -- 99.99% by Volume, Ethane -- 0.01% by Volume) V, cmVg 'at' t, °C 0 —5 —10 —20 —30 — 45 -60 -70 —80 —90 d — — — 1 s?n 1 .oou If) 2,005 1,938 I .o._o IS 2,124 2,001 — 8''4 20 2,285 2,116 1,997 1,931 1 874 I 25 2,273 2,109 — — . 30 2,406 2',260 2,103 1,989 1,925 I 869 1 820 35 2,595 2!388 2^250 2,096 — — 39 2,731 40 2,561 2,371 2,239 2,091 1,982 1,920 42 2,921 2,699 45 2,8G3 2,670 2,531 2,J07 2,230 2,086 48 2,8:3 2,643 50 2,506 2,343 2,221 2,080 1,975 1.914 1.860 1,813 51 2,771 2,619 54 2,733 2,597 55 2,483 2,329 2.212 2,076 57 2,701 2,577 60 2.6^5 2,558 2,462 2,315 2,204 2,071 1,969 1,909 1.855 1,810 The required correction for fluctuation of heat transfer conditions was determined by finding the dependence of the readings of the strain gauge installed on the top and bottom locking devices, on the pressure at a strictly fixed weighing unit temperature. Both dependences, as it turned out, coincide for the same compound, and this is reason to consider them uniquely when the strain gauge is operating normally. The correction for heat transfer is 2% of the measured specific volume, and the error of determination of the correction does not exceed 2.5%. During determination of the density of liquid ethylene the pressure in the system was created by the gas of the investigated compound, since the temperature of the weighing head was maintained at 323.15°K. The critical temperature of ethylene is 283.05°K. Data on the specific volume of liquid ethylene on the saturation curve at temperatures of 183. 15-273. 15°K were obtained by extrapolating the experimental isotherms to saturation pressure [3] . Analysis of these data (see Chapter III) confirms their high accuracy. The specific volume of liquid ethylene was investigated by Ye. A. Golovskiy, V. A. Yelema, V. A. Zagoruchenko and V. A. Tsymarnyy [4] (Table 13) by constant quantity piezometry in the temperature range from 202°K to the critical point at pressures up to 600 bar. The authors give the following measurement errors: Ap = 0.04-0.16 bar, 6V = 0.06%, 6G = = 0.009% and AT = 0.08 deg. Noteworthy is the work of Dick and Hedley [5], in which Michels' data [1] are smoothed for rounded off pressures. -40- Table 13. Experimental Data of Golovskiy, Yelema, Zagoruchenko and Tsymarnyy [4] on Density of Liquid Ethylene (Ethylene -- 99.66%, Ethane -- 0.34%) T\ K p, Kec/CM' p. 1/CM' T", K p. mc/cM' p. a/cM* 1 235,62 51,05 0,4668 259,37 113,52 0,4400 240,00 80,G3 0.4667 263.77 138,08 0,4400 245,28 115,63 0,4666 270,34 174.29 0,4398 249,01 144,69 0,4665 276.31 207,17 0,4396 255,66 185,95 0,4063 281,05 233,35 0.4395 263,22 234.23 0,4661 278,64 220,14 0.4396 270.61 282,55 0,4659 286,25 261,82 0,4394 270,48 282,39 0,4659 290,87 287,28 0.4393 278,79 331,21 0,4657 290,55 318,06 0.4.391 285,09 371.41 0,4655 301,52 348,14 0,4390 2yi,97 415,21 0,4653 254.43 37,66 0,4171 299,29 461,95 0,4651 260,08 64,76 0,4170 306,83 508,85 0,4650 205.79 91,70 0,4169 202,57 298,33 0,5542 270,05 111,90 0,4168 207,62 357,33 0,5540 272,54 121,82 0,4167 212,80 417,53 0,5538 2^8,88 151,86 0,4166 218,21 479,73 0,5536 284,87 180,11 0,4164 223,39 538.53 0,5534 2J0,44 206,63 0.4163 228,99 599,97 0,5532 :'95,83 231.83 0.4162 218,57 13,79 0,4900 i 202,02 512,44 0,4160 221,18 34,18 0,4899 202,11 513,24 0,5723 ; 228,93 94,82 0,4897 1 305,24 276,43 0,5723 234,00 134,48 0,4895 305,51 277,63 0,4160 241,10 189,96 0.4893 -505,27 42,75 0,3354 246,23 229,15 0,4891 208,11 53,33 0,3852 250,79 264.08 0,4890 271,48 67,35 0,3852 254,36 291,24 0,4889 276,39 82,81 0,3851 262,07 348,84 0,4837 282,28 105,03 0,3850 266,52 382.36 0,4885 287,36 124,25 0,3849 270,41 411,29 n 4884 293.87 149,23 0,3848 278,60 471,85} 0;4SS2 300,01 1 72,53 0,3846 286,25 527,92 0,4880 304,86 191,27 0,3845 293,93 583,36 0,4S77 .304,89 191,39 0,3845 207,86 26,87 0,5121 200,69 390.53 0,5642 211,43 59,55 0,5120 206,45 460,81 0,5640 217,42 114,17 0,5118 211,47 521,84 0,5638 223,33 167,10 0,5116 218,63 605,13 0,5635 228,19 210,40 0,5114 218,52 605,33 0,5635 228,34 211,72 0,5111 200,28 200,70 0,5460 236,15 280,78 0,51 12 206,30 256,82 0,5458 242,13 332,95 0,5110 211,56 315,96 0,5456 245,99 366,24 0,5109 216,97 375,52 0,5454 207,36 581,44 0,5722 222,57 436,36 0,5452 209,15 604,08 0,5721 227,37 486,7) 0,5450 242,79 21,87 0,4105 2 32,60 542,18 0,5448 247,45 48,32 0,4404 238,06 599,27 0,5447 253,63 82,9!^ 0,4402 A list of experimental works pertaining to investigation of the density of liquid propylene is given in Table 14. Vanghan and Graves [6] investigated density by constant quantity piezometry with an accuracy of ±1%. Their data are presented in Table 15. 1 Farrington and Sage, using a method described in [7], measured the specific volume of liquid propylene with an accuracy of 0,3%. Their data are given in Table 16. -41- Table 14. List of Experimental Works on Density of Liquid Propylene 1) 2) n Ai;T..i Boyre;i h FpoBC [6] 1940 0—91,4 6.9-82,8 ftappiiiiiroH H CeiiA>K [7J 1949 4.44—87,78 0,9—689,5 MiixcHbc 11 corpyAiiHKH [8] 1953 66,3—88,2 36,26—2192,86 jliiTMap, lily;ibu ii lilrpecce [9] 1962 (0) -(-1-90) 19,0-1028.7 BOKTIOK 19C7 (—90) _ (4-39,3) 5—60 KEY: 1. Authors 2. Year Vanghan and Graves [6] 3. Temperature range, °C Farrington and Sage [7] 4. Pressure range, bar Michels, et al [8] Dittmar, Schulz and Stresse [9] Voytyuk Table 15. Compressibility Factor Z for Liquid Propylene According to = Vanghan and Graves [6] for P^^ 45.4 atm, t^^ = 91.4°C, p^^ = 0.233 g/cm^ I z at t. "c p. 6ap 0 50 75 91.4 0,15 6,90 0,022 0.20 9.20 0,028 0,25 11,50 0,035 0.30 15,64 0,042 0,043 0.40 18,40 0,055 0,057 0,50 23,00 0.069 0,071 0,075 0,60 27,60 0.083 0,085 0,090 0,70 32,20 0.097 0.099 0,104 0,80 36,80 0.109 0,113 0.119 0.131 0,90 41,40 0.124 0,127 0,133 0,144 1.00 46,00 0.138 0,141 0,147 0,157 0.273 1,02 46,92 0,210 1,10 50,60 1,151 0,155 0,161 0.171 0,202 1,20 55,20 0,165 0,169 0,175 0.184 0,209 1,30 59.80 0,179 0,183 0,188 0.197 0,219 1,40 64.40 0.211 0,230 1,50 69,00 0,242 1.60 73,60 0,254 1,70 78.20 0.266 1.80 82,80 0.278 The results of experimental investigation of Michels and coworkers [8] on the 66.3, 74.8, 82.8 and 88.2°C isotherms at pressures up to 2,000 atm, were published in 1953. The error of the data was estimated by the authors to be 0.03%. The results of studies [8] are presented in Table 17. A rather detailed investigation of the specific volume of liquid propylene by means of a constant volume piezometer relieved of pressure was done by Dittmar, Schulz and Stresse [9] . The authors do not give a conclusive evaluation of the accuracy of their data, but state only the errors of measurement of temperature (0.01°C), pressure (0.06%) and volume of the measurement bomb (0.1%). The experimental data [9] are presented in Table 18. -42- ) Table 16. Experimental Data of Farrington and Sage [7] on Specific Volume of Liquid Propylene V. c.\i'U ii|iu /. "C p. Cap 4,44 21.11 37.78 £4.14 71.11 82.22 87,78 = 1 1,8529 A filQ 1,8516 ~i— Ifl "^JT . 1 U,OT ^ 1,8510 1,8479 1,9447 . _ zu»uoo 1,8429 1 ,9365 2,0620 1,8379 1.9290 2,0501 2,2181 1,8329 1.9215 2,0383 2,1981 2,4659 41.370 1,8279 1,9147 2,0277 2,1794 2.4116 2.7250 00,lo6 1.7992 1.8735 1 .9684 2,0832 2,2237 2,3442 2.4 1 60 J (JoWzj 1.7892 1.8001 1,9490 2,0545 2,1800 2^2817 2^3410 1 0A i^r^ 1,7792 1,8485 1,9315 2.0293 2,1444 2,2343 9 9«55 io/,yuu 1.7705 1.8373 i;J159 2,0077 2.1 126 2! 1975 9 9443 1 c r I oo 156, 13» 1,7617 1,8273 1/9022 I i9883 2.0895 2, 1 663 9 9068 172,3 / ,» 1.7536 1.8179 U8891 1,9709 2,0664 2!l400 2,1762 loy.ui J 1,7455 1.8085 l!8772 1 ,9552 2,0451 2ill38 2! 1481 1,7380 1,7998 1,8666 1,9403 2.0258 .2,0913 2! 1232 Oil "50 "^ 9'' 1,7213 1,7829 l..*-'- 172 1,9147 1 1 1 £L,\J i JO 275,800 1J118 UGSO |!82'j8 U8922 1,9621 2,0189 2.0420 31 0,2 /o 1,7005 1.7542 1.8142 1,8728 1,9365 1,9890 2.0102 344.730 1,6899 1.7417 1,8010 1,8547 1,9140 1,9634 1.9821 413,700 1,6712 1,7199 1.7730 1,8241 1,8766 1,9203 1.9353 482.650 1,6556 1.7012 1.7486 1,7967 1.8441 1,8803 1,8953 551,600 1.6418 1,6830 !,7268 1 ,7705 i,8160 1.8479 1,8016 620,55 1,6294 1,6608 !,7068 1,7474 1,7910 1.8192 1.8316 689,500 1,6175 1,6512 1,6862 1,7249 1,7667 1,7936 1,8073 1 Table 17. Experimental Data of Michels and Coworkers on Specific Volume of Liquid Propylene p, bar at' t, °C 0, CM*IZ 66.3 74.8 82,8 88.2 3,1461 43,504 2.9326 46.212 2.6477 46,967 2,4834 42,034 62,610 76,777 2,4176 50.788 73.114 2=?555 o6,256 2,2390 64,142 94,319 122,745 2,2253 68,692 99.404 128.486 148,278 2,0772 142.769 181,395 217,317 1,9989 209.522 293.405 321,030 1,9^47 285,783 333,883 379,081 1.8468 435.967 1,8212 492,742 550,942 605,445 642.023 1.7203 798,796 1,6615 1059,397 : 1 36.362 1208,575 1256.802 1,5363 1910.154 2039.289 ,2131.009 2192.857 -43- 7 , Table 18. Experimental Data of Dittmar, Schulz and Stresse [9] on Specific Volume of Liquid Propylene --- (• L>j t J t:. cm' /e 0 10 20 30 40 50 60 70 80 90 1,5873 757,1 868,9 977,7 1,6129 620,8 725,7 828,7 929,7 1028.7 1,6393 497.2 599,2 699,2 798,3 894,4 988,5 — — — — J. 6666 388.3 484,4 579,6 672,7 764.9 856,1 945.5 — 1,6949 291,3 382,5 472.7 561,9 649,2 735,5 820,8 905,2 989,5 — 1,7241 205,9 292,2 377,6 461.9 545,2 628,6 711,0 792,4 874,8 956,1 1,7543 134,4 214,8 295,2 374,6 454,0 532,5 611,0 684,4 766,9 843,4 1,7857 73,5 148.1 222,6 297,1 37 i, 445,2 518,8 591.3 662,9 734.5 1.8181 19,6 90,2 1(;0,8 220,6 300.1 .369,7 438,4 507,0 575.7 643,3 1,8518 — 41,2 106,9 172,6 237,3 302.0 366,8 431.5 496,2 560,0 1,8867 — — 61.8 123,6 184,4 245.2 305,9 367.7 428,6 488,4 1,9230 — — 26.5 83,4 140,2 196.1 253,0 309,9 366,8 423,6 1.9607 — — — 48,1 101,0 154,0 207,9 261,8 314,8 367,7 1,9999 19,6 69.6 119.6 169,7 219,7 269,7 319,7 2,0833 — — — 19,6 63.7 107.9 152.0 196,1 240,3 OZ.O lUz.U 14(J,J 1 / o,0 2,2727 (56,7 101,0 135,3 2,3S09 44.1 73,5 103,0 2.4999 55,9 81,4 2,6315 44,1 66,7 2.7777 56,9 2.9411 50,0 The experimental data are generalized in Lehman's review [10]. The tables which he compiled are based on the results of Vanghan and Graves [6] Farrington and Sage [7] and the data of Poll and Maas [11], Hanson [12], Lu, Newitt and Ruhemann [13] on the specific volume of the liquid on the saturation curve. Table 19. Experimental Data of Authors on Specific Volume of Liquid Propylene (Propylene -- 99.80% by Volume, Propane -- 0.15% by Volume, Ethane -- 0.01% by Volume, Ethylene -- 0.04% by Volume) V. cmVg at p, kg/cm^ t. °c 10 20 30 40 50 60 —90 1,515 1,514 1.513 1,512 1,511 1,510 1,509 —80 1.543 1,542 1.540 1,539 1.538 1,537 1,535 —70 1.572 1,571 1,568 1,566 1.564 1.562 1,560 —60 1.602 1,601 1.598 1.596 1,593 1.591 1,589 —50 1.634 1,632 1.629 1,626 1.624 1.621 1,619 —40 1,666 1,664 1.660 1,657 1.654 1,651 1,649 —30 1.701 1,699 1.695 1.692 1.688 1,685 1,682 —20 1.741 1,739 1.735 1,730 1,726 1,722 1,718 —10 1,790 1,787 1.780 1,774 1.768 1,762 1,757 0 1,837 1,828 1,820 1,813 1.806 1.800 14.27 1.913 1,903 1,894 1.886 1,877 1,869 16.58 1,926 1,916 1.907 1,899 1,891 1.883 25.83 1,976 1,964 1.953 1,942 1,931 32.23 2.027 2.013 1.999 1,985 1.973 39.31 2,086 2.067 2.050 2.034 2,020 -44- B. V. Voytyuk, using a method described in [2] , did experimental investigations of the specific volume of liquid propylene at temperatures from +4n°C to -90°C and at pressures up to 60 atm. Pressure in the system was created by nitrogen, since the critical point of propylene is 365.05°K. In this case nitrogen and liquid propylene came into contact in a connective tube 10 mm in diameter, which minimized the dissolving of nitrogen in the investigated liquid. An experiment was done at -45°C for liquid ethylene to determine the possible solubility of nitrogen in hydro- carbons. The pressure in the system was created first with gaseous ethylene and then with nitrogen. The scattering of experimental data did not exceed oAs%. Analysis of the composition of the investigated liquid in a KhL-4 chromatograph revealed no notable concentration of nitrogen. The accuracy of data on the specific volume of propylene is 0.15%. The data are listed in Table 19. Recommended Specific Volumes of Liquid Ethylene and Propylene The recommended specific volumes of liquid ethylene were found on the basis of experimental data [1, 4] and of the authors' present work. Results [4] agree quite well with. Michels ' data [1] on the 273.15°K isotherm. The data in the present work agree with the data in [1] with an accuracy of 0.15%. In view of the fact that data [4] are limited to comparatively high pressures it is difficult to check their concordance with the authors' data (see Table 12) by direct comparison. V. A. Zagoruchenko and V. A. Tsymarnyy reported at the Third Thermophysical Conference on the High-Temperature Properties of Matter (Baku, 1968) about the thermal equation of state of liquid ethylene, formu- lated on the basis of data [4] . The equation is pV^A(T) + BiT},y' + C(T)p\ ^ (36) where A (7) = 427 505 — 969 968 • lO' • T~' + 826 658 • lO'T"' — 84 221 x X 10~'r + 6447.5 . lO'-'r^; B (?) = —37,4967 + 132.707 • 10'r~' — 10^7^^ ~ 166,370 • + 3,308 • lO""?; C (T) = 0,5739 — 2,8167 X X 10V~' + 4,4402 . 10Y~'; (pi = kmole/m'; [pV] - kJ/kmole. The agreement of data [4] with the data presented in this monograph was checked with the aid of this equation. The discrepancy increases monotonically on the 60 bar isobar from 0 at 180 to 0.25% at 270*'K. Near the saturation curve the data calculated on the basis of specific volume are overstated by up to 0.6% .compared with the data of the authors, and the deviations decrease as the temperature drops. Thus, in the range of parameters of state where equation (36) is interpolated, satisfactory agreement of the results obtained by the authors of the present monograph and of results [4] is confirmed. -45- The specific volumes of liquid ethylene at pressures below 60 bar, ' found by graphic processing of experimental data of the authors of the j present book, are presented in Table II. The values at pressures from 70 i to 500 bar (see Table III) were calculated according to thermal equation of state (36) . j Comparison and analysis of the experimental data on the basis of ; the specific volume of liquid propylene revealed that the data of Dittmar, Schulz and Stresse [9] in overlapping temperature and pressure ranges | deviate from the data of Michels and coworkers [8] by 0.5-0.6%. Only on i the 50 bar isobar at temperatures above 350°K do the deviations exceed 0.6, and reach 3.6% near the critical point. The deviations of the data of Farrington and Sage [7] from the data | of Michels and coworkers is 0.3% on the 700 bar isobar and drops consider- ably as pressure decreases. Near the critical point, however, the deviations i reach 1%. ' j The data of Vanghan and Graves are considerably [6] inferior in terms | of accuracy to the data in [7, 8, 9]. In the overlapping temperature range i of 280-310°K the experimental results of the authors of this work agree with ,' the results of Farrington and Sage within the limits of 0.3-0.40%, and the deviations decrease as temperature drops. Deviations from the data of Dittmar, Schulz and Stresse in the same temperature range amount to 0.5-0.6%. There is good agreement between the experimental data of Farrington j j and Sage and test data on the saturation curve [11, 12, 13] in Lehman's review [10] . By extrapolating the experimental isotherms to the saturation pressures [10] the authors obtained data on the specific volume of liquid [ propylene at temperatures from 183.15 to 313.15°K. Analysis of these data (see Chapter III) confirm their high accuracy. | j I j The data of Michels and coworkers [8] , Farrington and Sage [7] , and | of the authors of this book were used on the basis of what has been stated above for compilation of Table VII of recommended specific volumes of j | liquid propylene. The accuracy of the data is 0.15% for pressures below | 60 bar, 0.3-0.5% for pressures above 60 bar. 1 -46- CHAPTER III. PROPERTIES OF ETHYLENE AND PROPYLENE ON SATURATION CURVE Pressure and Density of Saturated Vapor and Liquid Experimental investigation of the thermal properties of ethylene and propylene on the liquid-vapor equilibrium curve is the subject of a series of works, enumerated in Table 20. The data presented in the cited works are given in Tables 21 and 22. Experimental data on the pressure of saturated vapor of ethylene, found in the works of Michels and Wassenaar [8], Mathias, et al [5], Henning and Stock [1] , agree satisfactorily. The average divergence between them does not exceed 0.2%. The data of Egan and Kemp [6] are understated relative to the data of Michels by an average of 0.5%, and the data of Crommelin and Watts [3] are 0.9% higher than the data of Michels. The specific volume of saturated liquid ethylene was determined by Maass, Wrigt [2] and Mathias and coworkers [4] . Their data practically coincide at a temperature of 165°K. In the 170-200°K temperature interval, however, interpolation of Mathias' data yields specific volumes of the liquid up to 0.4% overstated in comparison with Maass' data. The specific volume of saturated ethylene vapor was investigated by Mathias and coworkers [4] . Deviations of the experimental points obtained in this work from the smooth curve amount to an average of 2%. It is noteworthy that not all thermal parameters were determined in [1-8] on the saturation curve. The data of B. V. Voytyuk on the specific volume of the liquid were obtained by extrapolating the experimental isotherms of compressibility (see Chapter II) to the saturation pressures of the vapors. The experimental data of Yu. F. Voynov, N. V. Pavlovich, D. L. Timrot [17] were obtained by direct measurement of the pressure of saturated vapors and specific volumes of equilibrium liquid and vapor. The specific volumes of the liquid and vapor were determined by hydrostatic weighing with the aid of double strain gauges. In this case the difference method of weighing was employed (quartz float and calibrated weight, placed in the investigated phase, were weighed), which excluded the effect of changing conditions of heat exchange in the weighing head. The limit relative error of determination of the specific volume of the vapor, attributed to errors in weighing and determination of the volume of the float, is 0.02-0.12%, and the limiting error of determination of the specific volume of the liquid is 0.06-0.7%. The maximum errors correspond to minimum densities. Table 20. List of Works Pertaining to Experimental Investigation of Thermal Properties of Ethylene and Propylene on Saturation Curve 31 1) J) ABTOpU Typa. 5 ) Sthjich 7) XeHHIIHT, UlroK [1] 1921 P 131—162 Maacc, Pafir |2| 1921 v' 164—203 KpoMMejiiiHr, yoTc [3j 1927 P 208—276 V', V' 209—282 AiarnriC, XpoMMCintir, Votc [4] 1927 v' 128—170 .MaTcac, KpoMMe.niinr, i'oTc i5] 1929 p 203—281 3raH, Ke.Mn (6| 1937 p 123—170 JlaM6, Poiiep [7] 1940 p 147—173 Mnxe-ibc h jp. [8] 1950 p 149—280 BoflTIOK 1967 v' 183—273 BOHHOP. H flp. ; 19G5— 1967 p. I)', v" 163—280 8) 6) ripOIlIMfcH Maac, PaAT [2] 1921 p 235—283 v' 194—292 riayeJi.i, R-A:av,oK [9| 1939 p 165—225 Boyren, Tpeuc [10) 1940 273—364 Jlavio, Ponep (7J 1940 151—235 Jly, Hbrom, PyxMaH (Ml 194! 243—365 TexHHMecKHii Komhtct NGAA [12] 1942 V 260—283 Aiapw.MaH H jip. 1 13| 1949 P, V 303—348 appii:!rron, CeiLl-K [I4J 1949 ?. v. 277—360 A\nxo.^i-c II ;:p. (15) 1953 P 297—363 .MopeKpc(})T [16] 1958 v' 273—348 Bo'lThiK 1967 v' 183—313 BOHfiOB )i ^p. [17] 1965-1967 173—362 KEY: 1. Authors 8. Maass, Wrigt [2] 2. Year Powell, Giaque [9] 3. Measured parameter Voughan, Graves [10] 4. Temperature, °K Lamb, Roper [7] 5. Ethylene Lu, Newitt, Ruheman [11] 6. Propylene Technical Committee NGAA [12] 7. Henning, Stock [1] Marchman, et al [13] Maass, Wrigt [2] Farrington, Sage [14] Crommelin, Watts, [3] Michels, et al [15] Mathias, Crommelin, Watts [4] Morecroft [16] Mathias, Crommelin, Watts [5] Voytyuk Egan, Kemp [6] Voynov, et al [17] Lamb, Roper [7] Michels, et al [8] Voytyuk Voynov, et al -48- 1 The recommended thermal parameters of ethylene and propylene on the saturation curve (Tables I, V) were found by graphic analysis of the experimental data listed in Tables 21 and 22. The data on the pressure of the saturation vapors of ethylene thus obtained coincide with an accuracy of 0.2% with the experimental data of Michels [8], Mathias [5], Henning and Stock [1] and of the authors of the present work. The data of Crommelin and Watts [3] are 1% overstated compared with the recommended values, and the data of Egan and Kemp [6] are 0.6% understated. Deviations of the recommended specific volumes of liquid ethylene from the experimental data of Maass [2] , Mathias [4] and the authors of the present work, fall within the limits of 0.5%. The data of B. V. Voytyuk and Yu. F. Voynov, et al, agree, also within the limits of 0.5%. Table 21. Experimental Data of Various Authors on Properties of Ethylene on Saturation Curve 2) 1) p. oap a'. At' /He 1921 131,69 0,05235 3) XeiiHHHr. I'Jtok (1 143.09 0.1553 152.13 0,3217 162,82 0.6775 164,45 0,001735 4) Maacc, Pafir [2] 1921 168.45 0,001756 171,10 0,001776 178,85 0,001799 183,75 0.001824 IS9,10 0.001852 198,95 0,001906 203,70 0,001933 5) KpoMMe;innr, Yore [3] 1927 208,11 6,314 210,65 8.602 223,60 1 1 .997 237.38 16.597 217.88 22.17 258,14 28.82 204.37 33.39 209,58 38,45 276,60 41.80 6) AiaTHiiC, KpoMv,c.iiii;r, 1927 128,08 0,001601 153.25 0.001654 VoTC [4] I [Continued on next page] KEY: 1. Authors 9. Lamb, Roper [7] 2. Year 10. Egan, Kemp [6] 3. Henning, Stock [1] 11. Michels, Wassenaar, Louwerse [8] 4. Maass, Wrigt [2] 12. Michels, Wassenaar, Louwerse [8] 5. Crommelin, Watts [3] 13. Voytyuk 6. Mathias, Crommelin, Watts [4] 14. Voynov, Pavlovich, Timrot 7. Mathias, Crommelin, Watts [4] 8. Mathias, Crommelin, Watts [5] -49- Table 21 (Continued) 7) M.irn3c, KpoMMe;iHHr, 1927 158,-i6 0,001713 r/0,14 0.001762 yoTC (4J 209,74 0.001977 0,07946 225,00 0.002091 0.04899 236.02 0,002192 0,03394 248,82 0.002344 0.02389 253,95 0.002421 0.01955 258.97 0.002509 0.01668 262,23 0.002576 0,01488 265,45 0,002651 0.01315 278,99 0.003242 0,007538 279.65 0,003296 0.007291 281.13 0.003481 0.006550 282,65 0.004630 0.004630 8) MaTtiac, KpoMMe.niHr, 1929 203.88 5.329 yoTC 15] 212.25 7.301 221,06 9.903 232.14 14.091 242.62 19,101 253,14 25,235 263.14 32,395 265,61 34,372 273.15 40.810 281,05 48,800 9) JlaMfi. Ponep [7] 1940 147.88 0,2318 154,91 0,3946 163.12 0,6973 168.30 0.9517 170.16 1,0587 173,24 1.2640 10) Bran, KeMn [6] 1937 123,51 0.02102 128..59 0.03781 135.96 0,0c082 140.93 0,12SG4 145,59 0.1914 151.05 0,2954 156,21 0,4313 161,67 0,6253 165.15 0,7812 167.80 0,9179 170,40 1 .0702 11) MKxe-nbc, BecccHap, Jloy- 1950 149.35 0.26030 uepse [8j 156.11 0,43040 159.74 0.55264 163,60 0.71116 166.61 0.85894 169.03 0.99.158 169.03 0.99368 169.04 0.99377 169.71 1.0338 169.70 1.0338 169.70 1,0339 172.44 1,2101 179.77 1,7983 . 183.96 2.2196 -188.56 2,7661 196.60 3,9575 204,23 5,4086 213.61 7,6782 223.33 10.688 233,10 14,501 243.07 19,314 [Continued on next page] -50- Table 21 (Continued) 1) p. Oao 12)MHxe;ihc, BacceHap, Jloy- 1950 249.67 23,087 Bepae (8J 255,26 26,677 261,89 31,438 267.84 36,231 273,59 41,354 277,30 44,946 279,61 47,306 280,54 48,279 13)B0HTlOK 1967 183,15 0,001831 193,15 0,001883 203,15 0,001941 213,15 0,002007 223,15 0,002084 233,15 0,002175 243,15 0,002286 253,15 0,002422 263,15 0,002610 268,15 0,002752 273,15 0,002934 14)liOHHOB, riaB.nonii'i, TiiMpoi 1965 163.3 0,001732 0,6757 1967 173,15 1,265 0,001785 0,3891 178.15 1 .659 0,001808 0,3023 1965 183,1 0,001824 0,2357 19G7 183,15 2,137 0,001832 0,2381 188,15 0,001856 0,1899 1966 193.15 3.409 0,001873 0,1541 1967 193.15 3,409 0,001883 0,1531 198,15 4,224 0,00)911 0,1250 203,15 5,178 0,00I'^41 0,1028 208,15 6,273 0,001972 0,08554 213,15 7.518 0,002006 0,07179 218.15 8,973 0,002042 0,06064 223,15 10,61 0,001'OSl 0,05171 228,15 12.46 0,002123 0.04427 19C6 233,15 I 1 ,52 0,002163 0,03755 1967 233.15 14. -19 0,002158 0,03788 238.15 16.78 0,002221 0,03239 1966 243,15 19,35 0,002272 0,02754 19(.7 243,15 19,34 0,002279 0,02775 1965 247,4 21,73 0,002317 0,02424 1967 248.15 22,12 0,002345 0,02375 1965 252,8 25,06 0,002401 0,02056 1966 253.15 25.28 0,002412 0,02029 1967 253.15 25,25 0,002420 0,02025 1965 257,2 27,99 0,002475 0,01799 1967 258.15 28,67 0,002510 0,01726 1965 261.8 31, .13 0,002562 0.01554 1966 263.15 32,45 0,002607 0.01485 1967 263.15 32,35 0,002622 0,01466 1965 264,7 33,65 0,002628 0.0141! 267,2 35,64 0,002688 0,01279 1966 268,15 36,53 0,002738 0,01264 1967 268,15 36,51 0.002771 1965 269,8 37,84 0.002764 0,01191 1965 272.2 39,99 0.002842 0,01090 1967 273,15 40,89 0.002965 1965 274.4 0.002924 0.00992 1965 276,1 43,75 0,00:^009 0.00912 1965 277.8 45,39 0,003111 0.00834 1965 280.9 48.64 0,003455 0,00666 -51- 5 p Table 22 Experimental Data of Various Authors on Properties of Propylene on Saturation Curve 1) 2) AsTopbl Foa p. 6a v' , ju'/Ke ti', M'iKe 3) ;iiaacc. PaHT (2) 1921 235,70 1,480 238.75 1,742 246.10 2,228 257.50 3,426 273,25 5.679 278,90 6,986 280.65 7.359 283.15 7.919 194,95 0,001542 214.65 0,001601 224.65 0,001037 235.70 0.001674 238.75 0.001684 245,50 0.001708 257.50 0.001752 273.15 0.00)827 292.15 0.001929 4) DayeJiJi, JhaaiioK [9] 1939 165.81 0,02130 172,77 0,03921 17G,52 0,05322 180.00 0,CG975 184.51 0.09768 189,50 0,1380 195.63 0,2060 202.72 0,3164 207.45 0,4132 213.39 0,5672 220,28 0.7977 225,98 1,0398 5) BoyreH, FpcBC [10] 1940 273,15 5.83 0.001695 0,08130 298,15 1 1 .53 0,001802 0,04065 323.15 20.55 0.002092 0,02183 348.15 33,94 0,002519 0,01 124 363. 1 44.76 0,003401 0,005747 364.15 45.68 0.00.^610 0,005291 364.55 46,00 0,C04292 0,004292 6) JlasiG, Poncp |7J 1940 151.72 0.005159 185.08 0,1010 198.47 0.2445 212,51 0.5394 222,52 0,8S36 227,58 1,1 !22 2.35.42 1.552! 7) Jly, HbK)HT. PyAMaH[ll] 1941 243.15 2,097 0.001703 253.17 3,010 0 001742 0,1462 203.15 4,306 0.001779 0,1096 273.15 5,807 0,00183! 0.08130 283,15 7,731 0,00 1 883 0.06211 293.15 10.26 0,001938 0.04717 303,15 13.19 0,002020 0.03610 313,15 16.54 0.002101 0.02833 323,15 20.66 0:o02i 83 0.02188 333,15 25.20 0.002288 0,01683 343,15 .30.40 0,002451 0.01312 353.15 . 36.73 0.002703 0,01000 363,15 44,60 0.007299 365,25 40.00 0,004167 0.004167 8) TcXHIiqcCKHfl KOMHTCT 1942 260,92 0,001775 NGAA I]2J 266.48 0,001801 277,59 0,001856 283,15 0,001886 [Continued on next page; key on page 54] -52- 5 1 Table 22 (Continued) n "2) 10,1 p. I'.av A\iipHM3H, IIpCiir.Tbt Alo- 1919 303. 1 13,00 0.03604 Tap;i, 323,15 20,56 0,02182 348,15 33,92 , 0,01 122 „ rid 1949 277,59 6.722 0,001853 007009 QappiiiinoH, Le)iA>K [14J 291,26 10^49 0,001948 0,04499 310,93 15,67 0,002071 0,02945 327,59 22^55 0!002230 0,01941 344,26 31,48 0,002486 0 01250 355,37 38 75 0 002810 0 008765 360,93 42*89 0 003121 0 006792 MiixciiiC, bcccoiiap, .ioy- 1953 297.93 1 1.494 317.28 18J03 Depsc 1 15] 339.48 28.735 347,91 33' 755 355,93 39.139 361 !o2 42,910 361 ,43 43'.274 36 1 56 !3!368 363,13 44.626 27.3, 1 0,001825 1 Joo 235,95 0,001896 298,15 0,001975 313,15 0,002090 323.15 0,002178 333, 1 O.OO23GO 343,15 0,002479 348,15 0.002598 Ri"^ Ti Tir>v 183,15 0,001506 193,15 0 00 1 533 203,15 0 00156'^ 213,15 0 00 1 593 u 001P'>6v/ 1 *i. vj 223.15 U , J \> 233, 1 _ 0 00ifi(jl 243,15 0 00 1 698 253. 15 0 001 739 263,15 0 00 1 783 273,15 — 0,001832 283,15 0 00 1 1^86 293,15 0 001946 303,15 0 0(V^ni 4 313.15 0 002094 17ji,2 0 00 1 498 \TX1 0 00 1 479 8,332 203,2 0 00 1 572 213,15 0.5591 0 00 1 596 0,7337 218,15 0.7190 0 001619 0,5787 223! 1 0,9131 0,001629 0,4632 0*3781 228,15 1.14G 0 00 1 646 233.15 1.420 0 00 1 G6 4 0 3094 238,15 1,744 0 00 1 683 0.2560 243,15 2,122 0 001701 0^2136 70*? 19G5 243,2 0 00 1 0,2141 248,15 2,557 0 001720 0, 1 790 3'059 253! 1 0 00 1 7 1 0,1509 258,15 3.G29 0 00 1 76 0,1284 263.' 15 4!275 0,001781 o!l097 268,15 5,009 0,001808 0,09434 273.15 5.831 0,001831 0,08137 I9G5 273.2 0.001829 0,08038 1967 278,15 6,757 0.001858 0.07042 1966 2C,3,I5 7.7&3 0.001884 0,06109 285,00 8.22 C.001888 0.05767 [Continued on next page] -53- Table 22 (Continued) 2) Abvopu r "K V. 6ap u'. M'iKi: ^oflHOB, naB^lOBHM, TllMpOT 1967 288.15 8,913 0.0OI9I4 0,05319 l'J6G 290,00 9,39 0.001928 — 1967 293.15 10,17 0,001943 0,04651 1966 295.00 10,69 0.001954 0,04427 1967 298.15 11,56 0.001578 0,04080 1966 300,00 12,11 — 0,03889 1967 303.15 13,08 0.002011 0,03597 1965 303.5 — 0.002014 0,03592 1966 305,00 13,65 0.002018 0.03436 1967 308.15 14,72 0,002051 0.03172 1965 309,6 — 0,002054 0.03050 1966 310,00 15.35 0.002061 0,0.':027 1967 313.15 16,51 0.002091 0,02803 1966 315,00 17.18 0,002094 0,02679 1965 31,5,6 — 0,002)09 0.02003 1967 318.15 18 45 0,002135 0,024?2 1966 320,00 19,19 — 0.02356 1965 322,0 — 0,002169 0.02233 1967 32:3.15 20,55 0.002185 0,02195 1966 325,00 21.33 0.002193 0.02084 1967 328,15 22,82 0,002239 0,01935 19G5 328,5 — 0.00V239 0,01904 1966 330,00 23,77 0,002254 — 1967 333.15 25,30 0,002305 0,01708 1965 334.4 — 0.002323 0,01624 1966 335,00 26,24 0,0023.33 0,01629 1907 338.15 27,95 0,002374 0,01491 1966 340,00 28,97 0.002415 0,01422 1965 340.7 — 0,002424 0,01371 1967 343,15 30,80 0,002460 0,01297 19G6 345,00 31,84 0,002518 0,01236 1965 347,0 — 0,002547 0,01155 1967 348,15 0,002574 0,01112 1 960 350,00 35,08 0,002630 0,01054 1965 353.1 0,002722 0.009515 1907 353.15 37.18 0.002734 0,009311 or.r. nn I yoo JJO.UU U,00//OU l),L)Uo/8/ 1905 355,6 0,002815 0,008680 358.0 • 0,002936 0,007825 .359.2 0,00.3006 0,007423 360,4 0,003101 0,006973 361,5 0,003210 0,006565 362,8 0,003389 0,005977 KEY: 1. Authors 9. Marchman, Prengie, Motard [13] 2. Year 10. Harrington, Sage [14] 3. Maass, Wrigt [2] 11. Michels, Wassenaar, Louwerse [15 4. Powell, Giaque [9] 12. Morecroft [16] 5. Voughan, Graves [10] 13. Voytyuk 6. Lamb, Roper [7] 14. Voynov, Pavlovich, Timrot 7. Lu, Newitt, Ruheman [11] 15. Voynov, Pavlovich, Timrot 8. Technical Conmittee NGAA [12] The recommended specific volumes of ethylene vapor coincide to 0.6% with the experimental data of the authors of the present book and diverge up to 3% from Mathias' data [4]. All thermal parameters on the saturation -54- curve of propylene were investigated in [10, 11, 13, 14]. The other works pertain to investigation of the thermal dependences of the saturation pressure of the vapors and specific volume of the liquid. Data on the saturation vapor pressure, obtained by Michels and coworkers [15] , Voughan and Graves [10], Farrington and Sage [14] and Marchman and coworkers [13], agree satisfactorily. The average scattering among them does not exceed 0.2%. The data of Lu, Newitt, Ruheman [11] differ by up to 1% from the data in [10, 13, 14, 15], and the data of Maass and Wrigt [2], by more than 2%. The data of Powell and Giaque [9] agree with the data of Lamb and Roper [7] with an accuracy of 0.5%. The discrepancies between the individual volumes of the liquid, obtained in the works of Maass and Wrigt [2] , NGAA Technical Committee [12] , Farrington and Sage [14] , Morecroft [16], do not exceed 0.2% on the average. The data of Lu, Newitt and Ruheman [11] far from the critical point agree satisfactorily with the data in [10, 13, 14, 15]. The scattering does not exceed 0.5%. Near the critical point, however, the discrepancies between the data of Farrington and Sage reach 0.8%, and Morecroft 's data more than 1%. The data of Voughan and Graves [10] on the specific volumes of the saturated liquid are strongly understated and deviations of the relative data of Farrington and Sage [14] and of the authors of [11, 12, 13, 16] reach up to 7%. The disagreement of the specific volumes of the saturated vapor obtained in [13, 14, 10] averages 0.5% with maximum deviations up to 2%. In terms of the pressure of saturated propylene vapors the recommended values coincide to 0.2% with the data of Marchman [13], Farrington [14], Michels [15], and the authors of this book. Disagreement with the data of Maass [2] reaches 6%, with the data of Voughan and Graves [10] and data of Powell [9], 0.4%. In terms of the specific volume of liquid propylene the data of Voughan and Graves [10] are up to 7% lower than recommended and the data of the other authors coincide with the recommended values with an accuracy of 0.5%. The data of B. V. Voytyuk , Yu. F. Voynov, et al [17] coincide within the same limits. In terms of the specific volumes of propylene vapor the recommended values coincide to 0.6% with the experimental data of Voughan and Graves [10] , Farrington [14] , Marchman [13] and the authors of this book. Heat of Evaporation Experimental works on the heat of evaporation of ethylene and propylene are listed in Table 23. Experimental data on the heat of evaporation near the normal boiling point were found by Egan and Kemp [6] (r = 483.1 ±0.4 kJ/kg at T = 169.45°K) and for propylene by Powell and Giaque [9] (r = 438.0 ± 0.3 kJ/kg at T = = 225.40°K). The heats of evaporation of ethylene and propylene were measured by Clusius and Konnertz [18]. The other works listed in Table 23 contain theoretical data. The discrepancies among the various authors reach 3%. Our heat of evaporation (Table I) was calculated according to the Clapeirone-Clusius equation using the recommended p, v, T-data on the -55- 1 saturation curve. To determine the pressure derivative in terms of temperature for ethylene we used the equation Ig/; - 3U/1 • ll,21392o -IgT— 7713+ 0,01102007 — (-34^ which describes our experimental data on the pressure of the saturated vapors with an accuracy of 0.2%. The pressure derivative in terms of temperature was determined for propylene by the graphoanalytic method. For the 160-250°K temperature range we used the equation Igp =^ 3.94400- ^-3^-1^3 + A, CO; (353 for temperatures above 250°K we used the equation Ig^ - 11,53578 0,00208316. 2.90052. Igr— + r- ---J.^ + A2 (7), (35) where p is pressure, bar; T is temperature, °K. Table 23. List of Works Containing Data on the Heats of Evaporation of Ethylene and Propylene Temperature Authors range, °K Ethylene 1) A\aTnac II ,\p. [5] 1929 128—281 3raH, Ke.Mii \C>] 1937 169 Kjiyanyc, KoiiKcpru, [18] 1946 143—254 Tn.nimeeEi 1 19| 1951 113—273 Kpa.Mcp (20j 1955 123—281 32ropy KJiysnyc, KomicpTu [ 18] 1946 193—288 Oappmir roil, CeiiAK 14j 1949 277—361 Kaiib5:p M ;ij> (22] 1951 225-361 T)i.'iimi:eH |)9] 1951 93—363 .Tc'.ian 1 23 1962 163—363 KEY: 1. Mathias, et al [5] 2. Powell, Giaque [9] Egan, Kemp [6] Voughan, Graves [10] Clusius, Konnertz [18] Clusius, Konnertz [18] Tilicheyev [19] Harrington, Sage [14] Cramer [20] Canjar, et al [22] Zagoruchenko [21] Tilicheyev [19] Lehman [23] -56- s The functions (T) and A^CT) were determined from the recommended saturation pressures according to Table V. The derivatives of the functions A^ (T) and A^CT) were found graphically. Near the normal boiling point of ethylene for T = 169.45°K interpolation of our data yields a heat of evaporation of ethylene r = 481.3 kJ/kg, which coincides with an accuracy of 0.4% with the r obtained experimentally by Egan and Kemp [6]. The experimental data of Clusius and Konnertz [18] coincide with the recommended data at temperatures of 177 and 226°K. At 210°K data [18] exceed the recommended values by 2%. At temperatures above 226°K the deviations change sign and reach 3-4% near the critical point. Our data coincide with an accuracy up to 1% with Zagoruchenko ' data [21] in the entire investigated temperature range. The deviation of the data of M. D. Tilicheyev [19] and Cramer [20] is analogous to those of Clusius and Konnertz [18]. Mathias' data [5] are lower than the recommended, the deviations do not exceed 2-3% and the mean deviation is 1.5%. Near the normal boiling point of propylene for T = 225.40°K interpolation of our data yields a heat of evaporation of propylene r = 437.2 kJ/kg, which coincides with an accuracy of 0.2% with the r obtained experimentally by Powell and Giaque [9]. The experimental data of Clusius and Konnertz [18] are 0.5-1.5% higher than the recommended. In the 210-320°K temperature range the discrepancies between the recommended data and the data of Voughan, Graves [10], M. D. Tilicheyev [19] and Canjar [22] do not exceed 1%. At 350°K our data coincide with the data of Farrington and Sage [14]; Lehman's data [23] fall 1.5% below, and Voughan and Graves' data [10] and those of M. D. Tilicheyev [19], 1.5% above our data. Analysis of the method of calculating our heats of evaporation of ethylene and propylene and the character of the difference of these data from the data of other authors made it possible to evaluate the accuracy of the recommended heats of evaporation of ethylene and propylene as not worse than ±1% in the temperature range from 160°K to the critical point. Critical Parameters The critical parameters of ethylene and propylene were determined in the works listed in Tables 24 and 25. The specific difficulties of experi- mental analysis of the critical parameters are the cause of considerable difference among the results obtained by the various authors. Detailed analysis of the methods and results of investigation of the critical parameters of ethylene and propylene is done in the work of Kobe and Lynn [38]. The critical pressure and temperature can be measured directly. The critical specific volume, however, because of the infinite compressibility of the compound in the critical state and difficulty of reaching thermo- dynamic equilibrium, is determined experimentally with great errors. Various empirical principles [28, 47, 48] yield more accurate results. -57- 1 ) Table 24. Critical Parameters of Ethylene According to Various Authors Authors Year r. p. Cap ^^^-=— Tr Ban Aep Baa.Tbc [24] 1^80 282.35 58.77 0,00278 Cappay [25] 1882 274.C5 44.08 0,00676 Ka^b'-Tc-T [20] 1S82 280.15 — — Abioap [271 1881 283,25 51.67 — KavTbCTei, AlaiHac [25] 1885 285,65 — 0,004762 O.TbiiieBCKiifi i'2rtj 18')5 283,15 51.67 — Bii.a.iapj (30 1897 283.15 — — Kapaoao, y\|.;"i (31) 1912 282,65 51.32 — Maarc, Te.i.^ec !937 282.65 0.004212 ( j2j 50,64 /i'iacc, Poi'-.r (21 1921 283,05 — — Whk HiiTOii;, i'MJuicc [33] 19iS 282.05 — — AiaK Hhtoui h ^ip. [3 i] 1939 233,05 51.17 0.00440 HaJib.if^T, Kc.ncc [35] 1940 282,36 — — Keii [36] 1948 282,40 50.71 rieppii [37] 1950 282.85 51.57 0.00154.5 Ko5c, Jlnnn |3S] 19 ")2 283.05 51.17 0,001405 /iiiii [30] 1956 282.65 50.04 0.004550 Craiun, To.vjc [-lOJ 19-H 282,4 50,60 O.niiHH, Torioc [1 ; 1962 283,1 0.004406 Baprad^TiiK [12j 1963 283,05 50,97 0.004739 Karu i; iS] 1965 283.05 51.17 0.004402 ap. [ ripilHHTbiC 3iia'IeHll.l 283,05 51,0 0.00409 KEY: 1. Van der Waals [24] Mcintosh, et al [34] Sarrau [25] Naldrett, Maass [35] Cailletet [26] Kay [36] Dewar [27] Perry [37] Cailletet, Mathias [28] Kobe, Lynn [38] Olszewski [29] Din [39] Villard [30] Stiel, Thodos [40] Cardoso, Arni [31] Flynn, Thodos [41] Maass, Geddes [32] Vargaftik [42] Maass, Wrigt [2] Katts, et al [43] Mcintosh, Maass [33] Accepted values The p, V, T-data of ethylene and propylene on the saturation curve which we recommend agree satisfactorily with the following critical para- meters: for ethylene T^ = 283.05°K, p^ = 51.0 bar, v^ = 0.00469 mVkg; for propylene T^ = 365.05°K, p^ = 46.4 bar, v^ = 0.00434 mVkg. These data were obtained in the following manner. The critical temperatures were taken from [42] . The critical pressures were found by graphic extrapolation to T^ of the recommended data in terms of the saturation pressure of the vapors. The critical volumes were determined according to the empirical law of averages. According to this rule the graphs of the functions 2 V' -f- V- /(Ig P ) -58- . in the range of temperatures from critical to a temperature 50°K below critical are linear to 0.5%, and the point of intersection of these curves d' + d" I with log -— - log /p'*p" corresponds to the logarithm of the critical ^ density (Figure 4) 2,7 2/ —7 1.S A'' / a 2 / ±J ^ 13 J 1 1.1 / 1 1.0. 1 2.r 2.2 2,3 2.^ 2.S 2,6 IgV^ Figure 4. Critical volumes: 1 -- ethylene; 2 -- propylene; 3 -- water; 4 -- carbon dioxide gas. The mean deviations between the data which we recommend and the data of other authors are: for pressure for ethylene 0.2, for propylene 0.9%, for specific volumes for ethylene 3.8, and for propylene 0.07%. -59- 1 Table 25. Critical Parameters of Propylene According to Various Authors Year T, "K D, tap e. M*lia 1— " — Ha,ie/i ,\\apMMan 11 Ap- (13] 1949 364,91 46,21 0.004539 OappHHrTOH, Cei(.i/K |14| 1949 364,82 46.06 0,004335 rieppii [37] 1950 365,45 45.60 Kooe, J\mn (38| 1953 364,95 46,20 0,004292 Cran.!, Toaoc (40) 1961 365,1 46.00 «lJ."inHii, Toaoc [41) 1962 306,0 0.004292 Bapra^jTiiK [42] 1963 365,05 46,00 0,004292 Karn II ;ip. (43) 1965 365.03 45.99 0,004430 npuHHTbje 3fiaMeiifia 365,05 46.4 0.00434 1 KEY: 1. Nadeydine [44] Harrington , Sage [14] Siebert, Burell [45] Perry [37] Maass, Wrigt [2] Kobe, Lynn [38] Winkler, Maass [46] Stiel, Thodos [40] Voughan, Graves [10] Flynn, Thodos [41] Zayders [10] Vargaftik [42] Lu, Newitt [11] Katts, et al [43] Marchman, et al [13] Accepted values -60- CHAPTER IV. THERMODYNAMIC FUNCTIONS OF ETHYLENE AND PROPYLENE IN PERFECT-GAS STATE Review of Data The perfect-gas functions of ethylene and propylene presented in various sources were obtained on the basis of experimental measurements of the heat capacity of these compounds at atmospheric pressure or by means of calculation on the basis of spectroscopic data. The primary sources, which contain either experimental data on heat capacity or the results of original calculation of the perfect-gas functions according to spectroscopic data for ethylene and propylene, are listed in Table 26. In the range of temperatures above 273° K the most reliable are considered the functions derived on the basis of spectroscopic data. At lower temperatures the only source of information concerning the perfect-gas functions of ethylene and propylene are experimental data on heat capacity. The works of House [1] , Eucken and Parts [2] , Burcik and coauthors [3] , Egan and Kemp [4] pertain to experimental analysis of the heat capacity of ethylene at low pressures. Heuse [1] determined the heat capacity of ethylene at atmospheric pressure in the 182-291°K temperature range by the flow method. The data of Eucken and Parts [2] were obtained by adiabatic expansion in accordance with the Lummer-Pringsteim method. Burcik and coworkers [3] determined the heat capacity C of ethylene at temperatures of 270.7, 300.0 and 320. 7° K by the same method. The essence of the method consists in determination of the change of temperature and pressure during adiabatic expansion of the gas. The heat capacity in the perfect-gas state is calculated according to the measured values using the known thermodynamic relations according to the equation [H=in; k=f; kp=cr] (37) -61- . . . . , I where p. , T. are the initial pressure and temperature; p-, are the m " ''t t final pressure and temperature; is the second Virial coefficient according to Keyes [17] Burcik and coworkers [3] analyzed and compared the results of all the listed works. Approximation of the experimental data is done in the very same work. The deviation of the experimental data from the dependence expressed by the equation I 10"' 10-' 10"^ Cp = 9,638 - 3, 109. 7 i- 1.551 • 7-2-1,426 • (-jg^ ; where T is temperature in °K, C° is heat capacity in cal/ (mole'deg) in j the 200-300°K temperature range, does not exceed 1%. i Eucken and Parts [2] determined the heat capacities at T equal to j 178,6, 192.8, 210.8, 231.4, 250.9, 272.1, 293.5 and 464. 0°K, equal i respectively to 8.293, 8.450, 8.86"0, 9.001, 9.332, 9.809, 10.257 and \ 14.161 cal/ (mole'deg) . Burcik and coworkers [3] determined the heat \ for T equal to 270.7, 300.0 and 320. 7°K, equal capacities respectively to ! 9.74, 10.39 and 10.99 cal/ (mole'deg) and House [1] determined the heat | capacities for T equal to 182.2, 205.2, 237.2 and 291.2, equal respectively [ to 8.28, 8.54, 9.02 and 10.14. ! ! One of the first studies on calculation of the thermodynamic functions' according to spectroscopic data was Kassel's work [9] -, in which is described j a method of calculating the entropy for multiatomic gases, and also the free | energy of ethylene in the 300-3, 000°K temperature range. The spectroscopic i data of Mecke [18] were analyzed in the work. The entropy of ethylene at the critical point T = 169.40°K was calculated by Egan and Kemp [4] on the basis of calorimetric measurements and was found to be = 47.36 cal/(mole*deg) . The entropies at the two temperatures were also calculated in this work on the basis of vibra- tion frequencies: S° = 47.35 and S°^gg = 52.47 cal/ (mole 'deg) Later on Thompson [10] , using the data of Conn and Sutherland [20] determined the heat capacity, entropy and enthalpy change of ethylene in the perfect-gas state. These data were subsequently refined by Kilpatrick and Pitzer [13] The thermodynamic functions of ethylene and propylene, calculated on the basis of spectroscopic data of Callaway and Barker [21] , are given in [13] . The heat capacity, entropy and enthalpy change determined by Kilpatrick and Pitzer [13] were used as the basis of tables on the caloric properties of ethylene and propylene presented in [22] Later on L. V. Curvich and coworkers [12] determined the new entropy and enthalpy change of ethylene in connection with more accurate spectro- scopic data, presented in [23, 24, 25]. -62- ) Table 26 2) 1 (I'M'JitUH.IMH'lCCKHr JjyHKUllH 1) _3) 6) HiiTe)ina^ TeMne- AUTOPU /iiiKOiin- 4) 5) pnxyp 7'. °K HHH ntx)niweHa Xefiae (1| 1919 Cp (3KCfICpMMeHf 182—291 193'j 9iiK0H II rinpTc [2] To -AiL- 8) 178—464 BypciiK 11 cuaDTopbi |3| !S1! 270—321 ' 9) 3raii H Ks-,n 193/ / |1| 1 09.4—298.1 ncpHMl'llT, paCMCT) KHc;>ii{oucKiiri, Pai'ic [5] 1910 (SKCIiepMM'.'HT) 272—366 p KHcinKOBCKin'i, /laxan, 1940 To >i riiii TOMITCOH flOl 1941 291 — 1500 (pacMci) 11) rpaw]'op,i 1 1 ! 1 939 1 S° (pac'ier) H) 298,15 rypnii>( 11 co.iHioDij [12| I9!,2 293—6000 (pacHCT) 11") KHJinarpnK, IlHTuep 13] 194G ; PaCMCT 11) 298—1500 fr-lCM'JT) 11 J CTajw (I (Maii({)n.i,i 1943 C^, (pacMfT) 11) To H .3 y , .0 ByKa.noBHM >< coaoTopu 1953 C- S;.H„^~fI, 273—1473 (161 (prc':::r) H) (pacHf-T) 11) KEY: 1. Authors 2. Year of publication Heuse [1] 3. Thermodynamic functions Eucken and Parts [2] 4. Ethylene Burcik, et al [3] 5. Propylene Eg an and Kemp [4] 6. Temperature range T, °K Kistiakowsky and Rice [5] 7. C° (experiment) Kistiakowsky, et al [6] 8 . Same Telfair [7] 9. (experiment, calculation) Powell and Giaque [8] 10. Calculation of change of Kassel [9] internal energy Thompson [10] 11. (calculation) Crawford [11] 12. Empirical equation for Gurvich, et al [12] Kilpatzick, Pitzer [13] Stull, Mayfield [14] Spenser [15] Vukalovich, et al [16] Deviations of the data from the values presented in [13] do not exceed 0.4%. Interpolation equations are also presented in [12] for determining the entropy and enthalpy change in the 293-1, 600° K temperature range. The -63- . , perfect-gas functions of ethylene, calculated on the basis of spectroscopic data, are presented in Tables 27, 28, and 29. Experimental data on the caloric properties of propylene are found in works by Kistiakowsky and Rice [5], Powell and Giaque [8], Kistiakowsky Lachar and Ransom [6] , and Telfair [7] Kistiakowsky and Rice [5] analyzed the heat capacity of propylene et al at 272-367°K by the Lummer-Pringsteim method. Kistiakowskiy , [6] determined the heat capacity of propylene at temperatures below 273°K by the relative heated wire method. The heat capacity of propylene according to Telfair [7] was calcu- lated on the basis of data on the speed of sound in propylene. Telfair's data agree satisfactorily with the experimental heat capacity values determined by Kistiakowsky, et al [5, 6]. The deviations of the experimental data from, the smooth curve do not exceed 0.5%. Table 27. Heat Capacity of Ethylene and Propylene According to Various Authors 1) c°. KaJl/(MC.l' •jix:o) no aaiiHbiM 2) - Ki: 'ini.rpHK.'.. nnTr(epa [13] ii Poi 3) T. "K '/riM.T.. . AiarKt/ii.iaa [14]. "iO!.;ncoiia [10] ClIHH 1:- 1 1 5) 4) 5) 4) npon:<.ieii 3TH.ieii 250 9,53 13,76 29i,!ti 10,23 298. IG 10,41 15,27 10,45 300 10.45 15,34 10.48 15,43 10.50 350 11.56 17,24 1 1 ,67 400 12.90 19,10 12,69 19,11 12,95 450 13,81 20,93 14,11 500 15.1*j 22,62 14,89 22,68 15,21 550 16,22 600 17.10 25,70 16.87 25.83 17,15 650 18,01 700 18.76 2»,37 18,61 28,55 18,30 800 20, -20 30,58 19,96 30.92 20,20 900 21,10 32.70 21,45 32,97 21,50 1000 22,57 3-!.46 22,62 34.75 22,60 lICO 23.5-t 35,99 23.63 36,29 23,60 1200 24.39 37,32 24,51 37,63 24,40 1300 25,14 38,49 25,26 3S,79 25,20 1400 25.79 39,51 25,92 39,79 25,80 1500 26,3d 40.39 26,50 40.60 26.40 KEY: 1. C^, cal/(mole-deg) according to data 4. Ethylene P . . Propylene r -, , r^-^-, 5. 2. Kilpatrick, Pitzer [13] and Rossini [22] 3. Stull, Mayfield [14], Thompson [10] -64- 6 Table 28. Entropy of Ethylene and Propylene in Perfect-Gas State According to Various Authors II', TT S , K.IA/[MUA'- -^I'llO) .I'lmiUM ii I'oc(.mh» iicoi i [lOj. ry;>F,ii>ia ii ooasTopoB 2XKJinaTpHi;a. I'MTUepj (2?! , gypM [12] 0 1/ / , K ^ 5) 4) J Sth.ich L'Ol.lG — 2'JJ,)0 ^9 d. 1 9 298, J b 52,45 C-3,80 300 52,51 63,90 350 400 55,89 68,86 00, /OO 450 57,48 50U 58,98 73,47 59,05 58,841 5[>0 60,52 600 61,92 77.82 61,97 61,740 G50 63,38 700 G4,G.S 62,04 64,73 64,473 too 67,2.> 85,98 67,35 67,050 900 69,74 S9,72 09.71 69,487 ICOO 72,0'j 9X26 72,13 71,792 1)00 74,2') 96,61 74,34 73,978 1200 76,0} 99,80 76,33 76.054 1300 78,32 102,84 78,40 78,028 MOO S0,21 105,98 80„30 79,908 1500 82,01 108,48 82,11 81,702 KEY: 1. S°, cal/ (mole -deg) according to data 4. Ethylene 2. Kilpatrick, Pitzer [13], Rossini [22] 5. Propylene 3. Thompson [10], Gurvich, et al [12] Table 29. Enthalpy of Ethylene and Propylene in Perfect-Gas State According to Various Authors o 1) ;/ - - - .'/,,, K,tA:'M 'Ab 2yn^naTprK;i. I'MTL'^r-na [I3j i; I-.X.-HIIH (L'l;'! 3}o. isa T. °K H coabropOB [12] 4) 5) 4) 3 in.'; OH I Ico;;h.im: 3tjI.tch 291,16 2456 29:^ 1 2465 298,16 2525 3237 2527 2516 300 2544 3265 2548 350 3100 400 3711 4990 8720 .3684 450 4100 500 5117 7076 51.30 5067 550 5920 600 6732 9492 6750 6661 650 7630 '/OO 8527 12200 8550 8436 800 10180 15150 10500 10367 900 12560 LS320 12500 12438 1000 1476') 21 ',90 14800 14626 1100 17070 2:2i0 171 10 16920 1200 19470 2 •iSO 19450 19306 1300 219.50 32760 21970 21774 1400 24490 30570 24J20 24311 1500 27100 40570 27160 26912 KEY: 1 . H° - H° cal/mole according to data 2-5. Same as Table 28 -65- . Tables of the heat capacity of propylene, tabulated on the basis of processing of experimental and theoretical data, are also presented in Lehman's work [26] for the 220-1, 270°K temperature range. Experimental data on the heat capacity of propylene in the perfect-gas state are given in Table 30. Table 30. Experimental Data on Heat Capacity of Propylene in Perfect-Gas State T) 1) Ka.ili U li Cp, KaA/(jUOAb X r. "K r. "K X epad) X cpjd) X zpad) 2) Tejib(f)e)) |7| >X'!CTnKOBCKnri, vlnxap, PainoM [6]l 4) Paiic [5] 148,1 10,63 272,29 14.36 270 12,30 f 280 12,70 148,3 10.64 299.33 15.47 290 i3.o:» 157,3 10,86 333,86 16.74 300 13,48 157,6 10,86 367.11 17,93 310 13,36 158.0 10,87 320 14,34 212.3 12,46 330 14,62 212,9 12.50 340 14,99 219,9 12.68 350 15,36 220,2 12,70 360 15,73 223,4 12,82 380 16,45 256,4 13,90 390 16,81 258.3 13,97 400 17.17 258.4 13,98 410 17,53 259,0 14,04 420 17,89 291.1 15,16, 430 18,24 440 18,59 450 18,94 460 19,29 470 19,63 480 19,98 490 20,32 500 20,33 510 21,00 KEY: 1. cal/ (mole-deg) 3. Kistiakowsky , Lachar, Ransom [6] 2. Telfair [7] 4. Rice [5] The entropy of propylene at the boiling point T = 225,39°K was deter- mined directly by caloric measurements by Powell and Giaque [8] and was found to be 59.93 cal/ (mole'deg) . This same researcher calculated the entropy of propylene on the basis of spectroscopic data for two temperatures ~ ^"^ " ^'^•lO cal/ (mole'deg) . Crawford and ^225 35 ^^'^ ^298 coworkers [11], using the corrected vibration frequencies, obtained the ~ following entropy for propylene at the boiling point: S"^^ ^5 59.87 cal/ (mole'deg) Of great importance in addition to the cited works are calculations on the basis of spectroscopic data by M. P. Vukalovich and coworkers [16], Stull and Mayfield [14] , in which the thermodynamic functions of a large number of gases, including ethylene and propylene, are determined. The comparisons of the results with existing literature data on the perfect-gas temperature of ethylene [2, 3, 10] made by Stull and Mayfield revealed that -66- the maximum deviations are, respectively, 0.7, 0.9 and 2.1%. The theoretical heat capacities of propylene were compared with the data in [5, 7]. The maximum deviations here are, respectively, 0.8 and 0.3%. M. P. Vukalovich and coworkers [16] give the perfect-gas heat capacities, enthalpies and entropies of ethylene and propylene at 273-1 ,473''K. The perfect-gas functions of ethylene and propylene, deter- mined by various authors on the basis of spectroscopic data, are presented in Tables 27, 28, 29. Recommended Isobaric Heat Capacity, Entropy and Enthalpy of Ethylene and Propylene in Perfect-Gas State At the present time the most reliable data on the entropy and enthalpy change of ethylene in the perfect-gas state are those of L. V. Gurvich and coworkers [12] . The entropy and enthalpy change of ethylene were calculated in the same work using current data on the ground frequencies and rotation constants of the ethylene molecule. Also given there are interpolation equations for calculating the entropy and enthalpy change of ethylene in the 293-6, 000°K temperature range. If the heat capacity of ethylene is calculated by converting the interpolation equation for entropy, the results obtained at temperatures above 700°K agree satisfactorily with M. P. Vukalovich' s data [16] and those of Kilpatrick [13]. The discrepancy does not exceed 0.5%. At temperatures of 298-500°K, however, the heat capacity of ethylene, calcu- lated according to the converted equation, differs from the heat capacity given in [13, 16] by more than 5%. Considering that the heat capacities of ethylene were computed directly in [13, 16] on the basis of spectroscopic data, these data were preferred for tabulation of the perfect-gas heat capacities in the 280-500°K temperature range (Tables II, VI). Data [13, 16] at these temperatures are quite satisfactorily transmitted (±0.4%) by the Spenser interpolation equation [15] presented below: Cl a -i- bT + -i- dT\ (39) where a = 1.003, b = 36.948*10"^ c = -193,81-10"^, d = 4.019*10"^ Using the known thermodynamic relations we find from equation (39) the expressions for the entropy of ethylene and for enthalpy change in the perfect-gas state: -h Si. (40) o o /,ra bfl cTi dXi c7'3 rfT" f (41) -67- The thermodynamic functions of ethylene, computed through equations (40) and (41) for the 280-500°K temperatures, differ from the data of L. V. Gurvich [12] in the case of entropy by 0.4%, and in the case of enthalpy by 0.7% (see Tables 28 and 29). The most recent works in which the thermodynamic functions of propylene are analyzed are those of M. P. Vukalovich and coworkers [16] and of Kilpatrick [13]. The heat capacity of propylene, computed from an equation of the type (39) in the 280-500°K temperature range for a = 0.790, b = 56.372, c = -281.07-10"^ d = 3.427'10"^ differs from the data of M. P. Vukalovich, et al [16] by not more than 0.5%. The entropy and enthalpy change obtained from equations of the type (40) and (41) , also agree satisfactorily with the data of M. P. Vukalovich and coworkers [16]. The deviations do not exceed 0.4%. The thermodynamic functions in the perfect-gas state, calculated according to equations (39), (40) and (41), were used by us for compiling Tables II and VI of the thermodynamic properties of ethylene and propylene at temperatures of 280-500°K. Spectroscopic data do not exist for temperatures below 273°K, and the only source of information about the perfect-gas functions of ethylene and propylene are the results of experimental measurements of the heat capacity or speed of sound in these gases at small pressures. The accuracy of such data is considerably less than that of the data calculated on the basis of spectroscopic data. In the 200-280°K range equation (41) of Burcik and coworkers [3] is recommended; for propylene (T = 148-291°K) the experimental data of Kistiakowsky and coworkers [6], presented in Table 30, are recommended. -68- CHAPTER V. SPEED OF SOUND AND HEAT CAPACITIES OF GASEOUS ETHYLENE AND PROPYLENE Review of Data on Heat Capacities of Gaseous Ethylene and Propylene The isochoric heat capacity of ethylene and propylene in a comparatively narrow temperature range and pressure range was measured by Nevers and Martin [1], Pall, Broughton and Maass [2]. Nevers and Martin [1] did their study in the 340-420°K temperature range for reduced densities oo equal to 0.218-0.726, in order to check the suitability of the Benedict-Webb-Rubin [3] and Martin-Hou [4] equations of state for calculating the isochoric heat capacity of propylene in the stated range of states. The investigated specimen of propylene was 99.0 mole % pure; the heat capacity was measured in a constant-volume adiabatic calorimeter of original design with a blower (mixer) , resistance heater and thermometer installed inside the calorimeter. The calorimeter was cali- brated for filling with propylene at low pressure. The perfect-gas heat capacity of propylene C^ was determined by the Kilpatrick-Pitzer method, and the small pressure correction factor was calculated on the basis of the Martin-Hou thermal equation of state. The heat capacity of propylene was 7% of the total heat capacity of the reactor and contents; the pressure correction factor AC was 0.1% of this value. The error in determination Vo of the calorimeter constant, according to the authors, did not exceed ±0.8%, and the scattering of individual measurements did not exceed ±0.4%. The calorimeter was filled from a light-weight steel container, which was weighed before and after filling of the apparatus. The density of the investigated compound in the calorimeter was determined with an error not exceeding ±0.3%. The temperature drift of the calorimeter, occurring during operation of the mixture and with the resistance thermometer turned on, a value of -0.002 deg/min, was taken into account in the processing of the results of the calorimetric experiment. The error of the isochoric heat capacity obtained for propylene as a function of the density of the investigated compound was ±1.1-3.2%. The experimental data obtained in [1] are presented in Table 31, The authors found [1] as a result of comparing the experimental data -69- . on isochoric heat capacity with the theoretical according to the above- described equations that the discrepancy in the investigated range of the compounds does not exceed 6.7% of the pressure correction factor AC^ for the perfect-gas heat capacity, but the isotherms of heat capacity in heat capacity-density coordinates haVe a varying qualitative path. The iso- therms plotted on the basis of experimental data have a positive second pressure derivative in the low pressure range and in the entire density range Table 31. Experimental Data [1] IK 0, e/cM' p. ejcj>i' I. °c p. 2/ cm' t. "C e-spad e-epad 0,04814 G7.I5 0,3903 0,09228 84,64 0,4380 0,1404 93,17 0,4842 82,14 0,3952 92,91 0,4337 99,58 0,4710 98.45 0,4047 103,71 0.4341 106,68 0,4659 111,62 0,4!59 115.36 0.4385 112.47 0.463S 123.90 G,4226 125,32 0.4439 140,21 0.4357 0.07219 75,09 0.41f30 0,1102 90,71 0,4486 0,1609 94.92 0.4991 85,2! 0,4163 95,75 0.4460 99.51 0,4840 99,93 0,4208 101.28 0,443S 104.51 0,4761 117,06 0,4:S05 107.59 0,4439 103.74 0.4768 133.72 0,44 12 113,37 0,4438 108.41 0.4704 145.92 0.4485 KEY: 1. C^, cal/Cg-deg) The theoretical data on the caloric properties and thermodynamic diagrams of ethylene and propylene at high pressures, presented in [5-9], were obtained on the basis of experimental p, v, T-data of Michels and coworkers [10, 11], or on the basis of thermal equations of state whose derivation was based on these p, v, T-data. Calculation of the isobaric and isochoric heat capacities and their ratio on the basis of the results of analysis of thermal properties necessitates, as we know, determination of the second derivatives of the thermal functions, which leads to considerable loss of accuracy, particularly in the near-critical and supercritical regions of state. As a rule, the errors of such calculations exceed by more than one order of magnitude the errors of the initial thermal data. In the range of state parameters where the heat capacities peak, the various equations of state, which describe the experimental p, v, T-data with the same accuracy, lead to heat capacities that differ by 30-60%. Calculation using the experimental data on the speed of sound occupies a special place, among the indirect methods of determining the heat capacity of gases. The use of p, v, T-data and the speed of sound, which are presently the most accurate measured properties of matter, in calculations of heat capacities C and C , their ratio k and adiabatics index k , makes it ^ p V V -70- possible to find the stated parameters with an accuracy much better than that of calculation simply on the basis of p, v, T-data. Review of Experimental Data on Speed of Sound in Gaseous Ethylene and Propylene Works pertaining to experimental analysis of the speed of sound in gaseous ethylene and propylene are listed in Table 32. Herget measured the speed of sound by acoustical interferometry on the frequencies 274.1 and 598 kHz at pressures of 35-70 bar on the 9.7, 18.7 and 23°C isotherms. The investigated ethylene was 99.7% pure. The pressure was measured with a class 0.5 piston manometer. The results of the measurements are presented in Table 33. The experimental data, in Herget 's opinion, have an accuracy of ±0.05% in the entire range of investigation, with the exception of range of minimum speed of sound on the 9.7°C isotherm, where the error of the data is estimated at ±3.5%. The information in the work is not enough for analysis of the accuracy of the speeds of sound presented. Graphic processing of the measurement results, however, shows that the scattering of the experimental points exceeds the stated error and averages ±0.2%. Table 32 pna.n KCC^eAOBaiiiibix 3 k..pMa npeflCT.nu;ieiiHH pfsyjibTaroB AriTopu 1 ) TenncpaTyp ii flaiuiciimi ncc.^e.1onaHH^l 4) 3TH;ieH Xcprer [12) ( = 9.7—23° C; 6)Ta{3;THUbi 3KcncpiiMenTajibHbix 3Ha- p — 33— 70 Cap =- nap6pyK H Pii'iapAcon (13) t 7— 1S.7" C 7) Ma.no(}x)pMaTiiL.iri rpa(pnK p 1 — 100 Gap M'XwpcH H Hypii 114) t =--=: 25—50^C 7)To >Ke p 30—1000 6ap Co'ijareHKO, /Iper^.anc T - 190—470^ K 6)TaG.iimbi SKcncpHMeHTa.ibnux sna- (15, 16J p 1- 100 6ap MCHHfl 5) nponii;ieH Te;ih4>eHp [17] /=--L'—217'^C; 8)Ta6;iHUbi TcnJiocMKocTH, paccMii- p -= I 6ap TaHHue no CKopocm snyKa &).W.rcnKO, JXpQryjinc T = 190—470' K; 6)TaOjiHUbi iKciiepiiMeHTa.abnbix 3Ha- [15. 181 p = 0.1 — 100 Gap KEY: 1. Authors 3. Form of presentation of results Herget [12] 4. Ethylene Parbrook, Richardson [13] 5. Propylene McHirsi, Houry [14] 6. Tables of experimental values Soldatenko, Dregulyas [15, 16] 7. Small-scale graphs Telfair [17] 8. Tables of heat capacity, Soldatenko, Dregulyas [15, 18] calculated by speed of sound , 2. Range of investigated temperatures and pressures -71- 1 1 Table 33 p. (>up w, MiceK p. 6ap w, M/ceK P. (>cip ttl, M/ceK 9,7" C t — 18.7° C t 23,0° C 35.73 265.3 36, io 276.8 36,2) 281,6 43,03 247.6 44,23 261,5 38.17 278,6 45,8 i 239.1 51,38 247.2 39,71 276,1 49,S1 222.0 55,73 236.8 41.1 273.6 51,32 202.8 58.96 230.6 4 1 .88 272.1 51,43 193,0 59.59 229,6 42,47 271,1 1 51. '55 I(')0.0 60.4 228,7 45.19 266,4 5!. 73 162,0 61,16 229,3 48.06 261,5 51,73 165,0 61,94 232,4 48,2! 261,1 51.94 196,2 62 25 234,1 50,34 257.4 52.35 2:>5,0 63 04 240,4 52.52 253,1 53.G5 263,0 63.73 246,5 53,50 256,1 54.11 280,8 64.46 254.8 54.90 249,0 54,08 290,0 66.48 275,5 57.73 244,2 55.31 298,6 68.68 300.3 60,28 240,7 5G,03 309,0 69,38 306.5 61.86 238.4 Oil r 0/,. 2 ol o,U /U.IO 31 1 ,5 62,48 237.2 59,25 348,5 71,31 322,8 63.71 237.7 71.48 325.6 65,23 240,3 72.72 65.8(i 242,1 67,05 246,3 67.66 249.9 Parbrook and Richardson [13] studied the speed of sound in ethylene by means of interferometry with a mobile reflector on frequencies 0.5 and 2 MHz. The measurements were done at 7°C in the 25-50 bar pressure range and at pressures from atmospheric to 100 bar on 18.7°C isotherm, on which the dispersion at atmospheric pressure was observed. The accuracy of the data obtained by the authors is not stated, and the published data do not permit evaluation of the possible error, McHirsi and Noury [14] measured the speed of sound in the 30 to 1,000 bar pressure range at 25 and 50°C by the light diffraction method on an ultrasonic network at 865, 2,590 and 4,320 kHz. According to the authors tiiere was no dispersion of the speed of sound and the maximum measurement error was ±1%. The results of the investigations [13, 14] are presented in the form of small-scale graphs, which hampers their use in the calculation of the thermodynamic functions. Yu. A. Soldatenko and E. K. Dregulyas [15, 16, 18] measured the speed of sound in ethylene and propylene by acoustic interferometry with variable emitter-reflector distance, ensuring high accuracy of measurements in the investigated range of state parameters. -72- Table 34. Speed of Sound in Ethylene According to Data of Yu. A. Soldatenko and E. K. Dregulyas 1 p. Cop W, MjCtf. P. Cap W. MlCCK p. 6ap w, m/cck 7 = 283,32" K T- 292,89° K 7= 193.15° K 3,95 319,3 58,57 233,3 0.61 274,8 4,68 317,9 59,64 232,3 0,88 274,0 10,59 309,5 60,82 230,7 1,01 273,3 10,82 308,9 61,16 230,9 1,75 269,0 12,88 306.2 61,56 231,4 1,95 267,8 16.31 300.5 62,53 233,4 2,76 264,4 23.06 289.2 63,57 2.38,1 2,97 262.8 29,55 278.4 63,65 240,0 3,35 262.3 35,03 267,5 65,76 258,3 3,40 261,1 39,05 257,8 68,57 286.2 39,32 258,4 70,71 307,4 r-r 213,15° K 43,22 248,7 73,36 329,0 1,49 284,2 46,11 239,6 79.63 371,4 5.22 273,4 47,49 235,1 90.24 427,2 6,30 270,3 49,44 226,5 99.39 469,2 49.85 223.2 T- 233,15° K 303,1 5»K 50,44 219,8 1,48 295,0 .S0,50 217,9 1,66 333,4 2,40 291,8 51,6i 205,6 2,76 331,9 5,22 285, [Continued on next page] -73- 2 Table 34 (Continued) r - 429.53'^ K T - 308,G7^K r-= 363.15" K 19,73 381.1 82,83 282.8 64.55 322,1 34,83 375,9 86,37 300,0 81.90 316.8 59,45 370,5 90,53 326.0 99,21 317,8 78,86 368,6 95,24 343.0 T = 385.84° K 95,73 368,1 r = 343.15' K T = 448,62° K 1,00 370.5 4,25 392,9 1,89 351.6 3,84 366,9 10,71 391,2 3,45 349,6 6,59 36(;,1 15,81 389,5 3,65 34£,9 13,32 362.7 388,3 5,40 347,6 23,75 358,0 24,54 385,4 8,84 315,2 41,60 349,5 37,48 50.43 383,8 9,82 344.7 57,98 3-12,6 381,9 23,95 332,6 79,99 337,7 59,74 75,68 380,3 39.7< 320,4 87,54 330,6 76,90 379,5 54,35 309,1 93,77 336,8 69,64 30 i, 83,67 378,9 99.12 338,2 80,29 298,9 88,97 379,3 88,33 300.4 98,02 378,9 r= 407.54° K 98,33 305,7 T 473,15° K 0,73 380.0 rr= 363,15= K 1,21 403.0 1.20 378.2 362,5 1.79 1,03 4,33 37h.3 403,5 1,98 359,5 11,49 373.3 16.41 400,6 26.99 368.0 2.86 357.9 27,00 399,1 43.46 362,0 4,63 356,5 39,84 63.57 356,5 397,3 6,88 355.9 84.06 353,4 52,97 395,5 12.77 352,0 98,28 352.9 68,38 394,5 18,35 349,4 T 429.53° K 84.72 393,7 27.37 343,8 0.96 385,6 94,07 393,5 44,44 333.0 1.52 385,0 98,09 393.7 S.6I 384,0 The purity of the investigated compounds was determined by chromato- graphic analysis. The ethylene specimen contained 99.97% of the basic component and 0.03% ethane; the propylene was 99.50% pure and the propane and ethane impurities amounted to 0.3 and 0.2%, respectively. The compound was not subjected to additional purification. The experimental investigations of the speed of sound in ethylene encompass the 193 to 473°K temperature and 1 to 100 bar pressure ranges. In this range of parameters, including the subcritical, near-critical and supercritical states of ethylene, 273 experimental points were obtained, measured on 18 isotherms and the liquid-vapor phase equilibrium line. The subcritical region of state was investigated on the saturation line and six isotherms, on which the speed of sound was measured at temperatures of 193 . 15-273 . 15°K and from atmospheric pressure to the vapor saturation pressure at the experimental temperature. The near-critical and supercritical regions of state were investi- gated on 12 isotherms in the 1-100 bar pressure range. The rather large -74- . number of points on each isotherm and the use of the variable pressure step for the measurement made it possible to determine reliably the coordinates of the characteristic points of the speed of sound isotherms (the position of the minimum and points of inflection) The results of the measurements of the speed of sound on the iso- therms are presented in Table 34 and Figure 5. The maximum scattering of the experimental points relative to the smooth curve does not exceed ±0.4 m/sec. Usually not more than 1-2 points with such scattering appeared on an isotherm. The mean scattering of the points is ±0.2 m/sec. 0 W 20 30 ^0 so 60 70 60 90 pjap Figure 5. Speed of sound in ethylene as function of temperature and pressure according to data: 1 -- authors of present book; 2 -- Herget [12]. The speed of sound on the liquid-vapor phase equilibrium line was investigated at 10 experimental points from temperatures of 193.15 to 282.15°K. The results of the measurements on the liquid-vapor phase equilibrium line are presented in Figure 5 and in Table 35. -75- Table 35. Experimental Speeds of Sound in Ethylene on Saturation Curve According to Soldatenko and Dregulyas 1 1 r. °K p. 6ap w, M/ceK T. °K p. 6ap w, M/ceK 193,15 3,40 261,1 263.15 32,38 263,3 203,15 5,12 264,2 273,15 40,91 224,8 223,15 10,61 262,7 277,29 44,98 218,0 243,15 19,29 254,0 280,53 48,22 210.5 253,15 ' 25,30 246,4 282.15 50,13 203,2 Yu. A. Soldatenko and E. K. Dregulyas measured speed of sound at several points of the isotherms investigated by Herget for the purpose of direct comparison of the measurement results with Herget's data [12]. The results of the measurements are presented in Table 36. ' Table 36 1 P, (jap w, M/ceK p, 6ap w, m/cck p. dap w, M/ceK j t= 18.7° C / = 23''C 51,21 200,2 60.28 229,6 44,64 266,9 18,7° C 62,28 235,9 52,92 252,0 31.79 283,4 63.42 246,0 65,18 241,3 37,77 273,0 65,63 269,9 65,63 241,9 43.66 262,2 69.55 310,2 67,77 251.1 55,36 237.0 72,52 334,3 Considering that the compared measurements were done in the ranges of temperatures and pressures close to critical, the discrepancies can be attributed to the different purities of the investigated specimens of ethylene or to the presence of systematic error in temperature measurements. This is confirmed by the fact that the least deviations take place at the point on the 23°C isotherm farthest from the critical point, and the discrepancies on the 18.7°C isotherm reach maximum values (1%) in the vicinity of the minimum speed of sound as pressure increases, and diminish with a further increase of pressure. Such character of deviations can be explained by the different purities of the compounds used for the experi- ments . The results of measurements [13, 14] coincide within the limits of accuracy of their graphic representation with the data of Yu. A. Soldatenko and E. K. Dregulyas [15, 16]. Telfair [17] measured the speed of sound in gaseous propylene at atmospheric pressure and at temperatures of 273-490°K. The experimental speeds of sound were not given in the publication. -76- . . Yu. A. Soldatenko and E. K. Dregulyas also did measurements in propylene [15, 18] in the 193-473°K temperature and 0.1-100 bar pressure ranges The speed of sound was' measured on 19 isotherms and on the liquid- vapor phase equilibrium curve. The results of the measurements are shown in Figure 6 and in Tables 37 and 38. The experimental points have a scattering relative to the smooth curves of ±0.2 m/sec. Figure 6. Speed of sound in propylene as function of temperature and pressure according to Soldatenko and Dregulyas Table 37. Speed of Sound in Propylene on Saturation Curve According to Soldatenko and Dregulyas T, *K p. Cap W, MlCtK r, °K p. Cap W, HiCtK 193,15 0.164 214,1 353,15 37,47 172,9 233.15 1,41 225.3 300,15 42,42 161.8 313.15 16,46 212,4 363,15 44,84 153,4 333,15 25,38 196,4 363.15 44.88 153,1 -77- I The maximum absolute error of measurement of the speed of sound in ethylene and propylene, calculated by the generally accepted method from the theoretical equation, is ±0.5 m/sec. The speeds of sound, as we know, can be used for calculating the thermodynamic functions only if they do not depend on frequency. In this connection discussion of the measurement results must start with definition of the boundaries of the region of dispersion of the speed of sound in the investigated compound. Table 38. Speed of Sound in Propylene According to Soldatenko and Dregulyas 1 6ap 7" 298,15= 365,15° T — 193,15 = K r= K 1,00 257.5 1,01 283,4 0,081 215,0 1,39 256,3 2,48 280,5 0,092 214,8 2,37 253,2 4,68 276.7 0,164 214,4 5,71 243,8 13.86 259,4 T = 213,15'^K 6,00 242,2 26,80 231,7 9,24 230.7 33.07 212,7 yjn ,zoio'Xi 223,1 40,14 189,8 222,8 9,97 227,9 42,29 179.8 0,445 221,4 7 = 323,15° K 43,87 171,8 0,537 221,1 1,00 267,8 44,65 165,6 2,37 264,4 T = 233,15° K 45,63 157.5 5.17 258,1 n 1 1 0 232,8 45,63 158,3 9,09 247,4 U,ioz 232,6 46,02 153,2 10,22 245,1 232,1 46,34 144,6 14,73 231.1 f\ ceo 230.4 46,61 160,6 0,553 14,93 230,1 4G,86 108,4 1,00 227,6 18,65 215.6 47,79 192,9 1,23 220,3 20,09 207.3 1 At 1,41 225,3 48,02 209,1 r = 348,15° K 50.04 227,2 250,9/ 1,01 277,1 55,28 281,8 0,102 240.5 1,98 275.3 60.78 325,9 0,547 23S,ii 2,86 273,1 69,61 372.1 1,244 235,0 3,26 273,0 79,02 412,0 1,97 231,4 G,79 265.3 91,48 455,0 2,46 228,8 6,79 205,7 95,89 466,8 2,53 229.1 10,22 238,4 98,78 474,5 11,05 250,2 T = 263,15 'K 373,15° K 11,54 255,3 0,171 245.3 16,89 241,9 1,01 286,3 0,570 244,2 17,38 240,2 1,99 285,2 1,144 241,2 18,55 237.4 6,80 276,6 2,17 237,3 21.84 228.9 12,68 266,4 3,14 233,0 24,45 26.50 2! 3,7 243,8 3,69 33,07 230,6 30,10 199.1 227,6 41,02 4,13 22S.7 32,44 188.5 202,4 46,12 186,0 r = 273.15 = K 33,17 184,2 47,94 178,7 r 360,15° 0,141 250,0 = K 48,17 178,6 0,501 248,4 1.00 281.6 50,53 170,0 0,991 247,2 1,98 279.7 50,73 169,5 1,902 243.8 5,71 272,6 51,52 166,4 2,77 240,3 10,32 264,0 52.00 164,1 3,00 239.6 I7,J8 249.7 52,69 164.5 3.92 236,2 24,29 233,3 53,4S 173,3 4,10 235,0 30,08 217,2 53,97 177,4 4.90 231.9 35,62 19S,6 57,30 217,3 5,35 229,8 40,72 174.0 58,97 233,7 5,59 227,7 42,42 162.1 70.34 313,2 [Continued on next pagej -78- Table 38 (Continued) 1 Oap 10, M/ceK p. Oap 01, At/ceK p. 6ap 0). MiCtK P. j 5" T--= 443.04= K r = 373,15° K r =398,1 K 5,28 305,8 81.-13 368,7 88,05 264,6 11,94 292,2 90.9G 403,3 291,8 94,86 25,04 286',5 423,1 311,6 96,82 98,98 36,02 274,9 98.34 428,0 T = 403,15° K 46.22 264,9 59.16 254,0 7 = 383.15° K 0,41 297,3 71,13 245,8 0,74 296,6 1.00 289,6 83.68 243,9 0,93 297,3 1.59 288,7 93,58 247,0 1,56 296,3 2,47 2S7.8 98,34 251.3 5,17 291,7 7.78 279,2 15,81 277,1 T 448.15° K 19,83 259,5 28,07 259,5 1,11 311.8 32,14 236.3 41,50 238,0 2,86 310.4 40,52 218,5 51.80 222,0 4,78 308,3 51,01 193,8 62,05 208,5 16,40 297,6 56,89 181,0 67,70 205,8 29,44 284,5 58,76 180,6 69,35 206,1 41,80 272,7 60,14 182.4 73,27 208.2 54,45 261,4 61.12 184,7 80,53 223,4 69,35 252,2 62,05 188,1 91,07 261,5 79,40 248,3 67,74 223.C. 97,30 284,1 83,29 248,3 75,95 276,0 250,1 84,30 318,1 423,15° K 92.84 r= 254,2 350.8 98,87 92,20 0,226 304,6 372,1 T = 473,15° K 97.84 0,333 304,5 0,549 304.4 1,01 319,9 2' 398,15° = K 0.902 303,9 1,60 319,3 7,97 314,6 1.72 294,0 1,57 303,4 8,27 285,4 5,18 299.2 15,23 308,5 296,0 18,76 270,1 7,97 22,98 303.1 245,4 15,23 287,4 34,26 30,92 296,7 49,65 218,9 25,76 274.3 287,0 57.10 205,8 42,10 25i,2 43,57 61,21 202.0 53,48 241,5 58,67 277,6 231,5 63,57 199,8 64,07 74,51 270,4 65,34 199,4 74,07 226.0 83,68 269,0 67.74 200,6 79,41 226,0 95,25 269,1 70,25 203,1 83.78 227,9 73,48 210,2 89,66 233,5 95,76 269,0 242,6 79.41 230,1 95,06 98,69 268.8 87.70 263,7 98,88 252,0 Analysis of the results of measurements in ethylene reveals that experimental points of the isotherms fall above the smooth curves, which pass through the speed of sound values corresponding to the perfect-gas state, in the investigated temperature range at pressures less than 3-4 bar (see Figure 5) . Deviations increase nonlinearly as pressure decreases and at 1 bar they amount to 2-3 m/sec. Such a form of dependence of the speed of sound on pressure, as we know, indicates that there is dispersion of the speed of sound in the range of pressures below 4 bar, and the lower boundary of the dispersion region, corresponding to "freezing" of vibration degrees of freedom of only part of the molecules, takes place for f/p 175 kHz/bar. These data agree satisfactorily with the results of experimental investigations of the speed of sound in ethylene, carried out by the -79- . 1 acoustical interferometry method by Namoto and coworkers [19] and by Richardson and Reid [20]. According to the data of these works, the disper- sion caused by relaxation of the vibration degrees of freedom, occurs in the range of values of f/p from 180 to 5,000 kHz/bar. The time of vibration relaxation at atmospheric pressure is 2.15 x 10 sec at 27°C according to [19] and 2.38 x lO" sec at 30°C according to [20]. The measured speed of sound in ethylene is thermodynamic, with the exception of that measured at pressures below 4 bar. The dispersion of the speed of sound in propylene was investigated by Pusat and coworkers [21] . The experimentally determined region of dispersion is bounded by values of f/p equal to 10-148 MHz/bar. The time of vibration relaxation at 30°C and at atmospheric pressure is 1.48 x X 10'^ sec. Investigations [15, 18] indicate the absence of dispersion at 690 kHz in the investigated range of pressures, which agrees completely with the conclusions of [21] Recommended Thermodynamic Speeds of Sound, Adiabatics Index, Heat Capacity Ratios and Isobaric Heat Capacity of Gaseous Ethylene and Propylene Detennination of the heat capacity ratio and adiabatics index on the basis of the speed of sound is most accurate of the known methods. Calculation of k and k is based on the Laplace equation for the speed of sound: (42) Using the known thermodynamic relations (3^) = k(^)^ and the ' dp S dp T equation of the adiabatics of a real gas in the form pv = const, it is possible to derive calculation equations for determination of k and k_^ on the basis of experimentally measured speeds of sound and p, v, T-data or using the thermal equation of state: X^jjf—; (43) 7^' (44) It is obvious from (43) and (44) that the speed of sound, density and the first derivatives of the temperature functions must be known in order to do the calculation. relation Equation (43) , together with the known thermodynamic -80- . Q ~ a. gives expressions for calculating heat capacities: c = Op — I I f (47) 8T d where R is universal gas constant; Y = is a dimensionless value. In order to calculate the heat capacities, as follows from equations (46) and (47) , it is essential to have data on the speed of sound and the first derivatives of the thermal functions. The method of calculation set forth herein makes it possible to determine the heat capacities with a higher accuracy than and calculated with the aid of the p, v, T-data and heat capacities in the perfect-gas state. Moreover, as follows from expressions (46) and (47), the contribution of the measurement error of the speed of sound to the overall error of determination of the heat capacities decreases by measure of approach to the region of their maximums. The accuracy of the values and in this region is limited basically by errors of determination of the derivative and complex Y. The recommended adiabatics indices, heat capacity ratios and isobaric heat capacity (Tables II, IV, VI, VIII), computed according to data on the speed of sound, were obtained by Yu. A. Soldatenko and E. K. Dregulyas. The thermal functions and their first derivatives, required for the calculation, were taken from the works of Michels and coworkers [10, 11] and were calculated according to the thermal equations of state. Comparison of the isochoric heat capacity of propylene with the heat capacities found by Nevers and Martin [1] revealed that they agree in overlapping temperature and pressure ranges within the limits of experi- mental error. The isobaric heat capacity and heat capacity ratio calculated according to p, v, T-data of Michels and coworkers [10, 11] are presented in [4, 7]. As seen in Figures 7, 8, 9, 10, these data agree with the values calculated on the basis of the speed of sound within the limits of a few percent. Maximum discrepancies occur in the region of extremal change of the compared values. The heat capacities at pressures above 100 bar in Tables II and VI were calculated from the thermal equations of state used in Chapter I -81- 1 ( o 1 * 1— r— f-l t/i u (/) 4-* vU 5-1 KA 4-1 r-* •H O • H o C u 1 • H 03 o 1 (-> o 03 0 o CN 5-1 • •y X -P to +-> 03 u •H U § o O Q) •H 03 +-> Ph E 03 +-> 03 (D i-H o +-> o tn •M 4-1 (D OS O 03 Sh o Pu o: c o 4-1 H O O 00 +J o (/) V) CD C +-> ?H 5-1 3 .-H O V) +-> • H (/) tu o3 Di 03 -82- -83- 1 11 i3 3 12 Vj: 5 o, -j^ f-. t-? ^ — •> ^ oc: 0) to 10 0 P< 05 (D u +J oJ +-> O o •H O c f\ ^> est CXj ^Ci-Vj I— I/) i-H t 1 (/) t— 0 rH X o Ph •H o IS Ph 1 1 o rsi •H o o o 05 p-1 05 U c (U +-> l/l Oj 0) 1—4 •H o -84- CHAPTER VI,. CALORIC PROPERTIES OF ETHYLENE AND PROPYLENE IN CONDENSED STATE Review of Experimental Data The experimental measurements of the isobaric heat capacity of ethylene and propylene and the heats of phase transitions are based on the determination of the caloric properties of these compounds in the solid and liquid states. The works containing the results of such analyses are listed in Table 39. Table 39. Caloric Properties of Solid and Liquid Ethylene and Propylene repBa.T iic- 1) 2) c..''aoaaiii:iJ.\ 4) ABTOptJ Von 3ea;ecTB0 h ero HswepeHHae cBoiXTBa v^;>inepaT> p, Shkch II FayK [Ij 1928 80—170 B) 3tii.ioii, n3o6apHa5J len.iocMKOCTb k Ten;io- ra n.iat ,.icM'H5i 3raH H KcMn [2] 1937 16— 1G9 5) Stimoh, ii3o6apfia5i Tcn^iocMKocTb, TciiJiora njiaujieiiiia n iiapooopajonaiiiis KocrpioKOB c corpya- 1954 35—115 7) Slil.ieH, H306apHa5T TCn^lOe.MKOCTb HHKaMli (3) ry({)MaH H riapKC (4] 1931 68—210 i) nponiKicH. n3o6apHa5i lenjioeMKocTb ii ren- /lora n.'iaH.ncHHa riaye^i^ h /I>Kar)OK |5) 1939 14—225 3) riponii.nc'H, n3o6apHas] Ten^noeMKOCTb, ren- jiora ri.iau.ieHHH n n,'ipooopa30BaHH5i AyepSax, Ceri;i>K ii 1950 300—330 LO Jnponiuen, n3o6apHa5i len^ioeMKocTb JlecH [6J KEY: 1. Authors 5. Ethylene, is obaric heat capacity Eucken and Hauck [1] and heat of fusion Egan and Kemp [2] 6. Ethylene, is obaric heat capacity, Kostryukov, et al [3] heat of fusi on and heat of evapo- Huffman and Parks [4] ration Powell and Giaque [5] 7. Ethylene, is obaric heat capacity Auerbach, Sage, Laccey [6] 8. Propylene, i sobaric heat capacity 2. Year and heat of fusion 3. Range of investigated 9. Propylene, i sobaric heat capacity, temperatures, °K heat of fusi on and heat of evapo- 4. Compound and its measured ration properties 10. Propylene, i sobaric heat capacity -85- All the works listed in the table were carried out by direct heating of the investigated compound in a constant -volume adiabatic calorimeter with a free interface between the gas and condensed phases in the calori- metric vessel. The ratio of the heats applied to the investigated compound to the rise of temperature, measured in such tests, as we know, is related to the thermodynamic functions of the compound by the expression ^r-"'A+„,.Cs + ^.r. IT (48, where is the heat capacity of the liquid on the saturation curve; Cy is the heat capacity of the vapor on the saturation curve; r is the heat of evaporation; "^-^^i the masses of the liquid and vapor phases, respectively, of the investigated compound. The desired isobaric heat capacity of the liquid is calculated by one of equations (48) of heat capacity on the saturation curve using the known thermodynamic relation (49) where v^^^ is the specific volume of the liquid. In the region of states far from critical all correction factors which, according to equations (48) and (49), must be reduced to the values measured in the experiment for determination of Cp^^, are negligibly small. At temperatures exceeding the normal boiling point, however, exact calcula- tion of the isobaric heat capacity according to these relations requires extremely reliable data on the thermal properties of the investigated liquid, its vapor and heat of evaporation. The heat capacity of ethylene in the condensed phase is measured by Eucken and Hauck [1], Egan and Kemp [2] at temperatures from 16°K to the normal boiling point 170. 4°K. The results of these investigations vary substantially both in the solid (up to 28%) and in the liquid (up to 17%) states and give a different temperature curve for the heat capacity of ethylene in the liquid state (Figure 11). Eucken and Hauck obtained four experimental points for the heat capacity of solid ethylene and 11 points for the liquid. They are all presented in [1] in the form of a small graph. The smooth values of heat capacity obtained in this work are: for solid ethylene 14.80, 15.35 and 16.00 cal/ (mole -deg) at 80, 90 and 100°K, respectively; for liquid ethylene 17.40, 17.80, 18.17, 18.50, 18.80 and 18.80 cal/ (mole -deg) at 110, 120, 130, 140, 150, 160 and 170°K, respectively The authors [1] estimate the accuracy of their data as ±1%. -86- i I . . , 6 P-Z • -J • • • 90 W 170 2W 250 7^ Figure 11. Isobaric heat capacity of ethylene on saturation curve according to: 1 -- Eucken and Hauck [1]; 2 -- Egan -- and Kemp [2] ; 3 Soldatenko and Vashchenko [10] Direct measurements are not given in [1] , in which connection it is impossible to establish the possible error or systematic error in the measurements and in the processing of the experimental data. Another important deficiency of the cited work is the absence of chemical analysis of the ethylene employed in the tests. Egan and Kemp [2] used 99.5% pure ethylene. They further purified it by drying over phosphorous pentoxide and distillation at low pressure (100-200 mm Hg) and pumping of the vapors over the solid phase, before filling the apparatus with it. The purity of the. thus prepared specimen was determined cryoscopical ly on the basis of residual impurities, amounting to not more than 0.001 mole %. The experimental data [2] on the isobaric heat capacity of ethylene are presented in Table 40. The same values are used as recommended values for technical calculations in many manuals, [7, 8] for instance. The heat of fusion of ethylene (X = 800.8 ± 0.8 cal/mole) and heat of evaporation (r = 3,237 ± ± 3 cal/mole) at normal pressure of 760 mm Hg, measured calorimetrically are also given in [2] The heats of evaporation stated above agree satisfactorily with those calculated by the authors (r = 3,222 cal/mole) according to the saturation pressure of the vapors. Egan and Kemp, on the basis of caloric data, calculated the entropy of ethylene in the perfect-gas state at the normal boiling point S°^g It is 47.36 ± 0.10 cal/ (mole'deg) and agrees very well with the results of later calculations on the basis of spectroscopic data. The entropy of ethylene in this state, according to [2], is 47.354 cal/ (mole'deg) . The -87- . Table 40. Experimental Data of Egan and Kemp [2] on Isobaric Heat Capacity of Ethylene Cp, KQAHMtAh /. Cp, KaxKMAb i X / K / • K T" K X ep.''') X eprt/) j 1 ) TBep;ioe cocTOflHiis 1 ) TtepAoc cocTOHHHe 1 ) TBepAoe cxiCToaHHe Kfl 7Q 1 1 ,/ u D,UU 1 103,81 1 34,96 18.81 1,299 86,77 12,65 2) )KHAKOe COCTOHHHe 21,91 1,921 92,11 13,83 106,69 16,51 25,17 2,556 94.40 74,55 108,58 16,49 29.10 3,362 95,48 14,94 112,28 16,43 33,16 4,288 98,10 16,03 119,03 16,33 37,35 5.187 98,99 16,44 125,90 16.28 43,08 6,045 100,94 17,65 132,60 16,21 47.29 6,932 101,39 17.97 139,08 16,11 52.52 7,809 101,90 18,48 145,38 16,09 57.60 8,598 102,28 18,59 151,88 16.08 62,80 9,279 103.03 19,52 158,55 16,03 1 68,41 9,980 103,36 20,77 164,23 16,04 74,70 10,79 103,59 20,58 168,71 16,09 j KEY: 1. Solid state 2. Liquid state coincidence of the stated entropy values is indirect proof of the reliability of the experimental data on the calorimetric properties of ethylene presented in [2] Some experimental points on the thermal capacity of ethylene are given by V. N. Kostryukov, et al [3] in graphic form. These values were obtained at the request of the authors during trial measurements, in which the opera- tion of the experimental apparatus was checked. The data obtained practicall| coincide with the data of Egan and Kemp [2], with the exception of the region;, very close to the melting point, where the authors [3] observed a very sharp j (4-5-fold) increase in the heat capacity. The authors [3] attribute the | increase in heat capacity to the insufficient purity of the investigated 'J ethylene specimen. The isobaric heat capacity of propylene in the condensed state was measured to the normal boiling point by Huffman, Parks, Barmore [4] and Powell and Giaque [5] . The purity of the investigated specimen of propylene in [4] was characterized by the presence of 0.1 mole % impurities, and in [5] the purity of the main component was 99.98%. i The experimental data obtained on isobaric heat capacity of propylene agree within the limits of the accuracy of experimental measurements of ±1%, , as requested by the authors, and the data in [4] are understated in rela- tion to the data in [5] within the limits of systematic error in the liquid 1 state. The experimental data derived from these investigations are listed f in Tables 41 and 42. j The data on the heat of fusion of propylene, measured in the cited works, diverge to a somewhat greater extent. -88- Table 41. Experimental Data of Huffman, Parks and Barmore [4] on » Isobaric Heat Capacity of Propylene • Katl(e-zpadi Cp, Ka.iHe-epad) Cp. KaAl(a-epad) r°, K Cp. l\ K r°. K 1) TflepAUii sTHJieH 2) >KHAKHH STH.ieU 68,9 0.273 93,1 0,523 153.9 0.490 72,0 0,280 93,5 0.522 165,3 0,492 73,5 0,286 98.6 0.516 189,5 0,502 76,5 0.296 108.7 0.504 210,3 0,512 76.7 0,295 125.2 0.494 81.6 0.317 144.6 0.490 KEY: 1. Solid ethylene 2. Liquid ethylene Table 42. Isobaric Heat Capacity of Propylene, Experimental Data of Powell and Giaque [5] • • cpad) Cp, KaAl(i-apad) ! Cp. kqaKc T". K Cp, Ka.:f{c epad) T\ K T\ K j G1.25 0,2438 115,64 0,5024 i I Bep,f^LJH npGi!n,neH ) 66.61 0,2609 128,09 0,4988 14,18 0.0271 71.46 0,2759 134,56 0,4974 16,66 0,0377 76.49 0,2920 141,21 0,4945 19,63 0,0523 76,59 0,2949 154,97 0,4950 0,4948 22.81 0.0726 . S1.6-J 0,3184 161,88 26.23 0.0924 ' .^i.37 0,3374 169,01 0,4960 f:6,i;' 0,3826 176,71 0,4986 29,87 0,1113 ! 33,62 0,1332 187,77 0,5005 2) HuiaKiiii nponiivien 37,46 0,1537 194.66 0,5036 41,29 0,1705 93,91 0.5235 201,77 0,5090 45,53 0,1865 98,66 0,517! 209,18 0,5121 ,. 50,66 0,2069 104.18 0,5107 216,41 0,5136 55,96 0,2243 109,98 0.5073 223,40 0,5195 1 KEY: 1. Solid Propylene 2. Liquid propylene According to measurements [4] the heat of fusion is 701.4 cal/mole, and in [5] it is 717.6 cal/mole. The 2% discrepancy in the heat of fusion is obviously related to the purity of the investigated specimens, as well as to the fact that the sharp increase in heat capacity of the solid propylene near the melting point, observed in [5] at temperatures from 82°K to the melting point (87.70°K) was taken into account in [4] during processing of the experimental data on the heat of fusion. The last experimental point in [4] in the region of the solid state was determined at T = 81.6°K. Thus, the heat of fusion of propylene A = 717.6 cal/mole, obtained in [5], should be considered more reliable. The heat of evaporation {x) of propylene at normal pressure was measured in [5] by the calorimetric method and is equal to 4,402 ± 3 cal/mole. The isobaric heat capacity of liquid propylene on the saturation -89- curve at temperatures above the normal boiling point were measured in a narrow temperature range by Auerbach, Sage and Laccey [6] in a constant- volume adiabatic calorimeter with the presence of a free interface between the liquid and gaseous phases. The isobaric heat capacity was calculated on the basis of two series of calorimetric measurements, taken with different concentrations of the investigated compound in the calorimetric vessel at 308-339°K. The basic calculation equation is V' — v' \ AT, ATo ( + /Til — ni^ „ dv' . dv V — V dT dT (5) dVy>: \ dPs rp dPs rp (dVn\ dpi dTjp dT dT jp dT dT \ "^1 "^2 where (^) and (.jTy—) are the ratios of the heats applied to the calorimetric 1 2 system to the temperature rise, measured directly in the first and second series of tests; m^ and m^ are the masses of propylene in the calorimeter in the first and second series of tests. The original propylene was 99.0% pure. It was subjected to additional purification by fractionation at low temperature and at atmospheric pressure in the ratio 40:1 before filling the apparatus, and at the beginning of purification more than 15% of the specimen was dis- carded, and 20% at the end of the purification process. The specimen used in the test changed temperature by not more than 0.05°K during evaporation at atmospheric pressure. "^2 '^l The difference required for calculating the isobaric heat at~-^ 1 2 capacity of the liquid in accordance with equation (50) , was determined in accordance with smooth curves plotted in coordinates q/AT - T for both series of tests. During investigation of propylene the scattering of the individual measurements in relation to the smooth curve constituted an extremely large part (±5%) of the above-mentioned difference. A consider- able drawback of the examined investigation, inherent to the experimental procedure, is the extremely large correction factor related to the presence of a two-phase system in the calorimeter, which must be reduced to values measured in the test in order to calculate the isobaric heat capacity of the liquid on the saturation curve (see equation (50)). According to data in [6] , the correction factor in the given temperature range is 16-45% of the isobaric heat capacity of the liquid. It is also noteworthy that this correction, due to the insufficient accuracy of the existing data on the thermal and caloric properties of liquid and gaseous propylene, cannot be calculated with sufficient accuracy. -90- . . 1 On the basis of what has just been said it can be concluded that the accuracy referred to by the authors of [6] of data on the isobaric heat capacity of liquid propylene on the saturation curve, ±3%, is hardly justified, and the smooth data (see Table 43) are not reliable. Yu. A. Soldatenko and D. M. Vashchenko [10] investigated in 1964-1968 the isobaric heat capacity of liquid ethylene and propylene at 170-280 and 170-360°K at pressures of 1 to 60 bar. The experimental apparatus used for these purposes accomplishes direct heating of the investigated compound in a calorimeter with an isothermic shell in the variation proposed by A. Ye.. Sheyndlin, S. G. Shleyfer and E. E. Shpil'rayn [11]. A characteristic feature of the method is the absence of a free liquid surface in the calorimeter, ensuring the capability of measuring the heat capacity of unsaturated liquids under pressure. The pressure is created in the apparatus by the vapors of the investigated liquid, and its free level extends beyond the limits of the calorimetric vessel into a region of higher temperatures than the temperature existing in the calorimeter. The amount of the investigated compound is determined by the known volume of the calorimetric vessel and the density of the liquid at the test temperature and pressure. The experimental apparatus is described in detail in [10] Table 43. Isobaric Heat Capacity of Liquid Propylene on Saturation Curve According to Auerbach, Sage and Laccey [6] 7-° Cp, Cp. kqaIU • apad) f F K KOMic-zpad) r- F T" K 80 299,8 0,5615* 130 327.6 0.6607 90 305,4 0.5747 * 140 333,2 0,6985 100 310,9 0,5917 150 338.7 0,7607 * 110 316,5 0.6102 160 344.3 0.8608 120 322.0 0.6329 *Values extrapolated by the authors [6] A new method of introducing the correction factor for heat exchange between the calorimeter and the isothermic shell is original in the given study. During calorimetry the temperature of the calorimeter is measured both during the main period of the test, including the operating time of the heater and time interval during which the temperature varies in the calorimeter, and in the final period. Here the time of passage of the "spot" of the galvanometer, hooked into the measurement circuit of a platinum resistance thermometer, through the zero graduation when certain a priori known temperatures are reached in the calorimeter, is recorded with the aid of a two-hand type 51 -SD stop watch. The temperature pitch between consecutive measurements was maintained constant. The curve of change of calorimeter temperature in time, thus obtained, was used for determining the "adiabatic" [13] temperature rise of the calorimeter, which is determined with the expression -91- . . At = At' + 6t (51) where At' is the observed temperature rise of the calorimeter on completion of the main period of the test; 6t is the correction factor for heat exchange between the calorimeter and the isothermic shell during the main period. The correction factor for heat exchange is found from the expression where k is the rate of cooling of the calorimeter; t is current temperature; tj^ is the convergence temperature [12] , equal in our case to the initial calorimeter temperature; is the time of completion of the main test period. The accuracy of calculation of the correction factor for heat exchange depends principally on the accuracy of determination of the cooling rate k, calculation of which is now done by a new method with high accuracy The generally accepted methods of calculating the rate of cooling [11, 12] are based on the assumption of linear change of calorimeter temperature in the final test period, which, as shown by experience, is at best a very rough approximation. Disregarding the nonlinearity of the temperature curve of the calorimeter in the final test period causes notable errors, particularly during testing in the negative temperature range A new method is based on the fact that at the end of the test the temperature drop of the calorimeter is governed only by heat losses from the calorimeter to the thermostat and consequently for any time interval (t , - t ) of the final period the heat exchange correction factor 6t, n+1 n ^ ^ calculated according to equation (52) , is equal to the observed temperature drop of the calorimeter: 6i = k (t-t,)dT=it„-i,+r). ^ (53) Writing expression (53) for the entire final period from to (time of completion of the test), we obtain (54) -92- i I Equation (54) is used for calculating the rate of cooling k. For the adiabatic rise of temperature of the calorimeter in the principal period we have, with consideration of what has been said above, - dx J /o) = (in - to) (/. - t,) _ + . (55) ^(t~lo)dx The integrals in equation (55) are calculated by the trapezoid method on the basis of calorimeter temperature measurements in the main and final test periods. The time of completion of the main period of the calorimetric test is determined quite distinctly within the frameworks of the given method. Actually, with consideration of the constant temperature pitch between consecutive measurements and conditions (53) , we may write for any interval of time between consecutive measurements in the final period, the following relation: ^1+1 k (t — dx = — = const. \ to) iti ti+i) Since the rate of cooling is constant for the entire calorimetric test it follows from expression (56) that f ii — t(,)dx = const, (57) for the entire final period, or calculating the integral as the area of a trapezoid, we obtain At, = const. ^^g^ Consequently the point on the curve of change of temperature in time, after which equation (58) is satisfied for all subsequent measurements, may be taken as the completion of the main period. Its shift toward an increase in time does not alter the results of the calculation by the equation At = At' + 6t. adJ The isobaric heat capacity of liquid ethylene and propylene was investigated at 170-280°K and 170-360°K at pressures from 1 to 60 bar. Ethylene and propylene were supplied in metal cylinders. The -93- — p concentration of the main component according to the data of factory chromatographic analysis in specimens taken from the cylinders is 99.98% for ethylene and 99.7% for propylene. The investigated compounds were not subjected to additional refining. o-J 0-4 I *-5 0-7 0-8 A „-9 II <>—<> ^ — ^ — Q_c —.— V U — T r 1 > » 10 10 30 ^0 SO P, 6a Figure 12. Experimental data on isobaric heat capacity of liquid ethylene at T equal to: 1 -- 168.90; 2 -- 196.65; 3 -- 232.65; 4 -- 249.65; 5 -- 257.25; 6 -- 262.65; 7 -- 266.65; 8 -- 270.35; 9 -- 273.65; 10 -- 277.65°K. KEY: 1. Saturation curve. Sixty-nine experimental points were obtained on the basis of the isobaric heat capacity of ethylene. During the calorimetric test the initial temperature of the specimen and the heat supplied were chosen from the consideration that the average temperatures of the series of tests conducted at different pressures be close to each other. Thus, the entire series of measurements was conducted on the same isotherm. The small correction factors that are inevitable in such a case at certain experi- mental points, for reduction to the temperature on the investigated isotherm, did not exceed 0.3% of the measured isobaric heat capacity. The correction factors were introduced by the successive approximation method during processing of the series of isotherms. Eleven isotherms were found for ethylene in the stated temperature range, each of which included at least five experimental points. Most of the experimental points were the result of averaging two identical measure- ments . The experimental points and the smooth curves (isotherms) are illustrated in Figure 12. Smoothing was done in the coordinates C^-p on the basis of the isotherms and in the coordinates C -T on the basis of the P isobars. Deviations of the experimental points from the smooth curves do -94- 1 not exceed ±1%. The isobaric heat capacity on the saturation curve was determined by extrapolating the isotherms to the saturation pressure, which on was taken the basis of the data in [7] . Seventy experimental points on 10 isotherms were obtained in the above-stated temperature and pressure ranges in terms of the isobaric heat capacity of propylene. The deviations of the experimental points from the smooth curves did not exceed ±1%. The experimental points and smooth curves (isotherms) are illustrated in Figure 13. Figure 13. Experimental data on isobaric heat capacity of liquid propylene at T equal to: 1 -- 360.35; 2 -- 358.65; 3 -- 355.15; 4 -- 352.55; 5 -- 344.64; 6 -- 335.15; 7 -- 325.65; 8 -- 301.65; 9 -- 274.57; 10 -- 197.55; 11 -- 164.65°K. KEY: 1. Saturation curve. Detailed analysis of the accuracy of experimental determination of the isobaric heat capacity yields a maximum possible error equal to ±1.5%. The accuracy of the extrapolated values of heat capacity on the saturation curve, by our estimate, is ±(2.5-3)% in the high-temperature range. Recommended Caloric Properties of Ethylene and Propylene in Condensed State Ethylene The review and comparison of existing experimental data on the isobaric heat capacity and heat of phase transitions of ethylene, presented in the preceding section, make it possible to recommend the following initial data as the most reliable: a) Egan and Kemp [2], presented in Table 44, on the isobaric heat capacity in the solid state from 15°K to the melting point (103.95°K) and on the heat capacity of the liquid in the range of temperatures from the melting point to the normal boiling point (169.37°K). -95- . The heats of phase transitions, found by the same authors, for the heat of fusion X = 119.26 ± 0.41 kJ/kg and heats of evaporation r = 483, 144 + 0.3 2 kJ/kg at the normal boiling point for p = 760 mm Hg, are also the must reliable values. b) Yu. A. Soldatenko and D. M. Vashchenko on the isobaric heat capacity of liquid ethylene in the temperature range above the normal boiling point, the results of which are presented in the preceding section (see Figure 12) The data of Egan and Kemp were used in the present work for calculating the enthalpy and entropy of liquid ethylene at the normal boiling point, measured from the crystal state at 0°K. Heat capacity below 15°K was found by extrapolating to 0°K according to the Debye theory [13] and agrees at 15°K with the data of Egan and Kemp. The enthalpy and entropy were obtained by graphic integration of the data on isobaric heat capacity. The heat of fusion was found on the basis of data [2] . The results of the values in the most characteristic points are presented in Table 44. Table 44. Heat of Fusion According to [2] 1) TeMneparypa 2) l^3MeHenne SMTa/ibniiH. uriyKlK? inMeiieHiic aiiTponnH. KdM/lKe-epadi 15° — = = 0.0357 O'K— K '15° K 'o- K ^ 15" - K '103,95=" K ~'l5° K ^ 115.86 119.53 ?./r„,= 1.149 T 158.204 =^ '-'^^ n.n —TH.K he^.v K '103.95° K " •^169,37° K ~ "^lOi.gS' K CvMMa ' ~ 394,00 4.214 169.37° K — 'o° K ^169.37^K = KEY: 1. Temperature 4. Total 2. Enthalpy change, kJ/kg 1^ = melt. 3. Entropy change, kJ/(kg-deg) H.k = normal boiling The enthalpy of gaseous ethylene, given in Table II, was also measured from the crystal state at 0°K. Conversion of the enthalpy change measured from the gas state at 0°K, to the zero reading employed, was done normal boiling point using the value i^^g P^^^ented above. at the 37°K It was found that t«r= +662.4), kJ/kg (59) -96- . where is the enthalpy at T and p = 0, measured from the crystal state at 0 0°K; (H^ - 11^) is the enthalpy of the gas in the same state, measured from the gaseous state at 0°K. The data of Yu, A. Soldatenko and D. M. Vashchenko were used for tabulating the isobaric heat capacity, enthalpy and entropy of liquid ethylene in the temperature i range above the normal boiling point and at pressures of 0.5-60 bar (Table II). The tabulated values of enthalpy and entropy were obtained by graphic integration of the smooth isobaric heat capacities in the temperature range from 169.37°K to the given tabular temperature every 10° (Table II) The enthalpy and entropy of the saturated liquid were determined by the same method with integration to the saturation temperature on the given isobar. The enthalpy and entropy of the saturated vapor were calcu- lated with consideration of the heat of evaporation at the given pressure. The enthalpy and entropy at the critical point were determined by extrapolating the top and bottom boundary curves in coordinates T - i and T - S to mutual intersection at T and in coordinates p - i and p - S to cr r r intersection at p . The tie-in of i and S was checked in coordinates ^cr cr cr 1 - S. Propylene The data of Powell and Giaque [5], presented in Table 42, are recommended on the basis of the isobaric heat capacity in the solid state from 15°K to the melting point (87.85°K) and on the basis of the heat capacity of the saturated liquid in the temperature range from the melting point to the normal boiling point (225.35®K). Also considered most reliable are data on the heat of fusion X = = 71.402 kJ/kg and heat of evaporation at the normal boiling point at p = = 760 mm Hg, r = 438.00 ± 0.3 kJ'kg. At temperatures above the normal boiling point the isobaric heat capacities obtained by Yu. A. Soldatenko and D. M. Vashchenko are used, both for the saturated and unsaturated liquid. The recommended values are compared with data in [6] in Figure 14. The comparison can be done only on the saturation curve, since data on the isobaric heat capacity of the liquid under pressure are found only in [10]. The data of [6], as seen in Figure 14, were obtained for 300-345°K, and are 12-18% lower than the data of [7]. Possible reasons for such great discrepancies are discussed in the preceding section. Powell's results [5] were used in our work for calculating the enthalpy and entropy of liquid propylene at the normal boiling point, measured from the 0°K crystal state. -97- . 6 330 T,°K Figure 14. Isobaric heat capacity of propylene on saturation curve according to: 1 -- Powell [5]; 2 -- Huffman, Parks [4]; 3 -- Yu. A. Soldatenko, D. M. Vashchenko [7]; 4 -- Auerbach, Sage, Laccey [6] Table 45. Heat, Enthalpy and Entropy 1 ) TeMncparypa 2) MsMeHCHiit; 3) ibMeHeiiiio siirpomiii, Kdx/iKa.epad) 0°K — 15=K S,5»K = 0.019 " =G0.958 1,159 '87.90'= K -1,3 •^r,,^ —5,5.^ = X = 71.402 Vr„^ = 0.812 ~ " 292,04 1-985 ' nji H.K '22.5. 45'K '87.90' K ~ '^F7.90'K ~ Cy.MMa = 424.40 4.005 4) . '225,45 K -«0K 5225.45°K = KEY: 1. Temperature 4. Total 2. Enthalpy change, kJ/kg nf^ = melt 3. Entropy change, kJ/(kg-deg) H.k = normal boiling The heat, enthalpy and entropy at the most characteristic points are given in Table 45. The enthalpy change in the perfect-gas state was con- verted to the employed zero according to the equation i'^ = KHr ~ Ho) + 635,3], kJ/kg . (60) All other data in Table VI were calculated by the same methods used for ethylene. -98- CHAPTER VII. VISCOSITY OF ETHYLENE AND PROPYLENE Viscosity of Gaseous Ethylene and Propylene at Atmospheric Pressure The viscosity of gaseous ethylene and propylene at atmospheric pressure has been thoroughly investigated. Studies pertaining to the experimental determination of the dynamic viscosity coefficient of gaseous ethylene and propylene at atmospheric pressure are given in Table 46 and the numerical values of these coefficients are listed in Table 47 and Table 48. Note- worthy are the calculated data of Trautz [17] for ethylene. On the basis of his measurements he calculated the dynamic viscosity coefficients of ethylene at atmospheric pressure at temperatures T = 1,165°K (ri = 2917 x X 10'^ N*sec/m^) and T = 1,270°K (n = 3060- lO"^ N'sec/m^) . The smoothed dynamic viscosity coefficients of gaseous ethylene at atmospheric pressure are presented in I . F. Golubev's review [13] for the 223°K to 773°K temperature range, and are given below: T, °K Tl-10 ^,H-CeKlM- \\-\0-^.H-ceKlM'^ 223,15 792 373,15 . 1260 248,15 864 423,15 1405 273,15 941 473,15 1545 293,15 1010 523,15 1670 298,15 1027 573,15 1810 323.15 1108 673,15 2049 348,15 1180 773,15 2260 These values were found as a result of processing experimental data of Trautz and coworkers [2, 3, 5 and 6] and data published in [1, 4]. The results of Braune and coworkers [18, 19] on the viscosity of gaseous NH^, H2O, HCN, I^, CI2, CHjCl, CH2CI2, CHCl^, HgCl2, HgBr2, Hgl^, SnCl^, Br2 and air at atmospheric pressure were used in the calculations. These investigators demonstrated that the experimental data for the above-listed compounds in the 270-900°K temperature range are described with high accuracy (mean deviations of the order of 0.2% with maximum up to 1.5%) by the Sutherland equation [20]. The smoothed dynamic viscosity coefficients of gaseoUs propylene at -99- 0 atmospheric pressure for the 193 . 15-1 , 273 . 15°K temperature range (see Table 49) are presented in Lehmart's review [21]. The author of the review asserts that they were obtained on the basis of numerous existing experi- mental data, but does not cite the sources. Table 46. List of Experimental Studies of Dynamic Viscosity Coefficient of Gaseous Ethylene and Propylene at Atmospheric Pressure T) --n ^i^.o/iimecTBo TeMrieparypa. I 1 ABTOpfal ) 2) rofl "[^ iKcnepHMeH- I Ta.iibi(bi.\ ToqeK 5) 3-ni.aen 7) 1 87^ Q OoepManep fl] 1 o/ o 1 OZO O BpeHxeiiuax c [1] ZO i — 0 / 0 1 Q1 1 oftf^ SiiMMep ( 1 9 Q7 ] 4 1 cion 1 OA O^'A TpayTU, Hapar [2] i yzL) J yo—zoD 5 1 no TpavTU, Ciaycji [3) 1 Q9Q ::;o ^ 13 TiiiaHii [4] I QOQ 6 TpavTU, Aiaibciep [5] 1930 292—374 3 Tpayxu, FeGcpnunr [6) 1931 291—523 10 BaH Kjihb, Maacc [7| 1935 192—296 11 KoM-'iHTc, MaiLiaHji, Stjih [8] 1944 303—368 5 FpaneH, JlaMoepx [9] 1951 193—523 5 3eH<})T;ie5ei! llOj 1953 303 1 ro.nv6eB, lleipoB [11] 1953 313 1 JlaMoepi |I2j 1955 308—3.64 9 Fo.TyCeB [13] 1959 297—423 4 M-.iSKK [14] 1961 293—523 5 He;iyHCHH, X.Mapa [15J 1967 193—297 6 8) 6) npoiniweK Tm-aHH [4] 1929 293—393 7 Tpaym, XycefiH!! [16] 1934 289—521 10 Ban K-xiiD, Maacc [7] 1935 193—297 13 FpaBen, JIn\i6epT [9] 1951 293—523 4 SeHcJjT.ieecH (10) 1953 303 . 1 .JlaMoepr [12) 1955 308—353 9 FoJiyoee [13| 1959 291—523 7 HeavHiiiii, X.Niapa [15] 1967 210—310 6 KEY: 1. Authors Senftleben [10] 2. Year Golubev, Petrov [11] 3. Temperature, °K Lambert [12] 4. Number of experimental points Golubev [13] 5. Ethylene Misic [14] 6. Propylene Neduzhiy, Khmara [15] 7. Obermayer [1] Titani [4] Breitenbach [1] Trautz, Husseini [16] Zimmer, [1] Van Cleave, Maass [7] Trautz, Narath [2] Graven, Lambert [9] Trautz, Stauf [3] Senftleben [10] Titani [4] Lambert [12] Trautz, Melster [5] Golubev [13] Trautz, Heberling [6] Neduzhiy, Khmara [15] Van Cleave, Maass [7] Comings, Mayland, Egly [8] Graven, Lambert [9] -100- It is well known that the viscosity of gases at atmospheric pressure in the moderate temperature range (up to T < 1,000°K) can be described with sufficient accuracy by means of equations of kinetic theory. At the present time the Girshfel'der equation [22], derived through the solution of the Boltzmann equation by Enskog's method for model of spherically symmetrical molecules with the Leonard-Jones potential (6-12) is considered most rigorous. When describing the viscosity of gases the parameters of the Leonard-Jones potential (6-12) are determined directly from the experi- mental data and depend on the temperature range due to scattering of the experimental data. For this reason the Girshfel'der equation, like other equations of kinetic theory, can be used only for interpolation and analysis of existing experimental data. The force constants of the Leonard-Jones potential (6-12), calculated through the Girshfel'der equation, yielded values e/k = 228°K and a = = 4.1385 A for ethylene; e/k = 296. 0°K and a = 4.5945 X for propylene. The deviations of the dynamic viscosity coefficients of ethylene and propylene at atmospheric pressure from the values obtained as a result of graphoanalytic processing of data [1-17, 21] are presented in Table 50. As seen, the force constants of the Leonard-Jones potential (6-12) can be considered as not depending on temperature and the values recommended for the calculations are presented in Table 50. The following values were obtained during calculation of the force constants by the Sutherland equation: i^ij) e/k = 236. 0°K, a = 3.895 X for ethylene; i (y) e/k = 320. 0°K, a = 4.387 X for propylene. The results of such calculations by the Sutherland equation [20] are presented in Table 51. It is obvious from the table that the force constants of the Sutherland potential also do not depend on temperature, and the Sutherland equation [20] is just as good in terms of the accuracy of description of experimental data as the Girshfel'der equation [22]. On this basis the Sutherland equation was used, being more convenient for the calculations than the Girshfel'der equation, for compiling Table X of recommended dynamic viscosity coefficients of gaseous ethylene and propylene at atmospheric pressure. Scattering of existing data relative to the smooth values is comparatively low. The following results were obtained from comparison of the recommended dynamic viscosity coefficients with the experimental data. The mean deviations of the experimental data [3, 5-8, 10, 13, 14] on the viscosity of gaseous ethylene at atmospheric pressure do not exceed 0.6%. The mean deviations of data [12, 15] do not exceed 0.8%. The mean deviations of data [1, 2, 4, 7, 9, 11] are about 2-2.5%. The maximum deviations are comparatively low. They do not exceed 2-4.5%, with the exception only of one point obtained by Trautz and Narath [2] at 244. 6°K, where the deviation is 7.9%. -101- Table 47. Experimental Data on Viscosity of Gaseous Ethyl at Atmospheric Pressure OSepMafiep 472.95 1540 523.65 261.65 851 1668 523.85 293.75 989 1667 326,65 1096 9) BaH K/iHB. Maacc 192,29 2) BpefiTeH6ax 652.1 204,63 697.2 251,95 891 212,77 704,2 288.15 1016 220,65 752,3 372,40 1278 235,15 802,5 455,55 1530 250,56 856,0 575,75 1826 264,13 900.8 273.08 932,2 3) SiiMNiep 284,38 969.6 197,45 699.3 290.33 990.7 229,07 768,5 296,50 1010.6 234,55 784.5 286,87 954,2 10)\oMHHrc, Mefwafu, 3r.iH 4) Tpaym, Hapai 303,15 1054 323,15 196,16 097 1093 343,15 229,15 766 1172 368,15 244,65 782 1255 273,15 903 11) FpaaeH, VlaMGepr 287,15 950 193.15 714 5) Tpayru, Ciaycj) 273.15 945 323.15 193,85 716 H06 423,15 235,45 816 1407 523.15 271,35 940 1680 287,15 990 12) Jla.MSepT 289,25 996 308,15 1059 291,35 1008 323.15 1110 292,25 1007 334.75 1157 294,95 1018 338,15 1163 324,15 1109 339,15 1168 373,75 1266 343,65 1187 422,35 1405 350,95 1209 470.55 1539 353,35 1217 525,45 16B7 361,35 1251 6) TllTaHH 13) roJiy6eB 295,15 970 297.15 1023 -313,15 1036 323.15 1108 333,15 J108 373,15 1260 353,15 1154 423,15 1405 373,15 12-:'0 393,15 127'j 14) MU3HK 7) Tpayru, Me.ibCTep 293.15 1008 323.15 1103 292,75 1008 373.15 1257 324,15 1109 473,15 374,15 1262 1541 523,15 1666 8) Tpaym, rcCcp.iiinr He;;yjKiiri. XMapa 291.75 1003 15) 299.45 1027 193,15 695 323.75 1105 213.15 75! 373.05 1256 233,15 808 373,15 125S 253,15 868 423.35 J 404 273,15 949 472,35 1539 297.15 1023 [Key on next page] -102- KEY: 1. Obermayer 9. Van Cleave, Maass 2. Rreitenbach 10. Comings, Mayland, Egly !, . Z i III in o r 11. Graven, Lambert 4. Trautz, Narath 12. Lambert 5. Trautz, Stauf 13. Golubev 6. Titani 14. Misic 7. Trautz, Melster 15. Neduzhiy, Khmara 8. Trautz, Heberling Table 48. Experimental Data on Viscosity of Gaseous Propylene at Atmospheric Pressure —8 10- H-ceKlM- T)- 10 1) TnTai!ii 4)rpaBeH, JIa.M6epT 293,15 833 293,15 843 294,65 856 323,15 933 313.15 843 423,15 1210 313,15 959 523,15 1467 353,15 1023 5 3eH4)T,neCeii 373,15 1071 ) 303,15 898 393.15 1122 I 27 pay™, Xyceftim 6 ) .na.M6epT 308,15 922 . 289,9 834 293,1 844 323,15 954 296,2 854 333,05 991 323,1 935 338,15 986 329,5 951 339,15 1000 373.3 1076 344,15 1024 423,1 1211 350,95 1023 425,9 1219 354,35 1056 472,6 1338 363.95 1080 521,7 1464 7) ro.ny6eB 3) Ban Kjihb, Maacc 291,15 839 193.43 561,5 326,15 942 197,45 572,4 358.15 1032 202,26 582,6 373,15 1075 212,45 611,9 423,15 1212 217,52 623,6 473,15 1340 234,40 670,4 523.15 1408 247,34 709,3 8) HeflyjKHH, Xxiapa 750,0 _-^61,36 210 586 273,0 78,3,9 230 640 273,15 784,1 250 736 813,3 282,51 270 800 291,84 840,6 29/) 828 858,3 297.31 310 904 KEY: 1. Titani 5. Senftleben 2. Trautz, Husseini 6. Lambert 3. Van Cleave, Maass 7. Golubev Khmara 4. Graven, Lambert 8. Neduzhiy, Deviations of the experimental data on the viscosity of gaseous are of the propylene at atmospheric pressure from the recommended values have a same order of magnitude. The experimental data [4, 16, 9, 13, 15] mean deviation of 0.4%. The maximum deviations do not exceed 3.6%. -103- Table 49. Smooth Data on Viscosity of Gaseous Propylene at Atmospheric Pressure, Presented in Lehman's Review [21] • 10—^, h-cck/m' r." K T) • 10—8, H-ceK/Mt T.° r," K \\ 1 K ll :93,15 560 423,15 1220 973,15 2123 223,15 639 1 473,15 1342 1073,15 2615 253,15 726 1 523,15 1468 1173,15 2785 273,15 784 573.15 1590 1273.15 2947 293,15 845 673,15 1816 323,15 933 773,15 1970 373.15 978 i 873.15 2235 i Table 50. Calculation of Numerical Constants According to Girshfel 'der ' s Equation ij 1) S 0/ T." K «. % T," K 3) 1 F, / ^rH;ieH -|-=228.0°K; a =--4,1385 Aj Hponiwen ^ = 296,0"K; a=4,5945 Aj 220 770 — 1.61 220 624 —1.21 260 903 —0,2 260 1748 +0,08 300 1033 —0,62 300 863 +0,02 400 1336 —0.29 400 1148 +0,47 500 1622 —0,03 500 1413 +0,52 600 1879 —0,12 600 1652 +0,28 800 2312 —1,36 800 2085 +0.13 1000 2465 —0,35 KEY: 1. u'lO'^ N'sec/ 2. Ethylene ngraph 3. Propylene Table 51. Calculation of Force Constants by Sutherland Equation 1) 1) , T.° K i. % T." K 10—^, H-CeKlM- 5. % 236.0^ A) e/'t 320,0° == 2) 3TH,aeH (/2 (7) zjk = K. o = 3,895 r^onH;ieH ( 2 (Y) = K. 0 4,387 A) 220 270 +0,61 220 624 —0,01 260 903 —0,10 2G0 747 +0,08 300 1033 —0,38 300 863 —0,31 400 1336 —0,71 400 1148 +0,03 500 1622 —0,18 500 1413 +0,034 600 1879 —0,07 GOO 1652 +0,14 800 2312 — 1,03 800 2085 —0,07 1000 2465 0,38 '10 2. KEY: 1. n , \ N'sec/m^ Ethylene graph _ _, ^ ^ 3. Propylene^ The smooth data on the viscosity of gaseous ethylene at atmospheric pressure, presented in I. F. Golubev's review [13], have a mean deviation -104- of 0.3% from the recommended values; the maximum deviation is +2.25%. The smooth data on the viscosity of gaseous propylene at atmospheric pressure according to Lehman [21] deviate by 0.35% on the average if one clearly falling point is excluded from the examination (T = 373.15°K, n = 978 x X lO'^ N*sec/m^; n = -9.0%); the maximum deviation is 3.6%. The error of the recommended data (Table X) is 2%. Viscosity of Gaseous Ethylene and Propylene at High Pressures The viscosity of ethylene was measured by Comings, Mayland and Egly [8] in the 303.15 to 368.15°K temperature range at pressures up to 173.3 bar. A capillary viscometer of the Renkin design was used for the measure- ments. Fifty experimental points were obtained (see Table 52); the measurement error did not exceed ±1.3%. I. F. Golubev and V. A. Petrov [11] and I. F. Golubev [13] investi- gated the viscosity of ethylene with capillary viscometers of original design. These viscometers, in addition to ease of handling, provide high measurement accuracy. The error is of the order of ±(l-2)%. The authors [11] analyzed experimentally the viscosity of ethylene at 313. 15°K at pressures up to 137.1 atm (10 experimental points). Investigations [13] were conducted at 297 . 15-423 . 15°K at pressures up to 810.6 bar (76 experimental points). Data [11] for t = 40°C are presented below: p, arrxM p, ani.H 11-10-8 H 1 IC93 67,4 1620 4.4 1101 79,3 2030 28,2 1192 89,5 2500 48,6 1330 103,1 2980 55,5 1410 137,1 3790 Data [13] are listed in Table 53. The viscosity of gaseous ethylene at 297.15°K at pressures up to 1,000 bar was investigated by M. G. Gonikberg and L. F. Vereshchagin [23] (10 experimental points). Measure- ment was done with an oscillating disc viscometer; the dynamic viscosity coefficient was calculated with the Macwood equations [24] . According to the authors' calculations the measurement error did not exceed ±2%. Their data on the dynamic viscosity coefficient of ethylene are presented below: p. aniM T1- JO H-ceKl.^i- p, amM 100 3800 600 9-100 200 5500 700 10 160 300 G810 800 10 940 400 7820 900 11 710 500 8G20 1000 12 430 The viscosity of gaseous ethylene at 193 . 15-297 . 15°K at pressures up to 39.2 bar was investigated experimentally by I. A. Neduzhiy and Yu. I. a capillary Khmara [15] (Table 54). The investigations were done with viscometer with annular weights of the Timrot design. The measurement error was ±3%. -105- The experimental data found in the present literature can be used as the basis for comparing tables of the dynamic viscosity coefficients of gaseous ethylene to densities p = 490 kg/m^. The viscosity of compressed gaseous propylene was investigated experimentally by I. F. Golubev [13] at 291 . 15-523 . 15°K and 1-800 atm (96 experimental points). I. A. Neduzhiy and Yu. I. Khmara [15] experi- mentally found the viscosity of gaseous propylene at 210-310°K at pressures up to 8 atm. The experimental data [13, 15] are presented in Tables 55 and 56. These data can be used as the basis for comparing the dynamic viscosity coefficients of propylene to density p = 620 kg/m^ . The results of Enskog's theory [25] were used for explaining the question of reliability of the experimental data. s As pointed out in [26] , there are certain dependences of the effective diameters of collisions of molecules on temperature and pressure. Table 52, Experimental Data of Comings, Mayland and Egly [8] on Viscosity of Ethylene T, . 10—^. H-CCK/M' npH /, C p. am 30 50 70 95 1,00 1054 1074 1093 1172 1255 5,08 lOGO lOSO 1099 1180 1258 28,2 1131 1150 1192 1243 1295 48,6 1299 1306 1305 1336 1389 55,6 1406 1369 1362 1381 1426 67.3 1775 1592 1505 1474 1498 79,1 2545 2003 1721 1606 1589 89.3 3047 2483 1975 1736 1681 103.1 3592 2997 2396 1919 1818 137.0 4347 3203 2558 2265 171,0 2773 Table 53. Experimental Data of I . F. Golubev [13] on Viscosity of Ethylene 10—^. H-ctKiM^ npii /. p, arrxM 04 50 100 130 b, aniM 24 50 !00 150 1 1023 1108 1260 1403 150 4885 3670 2380 2150 25 1096 1175 1290 1470 200 5524 4380 3027 2600 50 1410 1310 1395 1560 300 6520 5380 4095 3415 60 1813 1400 1600 400 7323 6180 4863 4150 70 2820 15(.0 1500 1640 500 8090 6890 5440 4770 80 3357 1760 1575 1685 000 8S20 7560 6147 5330 90 3667 2004 1730 700 9440 8140 6713 5860 100 3906 2VH} 1734 1760 800 9950 8670 7255 6360 125 4420 3010 2040 1950 ~ i -106- I Table 54. Experimental Data of I . A. Neduzhiy and Yu. I. Khmara [15] on Viscosity of Ethylene 1 • 10— ^ H-ceKiM' npii 7". '-K - 193.15 213. i:, 233, 15 iV3 15 •.1 Ot ' o 297,15 f noo 695 1 o\ 808 868 949 IUJ3 4,90 799 835 898 968 1026 9,61 869 922 1009 1034 13,73 889 939 1021 1049 19,61 970 1045 J 069 24,52 1018 1074 1096 29,42 1099 1128 34,32 1175 1172 39,23 1273 1231 ." Table 55. Experimental Data of I . F. Golubev [13] on Viscosity of Propylene Tl • 10—8. H •cck/m' npH I. "O p, amM )8 53 85 100 150 200 250 „. , * , ,. 1 839 942 1032 1075 1212 1340 1468 25 10 6S0 1192 1312 1423 1530 50 11 IGO 7780 5140 2805 1.550 1547 1600 75 11 620 8280 5880 4970 2400 1853 1820 100 12 050 8700 6400 5500 3405 2294 2060 125 12 480 9080 6570 6030 4100 2782 2350 150 12 880 9440 7280 6470 4600 3280 2695 200 13 650 10 130 8030 7240 5440 4085 3380 300 15 100 1 1 460 9350 8520 6740 5330 4465 400 16 400 12 700 10 460 9050 7850 6350 5420 500 17 700 13 900 1 1 500 10 680 8770 7270 6300 600 18 940 15 000 12 300 1 1 620 9670 8055 7050 700 20 120 16 100 13 460 12 500 10 480 8S05 7740 800 21 300 17 100 14 400 13 370 11 250 9500 8450 The calculations were done for ethylene and propylene using the experimental data on viscosi'^.y [13] and data on density and thermal pressure, found from the thermal equations of state [27, 28], derived by V. A. Zagoruchenko. It is obvious from Figure 15 that the character of dependence of the effective diameters of collisions a on temperature is identical for all pressures, and the ratio cf/a^ (a^ is the effective collision diameter at atmospheric pressure) is constant at pressures above 100 bar. At pressures below 100 bar the ratio diminishes monotonically from unity at atmospheric pressure to 0.92 for ethylene and 0.93 for propylene. The observed scattering of cy/a^ is attributed to errors in the experimental data on viscosity and to errors in the determination of the thermal pressure. Since the scattering of points is asymmetric and falls within the limits of possible errors, it can be concluded that the experimental data of I. F. Golubev are reliable and that these data can be used as references for compiling tables of the recommended dynamic viscosity coefficients of compressed gaseous ethylene and propylene. The experimental data of -107- : I. F. Golubev and V. A. Petrov [11] agree with I. F. Golubev's data within the limits of deviations up to 3.5%. The data of M. G. Gonikberg and L. F. Vereshchagin [23] deviate from I. F. Golubev's data [13] by up to 10%. The experimental data of Comings, Mayland and Egly [8] for ethylene are 5-7% understated in comparison with I. F. Golubev's data at 300.15°K, and 5% overstated at 103.1 atm and 368.15°K. The experimental data of I. A. Neduzhiy and Yu. I. Khmara [15] on the 297. 1°K isotherm coincide with I. F. Golubev's data [13] to 0.5%. These data confirm the uniqueness of the excess viscosity as a function of density for ethylene at temperatures below critical. The results of the measurements of I . A. Neduzhiy and Yu. I. Khmara [15] for gaseous propylene agree satisfactorily (deviations up to 2% in conversion to the dynamic viscosity coefficient) with I. F. Golubev's data [13] in these coordinates. Table 56. Experimental Data of Neduzhiy and Khmara [15] on Viscosity of Propylene 1 lO'"'', H-CCKiM- Iipil r, "K p. Cap 210 230 250 270 290 310 0,98 586 640 736 800 828 904 ' 1.96 808 835 909 3.92 824 846 920 5.88 860 931 7.84 875 944 Experimental data [13, 15] were used for plotting the analytic dependence of "excess viscosity" of ethylene and propylene on density. The approximating polynomials were found by computer using the method of least squares All 2,20841 • 10=^p • = + 7.26137 KPo^ 7,63700 • + lO'V — 2.72752 lOy -f (61) + 4.68144 • lOV— 1,25904 • 10^; At] = 5,36654- lO'p — 4.49091 • 10^ + 4.41389 -lOy — (62) - 1.16544 lOy + 1,10455 • loy. where An = lO"^ N'sec/m^; p = 10^ kg/m^ Polynomial (61) describes experimental data for ethylene in the density range p = 0-490 kg/m^ with an average error of 0.6%. For the calculation 129 points were used. Polynomial (62) describes the experimental data for propylene in the density range p = 0-620 kg/m^ with an average error of 1.6%. The approxi- mation was done on the basis of 88 points. Polynomials (61) and (62) were used for compilation of Tables XI and XII of recommended viscosity. The error of the data is 2-3%. -108- " . i 6/6, • • 0,99 Ethylene Propylene o-/ ( s-2 0.97 e-7 < c *>'8 ®-J . » a-4 : s Q9S • < • > o > o a' 0,93 -- 1 !> 1 1 — \ > , e < > 1 1 ( > e c \ e a . oeo o < >~ 0.91 o o e • 1. 0.90 wo 200 300 400 500 600 700 p, dap Figure 15. Ratio cj/a^ for ethylene and propylene according to I. F. Golubev [13]: 1 -- 293.15; 2 -- 333.15; 3 -- 373.15; 4 -- 410.15; 5 -- 433.15°K (ethylene); 6 -- 370; 7 -- 420; 8 -- 440°K (propylene) Viscosity of Ethylene and Propylene on Saturation Curve Experimental works on the viscosity of liquid ethylene and propylene near the saturation curve are listed in Table 57. Studies [29, 31, 34] were done by the capillary method. Studies [30, 32, 33] were done by the oscillating cylinder method. The experimental values of the dynamic viscosity coefficients are summarized in Tables 58 and 59. Data in various source on the viscosity of liquid ethylene and propylene near the saturation line are either repetition of data [29-33], or are the result of smoothing of these data. It follows from Tables 58 and 59 that ethylene is experimentally (the point of investigated in the 105 . 0-289 . 9°K temperature range melting = 283.05°K); propylene ethylene T , = 104.0, and the critical point T^^ ^ melt cr . range (the melting is investigated in the T = 88 . 7-361 95°K temperature point of propylene T^^j^^ = 87.9 and the critical point T^^ = 365.05°K). Since the existing experimental data are contradictory and are characterized by substantial scattering, the possibility of constructing tables of the dynamic viscosity coefficients without additional informa- tion is doubtful at the very least. This situation is not exceptional. coefficients can be deter- As pointed out in [26] , the dynamic viscosity mined with sufficient reliability for several n-paraffins if, in addition to viscosity data, data on density of the liquid and saturation vapor -109- tension are used. The correlations obtained in [26] ensure an accuracy of the order of 2-4% in the calculation of the dynamic viscosity coefficients of n-paraffins in the liquid saturation state. Table 57. List of Experimental Works on the Viscosity Coefficient of Liquid Ethylene and Propylene near Saturation Curve n 31 4 )Co/iiiqecTBo ABTOptJ ion CMneparypa. "K r-rccncpHMeH- 7) PyACHKO [29] 1934 110,6—108,3 9 P>WHKo [30] 1939 169.3—280.3 6 Fept}), FajiKoi! [31] 1940 105.0—168,2 9 ra.fiKOB, Fepc}) (32) 1941 183.8—273.1 5 npoiiH^icH 8) 6) Fepc}), Fa^HKOB [31] 1940 88.7—169.6 12 Fa;iKOB, Fep(Ji [33] 1941 119.0—174,8 5 HeayjKHH, X.Mapa [34] 1967 193,9—362.9 34 KEY: 1. Authors Rudenko [29] 2. Year Rudenko [30] 3. Temperature, °K Gerf, Galkov [31] 4. Number of experimental points Galkov, Gerf [32] 5. Ethylene Gerf, Galkov [31] 6. Propylene Galkov, Gerf [33] Neduzhiy, Khmara [34] Table 58. Experimental Data on Viscosity of Liquid Ethylene T) . 10—6. H-CCKiM' ^^ K Tj • 10 ^, h-cck/m- PyflCHKO Fepcj), Fa.'iKOB 110,5 522 105,0 660 126.0 402 108.0 600 127,2 388 110.4 553 128.1 369 129.8 334 134.1 333 138.4 282 141,2 261 148.8 231 155.0 215 156.8 197 160.0 207 168.2 164 168,3 181 183.8 135 169.3 167 204.6 115 206.1 96 226,4 92.0 233.9 77,5 252.2 72,0 240.9 75 273.1 64,0 273.1 65 280.9 02,5 -110- . Table 59. Experimental Data on Viscosity of Liquid Propylene . 10-^ T.' TJ T, . 10—6 10-6 K K n . H • CeK/M' rep({;. ra;iKOB 1 ) 2) Hc;iy>KJu"i X.\:apa 291,57 99,9 291,94 88.7 14 660 193.92 278,6 99,8 292,19 89,8 12 730 198.09 264.2 92,2 294,86 90.) 12 400 202,53 238,2 93,7 297,45 94,3 7840 20S,92 219,9 91.7 98.0 299,33 89.0 5370 » 213,03 214,0 301,i;3 102,6 35S0 217,62 208,8 88,4 304,3 82.9 111.1 2150 221.50 197.3 307,36 82,4 141,6 700 229.37 179.4 311,48 78.7 141,9 670 233,12 173,4 315,43 76,2 150,0 550 237,68 162.4 159,8 • 450 242.07 155,9 315.61 74.6 169,6 340 246,35 148,0 329,07 63.7 119.0 1550 251.75 143.3 340.68 52,4 123,0 1310 259,14 132,5 354,23 43.6 134.2 900 265.54 123,6 173.0 380 281,48 105,1 355,21 42,8 174,8 370 291,57 93,98 362,86 32,7 KEY: 1. Gerf, Galkov 2. Neduzhiy, Khmara o IS B. 0-/ o 10 e-2 o-J ^ © 0 8- o o o e o jo S eS~ st-t-S— 0,^ OS .0,6 0,7 0,8 09 a d,% • o-J . J5 er- • '4 10 • 0-6 • 6 0 • 1 -s. OA o.s 0.6 0,8 0,9 '•I Figure 16, Deviations of experimental data of specific volume of ethylene (a) and propylene (b) from theoretical according to: 1 -- Mathias, Crommelin, Wotts [35]; 2 -- V. A. Zagoruchenko [27, 28]; 3 -- Voytyuk (see Chapters II and III); 4 -- Rossini [37]; 5 -- Lehman [21]; 6 -- Morecroft [38]. As applies to ethylene and propylene, it is essential first of all to check how accurately the experimental data on density agree with the theoretical according to equations [26] -Ill- The deviations of the experimental values of specific volume on the saturation curve from the theoretical are shown in Figure 16. As seen, the data of Mathias, Crommelin and Wotts [35] are up to 0.9-0.4% under- stated in the range of reduced temperatures from t = 0.45 to t = 0.80, agree with the theoretical from t = 0.80 to t = 0.90 and then increasingly exceed the theoretical. The saturation parameters of ethylene were calcu- lated by V. A. Zagoruchenko [27] and are presented in [36] . As seen in Figure 16, these data have the same deviations from the theoretical as data [35]. B. V. Voytyuk's experimental data (see Figure 16), obtained by extrapolating experimental data on the density of the liquid to the saturation curve, have a 0.2% deviation from the theoretical in the x = = 0.65 to T = 0.90 temperature range. At higher temperatures the experi- mental specific volumes systematically exceed the theoretical. And so, according to experimental data on the density of liquid ethylene on the saturation curve, calculation using equations [26] is justified within 1-1.5% for reduced temperatures t < 0.95, i.e., just as in the case of n-paraffins. The experimental data of Farrington and Sage [40] and the calculated data of Canjar, Goldman and Marchman [41] are generalized in Lehman's review [21] . The specific volumes of liquid propylene presented in this review are 0.05-0.6% overstated in the range of reduced temperatures from T = 0.45 to T = 0.71, and the deviations are not systematic; in the reduced temperature range of t = 0.71 to t = 0.90 they change sign and amount to 0.25-1.1%. At higher temperatures the data have a certain amount of scattering, but the deviations from the theoretical values are characteristic of n-paraffin. Morecroft's data [38] on the density of propylene are up to 0.35% overstated in the temperature range from t = = 0.75 to T = 0.88; at x = 0.95 the data are 1.3% lower than the theoretical. B. V. Voytyuk's experimental data are an average of 0.5% higher than the theoretical in the range from x = 0.50 to x = 0.75, and in the temperature range from x = 0.75 to x = 0.85 the deviations amount to +0.2%. For ethylene 3 = 0.5414, which is close to 6 = 0.5129 for ethane; for propylene B = 0.5953, which is close to 3 = 0.6145 for propane. These results enable us to proceed to analysis of the existing experimental data on the viscosity of liquid ethylene and propylene on the saturation curve and, in the final analysis, to calculate the dynamic viscosity coefficients. According to [26] the viscosity of liquid n-paraffins on the saturation curve is described by the expressions: [kp=cr] '^^v^"-^ ! (63) iKp = — 40.795T — 1 1 4,647t2 1 94.005x3 i 67,925t* / (t) 9.7404 + + + ^^^^ 4- 57.47lT^ -112- . where a = 0.3026 does not change with temperature; 3 is a constant in the reduced temperature range from (0.35-0.45) to 0.95; n* is calculated according to the Licht -Stechert equation [39], the applicability of which is demonstrated in [26] As seen in Figure 17, N. S. Rudenko's data [29, 30] on the viscosity of ethylene are up to 27% overstated in the low temperature range, satisfy the Bachinskiy equation with up to 6% scattering in the 155.0 to 240. 9°K temperature range, and are substantially overstated at higher temperatures. The experimental data of S. F. Gerf and G. I. Galkov [31, 32] on the viscosity of ethylene have the same character, with the exception that substantial overstatement of the data compared with the theoretical occurs at a lower temperature (226. 4°K). Nevertheless the character of the curve of the constant 3 as a function of the reduced temperature is noteworthy. Its values are close to 0.541, found from data on density (this value is shown in Figure 17 as a segment of a straight line, denoting the range of temperatures where the Bachinskiy equation is used) . The same conclu- sions concerning the character of experimental data [29-35, 40, 41] can be made on the basis of examination of the results of calculation presented in Figure 18. o~J e »-2 e-J • e g> 0.9 \ — •• • > o • o ' o o- Q7 [ V • , 0. • o • eo ; e aoo—r>0|i|— Ti^Jwr ^ 0-1 *«3!r-B }—V- 1 a • 4J £(2 0,3 0.5 0.6 0,7 0.8 0,9 Figure 17. Values of 3 in expression (63) according to: 1 -- N. S. Rudenko [29]; 2 -- N. S. Rudenko [30]; 3 -- S. F. Gerf and G. I. Galkov [31, 32] (ethylene); 4 -- S. F. Gerf and G. I. Galkov [31, 33]; 5 -- I. A. Neduzhiy and Yu. I. Khmara [34] (propylene). Experimental data [31, 33] on the viscosity of liquid propylene near the saturation curve are up to 32% overstated at 111.1°K; at lower temperatures a systematic increase of 3 is observed, characteristic of the region near the solidification point. In the 193. 9-363. 0°K temperature range the experimental data are given by I. A. Neduzhiy and Yu. I. Khmara [34]. -113- Figure 18. Values of functions f(T) in expression (64) according to: 1 -- N. S. Rudenko [29]; 2 -- N. S. Rudenko [30]; 3 -- S. F. Gerf and G. I. Galkov [31, 32] (ethylene); 4 -- S. F. Gerf and G. I. Galkov [31, 33]; 5 -- I. A. Neduzhiy and Yu. I. Khmara [34]. As seen in Figures 17 and 18, the data satisfy both equations (63) and the generalized relation (64) with a mean error of 2%. It follows from these data that in order to calculate the viscosity of liquid propylene on the saturation curve it is necessary to take 3 equal to 0.5953, found from data on density. The data of S. F. Gerf and G. I. Galkov [31, 34] at 141 . 9-174 . 8°K also support this conclusion. Thus, by comparing the experimental data on viscosity of liquid ethylene and propylene near the saturation curve we can conclude that the calculation procedure developed on the basis of analysis of the experimental data for n-paraffins, is also applicable to ethylene and propylene. This conclusion is also verified by the good agreement between the experimental data on the viscosity of ethylene and propylene at high pressures and the theoretical values for the saturation curve, if they are represented in the form of excess viscosity as a function of density. Tables of the recommended dynamic viscosity coefficients of ethylene and propylene in the saturated liquid states have an accuracy of the order of 3-5% and were compiled on the basis of equations (63) and (64) . The following critical parameters were assumed [26]: ethylene -- p^^ = 50.97 bar, v = 0.00474 m^/kg, T = 283.05°K; propylene -- p = 46.41 bar, v = 0.00433 mVkg, T cr ' f fj r^^j. ^' cr = 365.05°K. In view of the lack of experimental data on the viscosity of gaseous ethylene and propylene on the saturation curve we checked only the agreement with data [15] on the viscosity of compressed gaseous ethylene and propylene at temperatures below critical when we compiled the tables of recommended values. The recommended values were computed according to polynomials (61) and (62). The accuracy of the data is -3%. -114- Viscosity of Liquid Ethylene and Propylene at High Pressures The viscosity of liquid ethylene at high pressures was not investigated. Therefore to compile tables of recommended values we used the fact that in view of the uniqueness of excess viscosity as a function of density it is possible to extrapolate into the high-pressure region on the basis of iso- chors ; here we used the recommended dynamic viscosity coefficients of liquid ethylene on the saturation curve (Table IX) as the reference data. Extrapolation by isochors was done on the basis of thermal equation of state (36) for liquid ethylene, which was reported by V. A. Zagoruchenko and Tsymarnyy at the Third All -Union Conference on Thermophysical Properties of Matter at High Temperatures (Baku, 1968) . The results of calculations are presented in Table XI. The accuracy of the data is ~5%. The -viscosity of liquid propylene at high pressures was investigated by I. F. Golubev [13]. The measurement results are given in Table 55. We used these data to construct interpolation polynomial (62) , on the basis of which we compiled Table XII of recommended viscosities. -115- CHAPTER VIII. THERMAL CONDUCTIVITY OF ETHYLENE AND PROPYLENE Thermal Conductivity of Ethylene and Propylene at Atmospheric Pressure Experimental works pertaining to investigations of the thermal conductivity of gaseous ethylene and propylene at atmospheric pressure are listed in Table 60. The results of investigations are listed in Table 61. Eucken [1, 2] measured the thermal conductivity of ethylene by the relative wire heating method in an apparatus consisting of two measurement tubes of different length for compensating the heat losses from the ends. For air, used as the reference gas, = 237'10~'* W/(m*deg) at 273. 1°K at 1 atm. Eucken's data are the only data available for temperatures below 273°K. Lambert, et al [7], for determining the thermal conductivity coefficient of several hydrocarbon gases (including ethylene and propylene at 339.15°K) also used the relative (in terms of air) hot wire method, employing, like Eucken, a measurement cell with two wires of different length. The thermal conductivity of air was assumed equal to 289*10 '* W/(m*deg) at 339.15°K. The thermal conductivity coefficient was calculated by two methods on the basis of measurement data, showing agreement within ±0.5%. The deviations of the data from existing data on for certain hydrocarbon gases, according to the authors, do not exceed ±(2-3)%. The thermal conductivity of ethylene and propylene at 70°C was determined by Senftleben and Gladisch [3] on the basis of a relation containing the Nu, Gr and Pr criteria for determining the amount of heat transmitted through a layer of gas between two horizontal coaxial cylinders with different diameters. By altering the procedure somewhat Senftleben [5, 10] determined the thermal conductivity of ethylene and propylene at 20-200°C at nearly atmospheric pressure. Equations of the thermal conductivity coefficients as functions of temperature were derived on the basis of experimental data for ethylene: 10-" ?.o= 175- + 122,7- 10-'/ + 147,8 10"' (65) -116- ) for propylene: • 10-" 10"' ?to = 145,7 105,9-10-' / 180 • + + (66) where t is measured in °C and in W/(m*deg). Table 60. List of Experimental Investigations of Thermal Conductivity Coefficient of Gaseous Ethylene and Propylene at Atmospheric Pressure 1 ABTOpbl 3) .in ) 2) roa TcMneparypa. "K HeCTBO TOncK 7) 5 ) 3ni;ieH SiiKCH ( 1 1913 202—273 SiiKGH 3 (2) 1940 273 3cH(j)iv]e6eH h 1 Vjiajiuui [3] 1949 343 /leiiyap h Komhutc 1 [4] 1951 314; 340 ScH^JT^ieOen 2 [5] 1953 303 KcHC 1 |6) 1954 345; 426 JlaMfiepT 2 H ap. [7] 1955 339 MafiKHH H MapKCDHM 1 (8J 1958 293—523 6 Meynr h ap. {9] 19G2 591 I 3eH(})T/ie6eH (10] 1964 273—673 8 He;;yjKHH, Kpaaeu, Kojiomhcu [I, 1967 250—400 16 6) ripoiiii^ieii 3eii(})T;ie6cfi h fjiaflHUj [3] 1949 343 1 3en(i)T;ie6eH [5] 1953 303 1 JlaMfiepT H up. [7] 1955 339 1 3eHc})T;ie6eii [lO] 1964 273—673 9 HeAy>KHH, Kpaneu, Ko;/OMneu [llj 1967 273—400 14 KEY: 1. Authors Lambert, et al [7] 2 . Year Chaykin, Markevich [8] 3. Temperature, °K Cheung [9] 4. Number of points Senftleben [10] 5. Ethylene Neduzhiy, Kravets, Kolomiyets [11] 6. Propylene 8. Senftleben, Gladisch [3] 7. Eucken [1] Senftleben [5] Eucken [2] Lambert, et al [7] Senftleben, Gladisch [3] Senftleben [10] Lenoir, Comings [4] Neduzhiy, Kravets, Kolomiyets [11] Senftleben [5] Keyes [6] The values of given by equations (65) and (66) were extrapolated to 0, 300 and 400°C. The error of the published data up to 200°C, according to the author, is less than ±1%, and at higher temperatures it may reach 3-4%. A. M. Chaykin and A. M. Markevich [8] published six values of the thermal conductivity coefficient of ethylene at temperatures of 293.15 to 523.15°K. The accuracy of these data, obtained with the aid of a simplified glass model of the coaxial cylinders method without strict consideration of all required corrections, was estimated by the authors themselves as ±5%. -117- Table 61. Experimental Data of Various Authors on Thermal Conductivity- Coefficient of Ethylene and Propylene at Atmospheric Pressure 1) I) T, "K .10<, em/(M- epad) T. "K X,.10«, am/(,M-epad) 2) Shkch (l) 9) MaHKHH, MapKCBHM [8] 202.0 108 293.15 197 235,8 136 273.1 171 323.15 247 373.15 310 2) Shkch (2] 423.15 368 273.1 173 503,15 477 3) Jlenyap h KoMHHrc,[41 523,15 515 ' HeayjKHH H [llj 314.3 221 10) flp. 1 340.4 256 250 148 Keflc 4) (6) 260 159 345.4 267 270 170 425.7 391 280 181 J]aM6epT H 5^ ;ip. [7) 290 193 339,15 257 I 300 204 6) Meynr h ;ip. [9] 310 217 591.15 641 320 229 j 330 242 7) 3eH4)TJie6eH ii Vjiaauui (3J 340 255 343.15 265 I 350 269 360 282 8) 3eH4)T.ne6en [5] 370 296 303.15 209 I 380 310 8) 3eH(J)T;ie6eH [lOJ 390 325 273.15 175 400 340 298.15 206 323,15 240 423,15 392 473.15 479 573,15 674 673,15 904 riporiH.ieH 5) JIaM6epT H jp. (7] 10) He^y^HH H up. (Ill 339.15 219 273,15 150 280 157 7) 3eH({)T.ie6eH H r.iaaHui (3) 290 167 343.15 220 300 178 303,15 178 310 188 8 ) 3eH(j)T.i c6eH [10] 320 199 273,15 146 330 210 298,15 173 340 221 ' 323,15 203 350 233 373,15 270 360 245 423,15 345 370 257 473.15 431 380 270 573,15 624 390 282 673,15 854 400 295 [Key on next page] -118- . KEY: 1. ^n'lO"' W/(m«deg) 6. Cheung, et al 7. Senftleben and Gladisch 2. Eucken 8. Senftleben 7). I,enoir, Comings 9. Chaykin, Markevich [8] 4 . Keyes 10. Neduzhiy, et al 5. Lambert, et al One experimental value of of ethylene at 318°C is presented in the work of Cheung, et al [9], which pertains to investigation of the thermal conductivity of binary and tertiary gaseous mixtures by the coaxial cylinders method. Experimental data on the thermal conductivity of ethylene and propylene at atmospheric pressure are compared graphically in Figure 19. As follows from the figure, the data of most authors agree within 4%. The exceptions are Eucken 's point [1] at 202°K and the values obtained by A. M. Chaykin and A. M. Markevich [8] and by Cheung [9] , the deviations of which from the data of the other authors reach 8%. The limited number of experimental points complicates generalization of data on the of ethylene and propylene. For this reason we used the conclusions of Owens and Thodos [12] for the purpose of matching them up and correlating them. Owens and Thodos, by processing a large volume of experimental data on the thermal conductivity of various hydrocarbon gases and their derivatives at atmospheric pressure, discovered that the dependence of the thermal conductivity coefficient in logarithmic coordinates on the reduced temperature is expressed by a straight line with the same slope for all hydrocarbons and their derivatives, excluding cyclic. The authors thereby discovered the identical temperature dependence of X^ of these gases at atmospheric pressure (the mean deviation for 414 experimental points is 1 .6%) Here, Owens and Thodos used N. V. Tsederberg's generalized method [13] for representing data on the thermal conductivity of gases at atmospheric pressure in dimensionless coordinates. The critical temperature T^ and thermal conductivity corresponding to it X were used cr as the reduction parameters. A single common straight line was obtained in logarithmic coordinates for all the gases they investigated, and this line is described by the equation [kp=cr] (67) where n = 1.786. -119- Figure 19. Thermal conductivity coefficients of ethylene (I) and propylene (II) at atmospheric pressure as functions of temperature according to: 1 -- Eucken [1, 2]; 2 -- Lenoir, Comings [4]; 3 -- A. M. Chaykin, A. M. Markevich [8]; 4 -- Keyes [6]; 5 -- Lambert, et al [7]; 6 -- Cheung, et al [9]; 7 -- Senftleben, Gladisch [3]; 8 -- Senftleben [5]; 9 -- Senftleben [10]; 10 -- I. A. Neduzhiy, et al [11] (for ethylene); 11 -- Senftleben [10]; 12 -- Senftleben, Gladisch -- -- [3]; 13 Senftleben[5] ; 14 -- Lambert, et al [7]; 15 I. A. Neduzhiy, et al [11] (for propylene). By converting expression (67) to an equation of the form [kp=cr] ^Kp ^.Kp I T^Kp.' (68) and using X = 504. 5*10"'* and A = 184. 2 •lO"'* W/(m'deg), Owens and Thodos cr ^cr . derived a final equation for describing the thermal conductivity of ethylene as a function of temperature at atmospheric pressure: = . >^np = 0.364 t'-^* (69) -120- . , f We used equation (67) for processing data on the thermal conductivity of ethylene and propylene at atmospheric pressure, since equation (69) introduces hard-to-determine A cr In equation \ = A-t" (70) the constant A = X /T^ is calculated by the method of least cr squares on the basis of experimental data for ethylene (with the exception of data [8, 9]) and the power index is the same as in [12]. The result is the equation >^o = 0,775. 10-^ 7'''^. (71) where X^ is measured in W/(m'deg) and T in °K, as recommended for calculating the thermal conductivity coefficient of ethylene at various temperatures and atmospheric pressure. The deviations of the experimental values of the thermal conductivity coefficient of ethylene from those calculated using equation (71) are shown in Figure 20. The data of all authors coincide only at temperatures close to 273°K. As the temperature rises, the deviations increase. The greatest deviations are found in the data of A. M. Chaykin and A. M. Markevich [8] Cheung [9] and Eucken [1] at 202°K. Here the temperature dependence of these data differ substantially from the most probable, described by equation (71) The deviations of the data of the other authors from the theoretical do not exceed ±2%. Only the deviation of Senftleben's data of 1964 [10] reaches +3.8% as temperature increases to 673°K, which otherwise coincides with the accuracy specified by the author. The reference thermal conductivity coefficients of ethylene at atmospheric pressure [14, 15, 16, 17] were also compared. These data are contradictory and substantially understated: to -12% [14, 15]; from -5.8 to -32.7% at 273-1, 073°K [16], and from 3.3 to -23.6% at 223-1, 273°K [17]. Thus it can be affirmed that equation (71) describes in the 200-700°K temperature range the dependence of the coefficient of thermal conductivity of ethylene at atmospheric pressure on temperature with a maximum error of 4%. The actual deviations, however, should be considerably lower, since the experimental data of most authors [1-7, 11] agree within ±2%. When plotting the experimental data on the coefficient of thermal conductivity of propylene at atmospheric pressure on the graph (see Figure 19 and Table 61) what stands out most is the irregular temperature -121- . — r- • - • • • • • # ^ , » • e o-o——- T > A A-4( ^ —, e-5 o-/^ 200 300 ' ' TiOO sod 600 7^ Figure 20. Deviations of 6 = (X - X , )/A '100% of ^ exp theo theo^ experimental values of thermal conductivity coefficient of ethylene at atmospheric pressure from values computed by equation (71) according to: 1 -- Eucken [1, 2]; 2 -- Lenoir and Comings [4]; 3 -- A. M. Chaykin, A. M. Markevich [8]; 4 -- Keyes [6]; 5 -- Lambert, et al [7]; 6 -- Cheung, et al [9]; 7 -- Senftleben, Gladisch [3]; 8 -- Senftleben [5]; 9 -- Senftleben [10]; 10 -- I. A. Neduzhiy, et al [11]. path of the data of Senftleben of 1964 [10] . This indicates that as the molecular weight of the investigated gas increases, the accuracy of the Senftleben method decreases. Therefore the constant A of equation (70) was calculated for propylene only on the basis of the close experimental data of [3, 5, 11] The equation which we used for calculating the dependence of the thermal conductivity coefficient of propylene at atmospheric pressure on temperature has the form 10-' ?.o = 0,667. -T^-^"^. (72) Comparison shows that the experimental point of Lambert, et al [7] at 339. 2°K deviates from the theoretical curve by -0.5%. The data of I. A. Neduzhiy, et al [11] deviate from +0.5 to -0.4% as the temperature increases from 273 to 400°K. Senftleben's data of 1964 [10] are 6% overstated even at 400°K, and 14% at 673°K. The tabular values of the thermal conductivity coefficient of propylene given by Lehman [18] and presented in [17], as for ethylene, are substantially understated. The divergence of data [18] , calculated with the Eucken equation, is (+1 . 3) - (-10) % when the temperature is changed from 273 to 573°K. -122- . The deviations of the data of propylene, published in [17], are (-19.2)-(-13.S)% in the 223-1, 273°K range. I'hc recommended thermal conductivity coefficients of gaseous ethylene and propylene (Tables XI, XII) were calculated through equations (71) and (72). The accuracy of the data is ~4%. Thermal Conductivity of Ethylene and Propylene at High Pressures The thermal conductivity of gaseous ethylene at high pressures was investigated by Lenoir and Comings [14] . The investigations were done by the relative coaxial cylinders method on the 314. 3°K isotherm at pressures from 1 to 205.1 bar and on the 340. 4° K isotherm at pressures from 1 to 230 bar. Nitrogen, methane, carbon dioxide and helium were used as standard gases. To prevent convections the conditions under which the Gr-Pr product was less than 600 in all cases, were maintained in the experiments. The absence of convection was checked by changing the temperature difference in the gas layers. The thermal conductivity coefficients were not changed in the process. The error of the experimental data is from 1% at low to 3% at high pressures The experimental data of Lenoir and Comings [4] are summarized in Table 62. Table 62. Data of Lenoir and Comings [4] on Thermal Conductivity of Gaseous Ethylene ' 1 10«. p. Cap ) • ID*. em/(M- epaa) P. 6ap em/(M-epad) T = 314.3° K 7 = 340.4° K 1.01 222 1,01 256 19.6 241 21,7 272 41.9 277 50,5 313 60.2 339 62.7 336 83.6 530 89.3 434 104.4 659 104.7 492 124.7 729 131.3 590 146.9 794 163.1 698 166,3 850 206,0 801 179.2 884 229.0 845 205,7 967 The thermal conductivity of gaseous ethylene under pressure was also range. investigated by Keyes [6], but in a considerably narrower pressure The data were obtained by the relative vertical coaxial cylinders method at 345.4 and 425. 7°K: T = 345.4" K T - 425,7° X-IO*. em/(M-epad) p. Cap k-lO*. ernfiM-epad) Cap 0 267 0 391 10.5 274 5.0 394 15.7 281 9,0 399 -123- The error of the experimental data was not indicated. Keyes offers an empirical equation of calculating the thermal conductivity coefficient of ethylene at pressures up to 16 bar, derived on the basis of his own experimental data: ^ = ^^0(1 +0.75 . 9,7"/^), -f (73) where p is measured in bar and T in °K. The thermal conductivity of gaseous ethylene and propylene at 250-400°K and at pressures up to 40 bar was measured by I . A. Neduzhiy, V. A. Kravets and A. Ya. Kolomiyets [11] by the regular method with an apparatus with a spherical bicalorimeter (the diameter of the copper core is 41.50 ± 0.01 mm and the thickness of the gap for the investigated gas is 1.15 ± 0.01 mm). The inner core of the bicalorimeter was centered with the aid of a rigidly attached tube of special construction, made of a heat insulating material, through which differential copper-constantan thermocouple is soldered inside the core. The surfaces bounding the layer of the investigated compound were nickel-plated and carefully polished to minimize heat losses. The design features of the bicalorimeter, designed for investigation under pressure, necessitated the introduction of a number of correction factors, which are impossible to determine analytically. Therefore the relative method was used to investigate the thermal conductivity coefficient. The apparatus was calibrated on nitrogen using data [19], which made it possible to determine its constant at various temperatures and pressures. Particular attention was devoted to preventing convection. The tests were conducted under conditions such that the Gr-Pr product would not exceed 1,000. The reproducibility of X values within 0.5-1% at various temperatures and pressures was also evidence of the lack of convection in the investigated gas. The results of the investigation are summarized in Tables 63 and 64. Comparison of the thermal conductivity coefficients of ethylene at atmospheric pressure in [11] (see Figure 19) established that the deviation of these data and the data of Lenoir and Comings [4], Lambert, et al [7], Senftleben [5], does not exceed 1.5%. The data of Keyes [6], Senftleben [10] (1964) and especially of A. M. Chaykin and A. M. Markevich [8], Cheung, et al [9], deviate to a much greater extent from the data in [11]. Data [11] on the thermal conductivity of ethylene at high pressures agree satisfactorily (to ±1%) with the data of Lenoir and Comings [4], where they overlap; somewhat less satisfactorily with Keyes' data [6], which are somewhat higher than the data in [4, 11]. -124- ! 9 1 Table 63. Thermal Conductivity Coefficient of Gaseous Ethylene According to I. A. Neduzhiy, et al [11] III* pt uCp 250 260 270 2S0 '200 300 310 320 330 340 350 360 370 380 390 400 1 1 O 1 OA 1 O O A O AA O 1 A O j< A 1 148 159 1 / 0 19 j JO 1 217 229 242 255 269 282 29o 310 325 340 o o o OAT Oil O /I 1 2 149 160 171 20o 218 230 243 256 270 283 29/ 31 326 341 t "7 O O ^ A 4 151 162 173 184 19o 207 219 231 244 257 271 284 298 312 327 342 6 154 165 175 186 197 209 220 233 245 258 272 ZOO 300 314O 1 ,< 328 343 8 156 166 1 1/ 1S8 199 210 222 234 217 260 273 287 301 315 329 344 OO (J O A O 1 c 10 159 168 1 ( 190 20 1\ 212 224 236 248 261 274 288 302 316 3o0 345 O AA '} OO 12 162 171 181 192 203 21 ! 226 238 250 263 276 290 304 318 346 OA 1 O 1 A O OO 14 166 174 183 194 205 2)6 227 239 252 264 277 30 0 319 34o ono O O 1 OO c 16 169 177 186 197 208 218 230 241 253 266 279 30/ 321 o4y OO A 18 173 180 189 199 210 221 232 243 255 208 281 294 308 322 336 3ol 2J) 178 184 193 202 213 224 234 246 257 270 2S3 290 310 324 338 352 O AO O C < 22 178 189 196 205 210 22(j 237 248 200 272 285 298 312 326 340 354 Oi37 o -* o o c 24 195 201 208 219 229 2-tO _'ol JiS / 300 314 328 342 35o 26 z 202 206 213 223 233 243 253 264 276 289 302 315 329 343 357 28 213 218 228 237 246 256 207 279 291 304 3!8 331 345 358 30 220 223 233 241 250 260 270 281 294 307 320 333 347 360 32 230 238 245 253 263 273 284 296 309 322 336 349 362 34 237 243 249 257 266 276 286 299 312 325 338 35! 364 36 245 248 254 261 269 279 290 301 314 327 340 353 366 38 253 254 258 265 273 282 293 304 316 330 342 355 368 40 260 259 262 268 276 285 296 307 319 332 345 358 370 Table 64. Thermal Conductivity Coefficient of Gaseous Propylene According to I. A. Neduzhiy, et al [11] am/(x epao) iipii T. p. 6ap 273. 15 280 290 300 310 320 3:,o 340 350 360 370 380 390 400 1 150 157 167 178 188 199 210 221 233 245 257 270 282 295 2 152 159 169 179 189 200 2ll 223 234 240 259 27] 284 297 4 156 163 172 182 192 203 214 226 237 249 262 274 286 299 6 167 176 186 190 207 217 229 240 252 204 276 289 302 8 181 190 200 211 221 232 243 255 207 279 292 304 10 195 205 215 224 235 246 258 270 282 295 307 12 210 220 229 239 249 262 273 285 298 310 14 216 220 233 243 253 2(j5 277 288 301 313 16 232 239 248 258 269 280 292 304 316 18. 245 254 204 274 285 290 308 320 20 254 261 270 279 290 301 312 323 22 264 270 278 285 290 307 317 327 24 281 287 293, 302 312 322 332 26 292 296 301 309 318 328 336 28 306 310 317 325 334 341 30 320 325 332 340 3.10 32 330 333 339 340 352 34 341 312 34H 352 358 36 352 351 353 358 304 propylene at Comparison of data [11] on the thermal conductivity of the experi- atmospheric pressure shows an error of ±0.5% in relation to not support Senftleben's mental point of Lambert, et al [7]. Data [11] did results of the latter works are +(3-14)-o. data [10] (1964). Deviations of -125- At higher pressures, in view of the lack of other experimental data on the thermal conductivity of propylene, we did a comparison with the diagram proposed by Owens and Thodos [12] for ethylene, illustrated in Figure 21. The pseudocritical thermal conductivity of propylene, calcu- lated on the basis of data at atmospheric pressure, is = 690 x X lO"'* W/(m*deg). The deviation is 0.5-2.5%, which indicates the reliability of the data obtained for the thermal conductivity of propylene. Figure 21. Reduced ethylene thermal conductivity diagram of Owens and Thodos [12]. The authors used the following: T = 282. 4°K, p = 50.66 bar, X = 504. 5*10"'* W/(m'deg). cr ^cr cr The limited number of experimental data on the thermal conductivity of ethylene and propylene, encompassing a narrow range of parameters, cannot be used directly for compiling tables of the thermal conductivity coefficients of these compounds without involving calculation methods. -126- Figure 22. Excess thermal conductivity AX = A - as function of density according to: 1 -- Lenoir and Comings [4]; 2 -- Keyes [6]; 3 -- Ye. Borovik, et al [20]; 4 -- Ye. Borovik [21]; 5 -- I. A. Neduzhiy, et al [11]. no Figure 23. Excess thermal conductivity of propylene as function of density according to I. A. Neduzhiy, et al [11]. - When the coordinate system AX = (X X^) , p is used for generalizing the experimental conductivity coefficients, the experimental errors obey the simplest law in the widest range of parameters and are described by a curve that is common to the gaseous and liquid states. -127- . A uniparametric dependence of excess thermal conductivity on density is used in the vast majority of cases, since the question of deviation from it has not yet been answered for thermal conductivity near the critical point and near the saturation curve. Experimental data [4, 6, 11] for gaseous and [20, 21] liquid ethylene are presented in Figure 22 in the form of excess thermal conductivi as a function of density; data [11] for gaseous propylene are given in Figure 23. The dependences of excess thermal conductivity on density are approximated by computer by the method of least squares using orthogonal polynomials For ethylene is derived the equation . 10^ • • • ]0~^ AX - 0,5358 p 0,9365 — 0,6809 • + 10"V p' -f- 10-* -p*- 10"' 0,3635. • + 0,1056 • p^ + 0,1550 lO"" -p' — (74) 10~'^ — 0,8634 . p^ which is valid in the 0-650 kg/m^ density range; for propylene AX . 10* • • • = -0.984 + 0,8270 p + 0,3419 lO"' p2 + 0,1406 • lO"" • p^ — 10"' ^"^^^ — 0,1374 • • pS which is valid in the 2.5-80 kg/m density range. The recommended thermal conductivity coefficients of gaseous ethylene computed using equation (74) , are presented in Table XI for T = 180-450°K and p = 1-3,000 bar. Considering the good agreement between the experi- mental data of various researchers, obtained by various methods (see Figure 22) and the validity of the reference curve AX = f(p), it can be assumed that the error of the tabular thermal conductivity coefficients of ethylene is ±2 to ±6%. Data on the thermal conductivity of gaseous propylene, computed by equation (75), are presented in Table XII and encompass the 300-450°K temperature range and 1-50 bar pressure range. The reduced diagram of thermal conductivity for ethylene can be used for determining the thermal conductivity of propylene at pressures above 50 bar (see Figure 21) . The pseudocritical conductivity of propylene is XJ^ = 690* lO'"* W/(m»deg). Comparison of the data in Table XII with the reduced diagram shows agreement within ±2.5%. -128- Thermal Conductivity of Liquid Ethylene Experimental data on the thermal conductivity of liquid ethylene are presented in [20, 21] (no data, are available for propylene). Ye. Borovik, A. Matveyev and Ye. Panina [20] used the hot wire method for studying the thermal conductivity of liquid ethylene. They used two vertical measurement tubes of different length, made of copper, to prevent end losses. All measurements were done with different temperature drops between a filament and tube wall, not exceeding, however, 0.5-1 deg, to prevent convection. The pressure of the investigated compounds was maintained a few atmospheres above the saturation vapor pressure at the test temperature. The thermal conductivity measurements encompass a wide range of temperatures. The extreme measured points are 8.7 and 9.6 deg, respectively, from the melting and critical points. The experimental data are presented below T, °K X, W/(m'deg) 112.65 0,254 144.15 0,222 172,15 0.184 199,15 0,156 244,35 0.126 273,45 0,080 The errors of the data are ±2.6%. Borovik [21] measured the thermal conductivity of liquid ethylene at 171.25°K using the parallel plate method, which creates the best condi- tions for the prevention of convection. The temperature in the instrument was measured with calibrated resistance thermometers. The measurement error was 1% for points far from the critical and up to 3% near the critical point. The temperature drop in the tests was 0.3-3 deg. The thermal conductivity coefficients of liquid ethylene at 171.25°K and 4.97 and 52.99 bar, were found to be 0.182 and 0.185 W/(m'deg), respectively. Data [20, 21] on the thermal conductivity of liquid ethylene, obtained by two different methods, agree satisfactorily, which confirms their reliability. IX Data [20, 21] were used for derivation of equation (77). Tables and XI of the thermal conductivity coefficients of liquid ethylene, including the liquid saturation state, were compiled with the aid of this equation. The accuracy of the data is ±(3-6)%. -129- ; V PART II TABLES OF THERMODYNAMIC AND TRANSPORT PROPERTIES OF ETHYLENE AND PROPYLENE Units of Measurements Used in Tables Temperature, T, °K; Pressure, p, bar; Specific volume, v, m^/kg; i, kJ/kg; r, kJ/kg; s, kJ/(kg'deg) Specific heat C^, kJ/(kg*deg); Speed of sound, w, m/sec; Viscosity, rij N»sec/m^; Thermoconductivity , X, W/(m*deg). -130- > . . • • ^ lO Ol f t-» o to o oo lOcOOiOC^OOiOOOO 05 0)0 o — — CS CO o CO s COOO — t^cDOOt^OO) CO CO in tOr-COCT)OCMrT't~~C^ICr) CM CM CM CM CM CM CS CS CS CM CM CM CM CM CM CS CS CO co" CO" CO* • CT> O lO CS o 00 00 o — CO — CO co O) csomr-~oooocO'>*'ro CO O 00 lO CSCDin- . — COTTCDLOCJiO O C7> CT) 00 CO in es — f • oo OtOCOOtJJOO — COOOCTi—'CO in CM CT> in — h". 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