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The Thermodynamic Properties of Nitrogen from 64 to 300* K Between Lonal Bureau of btaudaj a.^ Lilarary, M.W. Bldg JUIV 6 1962 PB 161630 ^ecknlcciL ^^ote 129 THE THERMODYNAMIC PROPERTIES OF NITROGEN FROM 64 TO 300^ K BETWEEN 0.1 AND 200 ATMOSPHERES THOMAS R. STROBRIDGE U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the na- tional standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,- devices, and structures; advisory services to government agen- cies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Reseeirch projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's research are published either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bureau itself publishes three periodicals avail- able from the Government Printing Office: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio communications throughout the world. There are also five series of non- periodical publications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications, and Technical Notes. A complete listing of the Bureau's publications can be found in National Bureau, of Standards Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 ($1.25), and the Supplement to Na- tional Bureau of Standards Circular 460, July 1947 to June 1957 ($1.50), and Miscellaneous Publication 240, July 1957 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) ($2.25); avail- able from the Superintendent of Documents, Government Printing Office, Washington 25, D. C. NATIONAL BUREAU OF STANDARDS technical ^^ote 129 JANUARY 1962 THE THERMODYNAMIC PROPERTIES OF NITROGEN FROM 64 TO 300.« K BETWEEN 0.1 AND 200 ATMOSPHERES Thomas R. Strobridge Cryogenic Engineering Laboratory NBS Boulder Laboratories NBS Technical Notes are designed to supplement the Bu- reau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. They are for sale by the Office of Technical Services, U. S. Depart- ment of Commerce, Washington 25, D. C. DISTRIBUTED BY UNITED STATES DEPARTMENT OF COMMERCE OFFICE OF TECHNICAL SERVICES WASHINGTON 25, D. C. Price $2.25 CONTENTS Page List of Figures Iv List of Tables iv Abstract 1 Introduction 2 Symbols 2 Values UsecJ for Some Physical Constants and Conversion Factors 3 Vapor Pressure 3 Density of Saturated Liquid 4 Specific Heat of Saturated Liquid 5 Specific Heat at Zero Pressure 6 Data of State 6 Derived Properties 10 Acknowledgement 14 References 15 lil LIST OF FIGURES Figure Page Figure 1 Comparison of experimental and calculated second virial coefficients 9 Figure 2 Regions of different calculational procedures 10 LIST OF TABLES Page Table 1 Corrections for entropy of vaporization 13 Table 2 Thermodynamic properties of nitrogen at saturation 17 Tables of thermodynamic properties 18 iv THE THERMODYNAMIC PROPERTIES OF NITROGEN FROM 64 TO 300°K BETWEEN 0. 1 AND 200 ATMOSPHERES iby Thomas R. Strobridge ABSTRACT The internal energy, enthalpy, entropy, and specific volume of molecular nitrogen are derived and tabulated as functions of temp- erature and pressure. In addition to a mathematical model for the pressure -volume-temperature surface, accurate fujictions are given for the representation of the vapor pressure, density of saturated liquid, specific heat of saturated liquid, and the specific heat at zero pressure. Tabxilar values in British units over the same pressure and temperature range are available as Supplement A of this Technical Note. 1. INTRODUCTION Cryogenic process calculations involving molecular nitrogen as a refrigeration medium require a continuous set of da-ta over a wide pressure and temperature range. Such data in tabulated form suitable for digital computer use are not available in the literature. Experi- mental data from the literature were correlated and analytical expres- sions for the representation of certain properties were derived. These expressions were then used to generate tables of values of internal energy, enthalpy, entropy, and specific volume as functions of pres- sure and temperature. 2. SYMBOLS R - Gas constant in liter atm/gn:i-inol°K P - Pressure in atmospheres T - Temperature in degrees Kelvin V - Molar volume in liter/gnm-mol. P - Density in gm-mol/liter PV - Compressibility factor, RT . u - Internal energy. H - Enthalpy S - Entropy OK - Degree Kelvin °C - Degree Celsius T - Tenaperature at saturation at 1 atm (77. 364*^K) o - Coefficients for vapor pressure h' h kj. ^2 - Coefficients for density of saturated liquid - Coefficients for specific heat of saturated liquid 'v 'z m^ "^2 - Coefficients for specific heat at zero pressure ^' "2 - Coefficients for model of PVT surface in - Natural logarithm Subscripts sat - Saturated liquid state p - Constant pressure - p Constant density or a state at density p T - Constant temperature or a state at temperature T V - Constant volume vap - Vaporization Superscript o - Ideal gas state or zero pressure 3. VALUES USED FOR SOME PHYSICAL CONSTANTS AND CONVERSION FACTORS R = 8. 20574 (lO"^) liter atm/gm-mol°K 6 / 2 1 atmosphere = 1. 013250 (10 ) dynes/cm 0°C = 273.15°K Molecular weight of Nitrogen = 28. 016 -3 1 joule = 9.86896 (10 ) liter atm 4. VAPOR PRESSURE An accurate representation of the vapor pressure -temperature relationship from the triple point to the critical point was needed for interpolation between experimental data and for obtaining the deriva- dP tive, ~J7^ > along the two-phase boundary. Experimental values for the critical pressure and temperature have been published by White, Friedman, and Johnston [ 1951 ] . Armstrong [ 1954] , and Friedman and White [ 1950] have published vapor pressure data which, when combined, extend from the triple point up to within 1 K° of the critical temperature. These sources of data were chosen from those available because of the apparently reasonable agreement in temperature .scales used and the consistency of the three sets of data, A total of 91 points was then available for consideration. The constants for (1) were foiond by the method of least squares [ Jones, 1962] . Log^QP(atm) = j^ + j^/T + j^T + j^T^ + j^T + j^T + J^T^ (1) where j 5.27805 (10""^) \ = 2.9857103 (lO"^) 1 5 j^ = -3.0507339 (10 ) j, = -1.4238458 (lO"^) 6 j„ = 1. 6441101 (10"S \ = 2. 7375282 (lO"'^^) (10" J. -3. 1389205 ) Armstrong [ 1954] gave an equation which represented his data with a mean absolute deviation of 0. 063 mm Hg. The agreement between (1) and the Armstrong data is excellent; the mean absolute deviation is 0. 061 mm Hg. Equation (1) more closely represents the data of Friedman and White [ 1950] than an equation given in their paper except at one observed point. The critical point (126. 26 ± 0. 04°K and 33. 54 ± 0. 02 atm) according to White, Friedman, and Johnston [ 1951 ] is approximated by (1) within the estimated errors. The temperature of the normal boiling point (77. 3640 + °K) predicted by (1) agrees to five places with the figure given by Armstrong [ 1954] . 5. DENSITY OF SATURATED LIQUID The functional form of (2), which may be used to represent the density of saturated liquid, was suggested by Hou and Martin [ 1959] . (gin-nnol/j^) P , = k + k X + k X +k x +k x (2) sat i c. J 4 5 1/3 where x 1 and 126. 26 .1 k 1. 1230207 (10*) k. = 2. 7790397 (10 ) 1 2. 1082073 (10^) = -1. 1764704 (loS -9.8177403 Equation (2) was fitted [Jones, 1962] to the data of Mathias, Kamer- lingh Onnes, and Crommelin [ 1914] with a maximum error of 0. 85%. With the exception of two points the agreement with the data, which extend almost from the triple point to the critical point, is better than 0. 13%. A deviation plot shows that the largest differences are near the critical point. The experimenters remarked that the greatest experimental difficulties occurred near the critical and that there is a larger uncertainty in the data in this region. 6. SPECIFIC HEAT OF SATURATED LIQUID The available experimental data (65, 02 to 116. 99°K) on the specific heat of saturated liquid appeared to be of the lowest accuracy of the various types of data considered. The differences between (3) and the data of Giauque and Clayton [ 1933] and of Wiebe and Brevoort [1930] are in some instances almost 2%. There is not, however, any significant trend in the deviations which, if present, would indicate an unsatisfactory form for (3). 2 3 ^ (3) Sat^j/§"^""^°^^ 2 2 3 4 5 ^ (126.26-T) where S. 6. 246881860 i, = -\. 052432772 (10 ) 4 3.939006895 (10) 6. 001046981 (10"^) 6.
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