Journal of Research of the National Bureau of Standards Vol. 58, No.5, May 1957 Research Paper 2760
Thermal Conductivity of Nitrogen from 500 to 500°C and 1 to 100 Atmospheres*
R. 1. Nuttall! and D. C. Ginnings
A new apparatus has been constructed for measurements of the thermal conductivity of gases up to 500°C and 100-atmosphere p ressure. The parallel-plate m ethod was used with a spacing of about 0.5 millimeter between the hotplate and coldplate. A capacitance method was used to measure the effective spacing and area of t he plates under the conditions of the experim ent. No solid material was used bet,,'ecn the plates. The e ffect of radiation was minimized by use of polished s ilver parts a nd I\"aS accounted for by experiments with the conductivity cell evacuatcd. ~1ea s ure m e llt s on nit roge n were made at J, 50, and 100 atmospheres, and from 50° to 500°C. It is beli el'ed that. the accuracy of the r esul ts is about 0.5 percent, except at the highest gas densities.
1. Introduction T he correction for heat transfer by radiation between t he hotplate and the coldplate was evalu ated Accurate data on the thermal conductivity of gases by an experiment with the condu ct i v i t ~ · cell evacu are needed for two reasons. First, they arc needed ated. Of course, this assumes t hat no appreciable to check present theories of heat conduction in gases. part of t he radi ation is absorbed b.\- tll e gas in the Experimental measurements at very hi gh tempera co nduetivi ty experimen t. III all Lhe experiments, it tures and pressures arc ext r e m el~T diffi cult, so that was neC'essary to know t he efrective spaC'i ng between theoretical means of predicting thermal co ndu ctiv t he plates. Frequently, solid spaC'ers (of known ities in this range arc needed. Second, accurate data dimel1 sions) are used between t he hotplate and cold are needed on at least one gas so t1tat engin eering plate. Ko su ch spacers were used in this apparatus data on other gases can be obtained with relatively because it was bel ieved that the heat transfer simple apparatus by a comparison method. The t hrough t he contaC't area of t he spacers and plates present apparatus was co nstructed primarily to fur might be d ifferent with gas present than with the nish very accurate data for use as standards by C'ell evacuated. The radiation correction experi· others making thermal-co nductivity measurements mrll t would thu s be partially invalidated. The on gases. Nitrogen was chosen as the first gas to effeC'Live spacing was m easured by a capaci tance be measured for several reasons. ~l ore measure method under the actual cond itions of the experi · ments have been made on nitrogen than 0 11 any other ment. T hi s method has several advantages over the pure gas. It is readily available in a state of high usual method with measurecl spacers. F irst, the purit~- and is entirely sui table as a standard reference above-m entioned uncertainty in t he effect of contact gas for use in calibrating apparatus for relative is eliminated. Second, t he capacitanC'e method measuremen ts. au tornatically accot! nts for an ~- change in dimensions. Third, because the direct capacitance between the 2. Method hotplate and. coldplate is measured, nonli near hrat fl ow at the C' irC' umferrnce of the hotplate is accounted. ~Iea s uremen ts of thermal co nductivi ty of gases for. in a steady state have been made by two general The thermal C'ol1ductivity, k (w C'm - 1 deg C-l) , for methods, radial heat flow and linear heat flow. ll eat flow between parallel plates is given by the ~Io st measurements have been made with radial equation heat flow, either from a hot wire or between coaxial cylinders. In principle, these measurements are S llS (1) ceptible to co nvection errors. Elimination of these errors aL the high pressures requires extremely small dimensions, which may be difficult to determine. where Q is the rate of heat (walts) flowing only b~ The linear heat flow method is free from co nvection C'onduction from the hotplate throug'h the gas to lilr if the heat flow is downward . For this reason, the colclplate, t:..t is t he temperature . difference ( de ~ C) parallel-plate method was chosell for these measure between t he ho t pla.te and C'oldplate, t:..X is the ments up to 100 atm. The spacing between the effective distance (cm) betweell the two plates, 9,nd plates was made small to minimize the errol' caused A is the d l' ective area (cm 2) of t he ho tplate. The by radial heat transfer. In addition , the small spac fa.ctor t:..X/A may be considered as the constant of ing reduces the possibility of convection in case the t he "C'ollducLiv ity cell" determined b.\- lhe capfLci plates are not quite horizontal. tanC'e method, so that
*rphi s work was supported in part by t he National Advisory Committee for 0.0885516Q A l1fonau tics. k (2) I Pn'Sf'llt address },ryonnc Nationa l Laboratory, Lemon t, ]11 . Ct:..t ' 271 wh ere C is the direc t capaci tance (micl'omicrofarads) between the hotplate and t be cold plate, assuming the material between the plates to have a dielec tric cO llstant of unity corresponding to a vacuum. "Vith ~ Aluminum the gas between the plates, a small correction must be made for its di electric constant. The conduction ~ Stainle ss Steel equation (2) would apply, of course, to an~~ two surfaces, as well as to parallel plates, provided only BlSilver that the temperature and electric fielcls arr geo metrically similar.
3. Experimental Procedure
3.1. Apparatus 1W0flf.- --- C The general assembl~~ of the tllermal-condu<:tivit.," cell, the pressure vessel, and the surrounding furnace is shown in figure 1. The hotplate (H ), coldplatr (J), guard (F), and auxiliary guard (E) are showll schematicall.Y . The pressure vessel (G) is made of stainless steel and is sealed with a Monel gasket (D). ~§~~;;J_F This vessel is surrounded by a furnace (K) and H~~~~~H furna,ce "neel,," (C), which are made of aluminum and are equipped wit h electric heaters ill numerous K porcelain tubes in the aluminum. The furnace temperature was au to maticall~~ controlled b~T means of a plati num resistallce thermometer n.nd bridge circuit. The furnace neck was controlled r elative to the fmnace b.,- means of a thermocouple. The pressure vessel extends upward out of the furnace region so that t he electric leads can be brought out of t he pressure vessel in a cold r egion. The cooling o 2 4 INCHES coil (B) dissipates the heat from the furnace, so that I I I t he top is cool. The eleetric leads (all No. 32 gold F I G(;RE 1. Thermal-conductivity apparatus. wire) ar e brought up from the a uxiliary guard A, Pressure seal for electric loads; B , cooli ng co il ; OJ furnace neck; D, wIonel through t hree 1n conel tubes, which serve as electro g~s kc t; E, auxiliary guard; F, guard; G, pressure vessel; H , hotplate; J, cold p late; static shi elds, as described later. There are 29 of ] ..... , fu rnacc. th ese leads, which are brought out of the pressure vessel through a pressure seal, A. These leads go A out radially between two " Kel-F" (polychlorotri fluorocthylene) disks, which are pressed together for the seal. A number of difficulties were encountered before obtaining a successful seal at A. At first, the material T eflon (polytetl'afluOl'o ethylene) was used, o --t<:~~+--.... but it was found to flow excessively at the high E ---+;>~' pressures necessary for th e seal. The method finallv used for this seal was to mold Kel-F around 0 the gold wires at about 200 C. G The vital parts of the the rm al- co ndu ct ivit~ - eell al'e shown in fi gure 2. The hotplate (':'1 ), coldplate (0 ), guard (E), and auxiliar:v guard (B ) are all made of silver to minimize temperature gradients and h eat transfer by radiation. The hot plate is made of three parts, silver-soldered together. The hotplate heater (L) is located between the lower parts and consists of about 55 ohms (at 25 0 0 ) of (0.05-mm diameter) o 0.5 1.0 INCHE S platinum wire insulated with mica. Gold leads I from this h eater are brought out through the tem FIGURE 2. Thermal-wnductivity cell. pering region located at H between the upper two A, C, V', H , P, '"!"'hermal tic·downs for electric leads; B, a l1 xiliar~.r guard; D. Q. silve], pieces of the hotplate and then to the therma.l platinum resistance thermometers; E , guard; OJ silver screw; J . quartz supports for hotplate; K, aluminum insert; L, hotplate heater; ::V[ , hotplate; X, quartz tie-down, F. The purpose of this thermal tic-d own spacers; 0, coldplate. . 272 is to bring the leads as dose as possible to the tem hotplate b:," m eall S of the differential tllCrmopile pre peratUl'e of the silver. This type of t ie-down IS used viously m ent ioned. This t emperature co utrol was extensively throughout the apparatus and consists the most important; it maintained cO ll stanc:'" of of a gold terminal insulated bet wee n thin mica disks temperat ure to about 0.001 deg C. The auxilialY and held down t o the silver by a nut threaded OJI a guard was maintained at the same temprrat ul'e as madline screw. The gold terminal is spaced aroulld the guard b:," a single differential thermocouple. As the scr ew so that it is ins ulated from it. a result of the effe ctiveness of the thermoregulation The hotplate is supported by the guard ring at in the thermal-conductivity apparatus, all the ob three points, using quartz supports (J ), so that the servations 011 the thermal condu ct ivit~ " of nitrogen bottom plane of the hotplate is ill the same plalle as were made b:v one person. Both the ele ctric power the bottom of the guard ring. Because the co in the hotplate heater and the thermocouple readings efficient of thermal expensioll of quart z is lower than were observed with a precision potentiometer. t bat of silver, an aluminum inser t (Ie) having a A capacitance bridge was used to measure toe high er coefficient tha n quartz was used with the capacitance between the ho tplate and the coldplate. quartz for compensation. The quart z is held tightl:l" This bridge permitted the accurate m easurement of against the hotplat e by the silver screw (0) pressing small direct capacitances, even t hough relativelv against the aluminum inser t . The guard (E ) sur large capaci tances exist betwee n the "ground" and rounds the hotplate, except where it is exposed to the plates. To eliminate, as far as possible, enol'S of t he coldplate. III the vital region near the cold m easuremell t in capacitance, a calib rated capacitor plate, the guard is spaced about 0.5 mm from the having about the capacitance of the thermal-con h otplate. The assembl.'T of th e guard and hotplate ductivit.v cell (about 10 f.i./.d ) was used as a refer ence is held about 0. 5 mm from the cold plate b.," three and the measurements made bv a substitution quartz spacers (N) between th e guard a nd coldplate . m ethod. III t his measurement, the same internal In this region, the sil ver was highly polished to eapacitall ce to groun d was kept in the bridge circuit, reduce heat transfer by radiation. H eaters ( L1 ot so that the capacitance measurement approached shown) are installed in both th e guard aud coldplate. very closely to the ideal comparative measurement, The temperatures of the guard a nd coldplate are givill g an accuracy comparable with the accurac.,- of measured b:v using the platinum resistall ce ther tlte calibrated capaeitor. Much care was ta ken to mometers (D ) and (Q ), respectivel.I", in conjullctiolJ avoid significant capacitall ce betwee n the le ads from with a Mueller bridge . These strain-free ther the hotplate and eoldpla.te. The.,~ were effectively mometers are not scaled. All leads (gold ) from shi elded from ea.ch other b~ ' bringing leads out these two thermometers arc t hermall v ticd dow n at through sep~rat e grounded Incollel tu bes a nd by C and P , respectivel:I', so that the temperatures of proper locatIOn of th e leads t hat pass through the the platinum res istance th ermometers a rc not pressure seal. affected by h ea"t co ndu ction along th e leads. The For the measurement of the pressure of t he ga.s in temperature differellce between the guard a nd hot the co n~u ct i v i t.v.ce Jl , cal.i.brated Bourdon l;iages ,\"ere plate is determined by means of a multiple-junction used. 1: he r eq LUremell t for accurac.'T Oil tJlCse gages thermopile, using fo ur 1\0. 36 Chromc1 P-Alumel was not great because t he variation of thcrmal co n t hermocouples in series. This thermopile has one ductivity wit lt pressure was much smaller than t hc se t of clectricall:I' ins ulated j ulletions at F on t.he change with temperature. hotplate and t he other set at C on the guard. Experiments indicated tlte clesirabiIit:v of providing 3.2. Purity of Nitrogen a nother thermal tic-down zo ne for all electri c leads before they go out from C to the cold region. For The lli trogell used was extra-dry high-purity, this purpose, the s ilver auxiliary guard (B ) was used obtain ed from the Linde Air Products Co., who II"itlt a heater built in to provide the bulk of the heat stated that impurities did not exceed 100 ppm. flow up along the electric leads. All three silver Cryoscopic measurements made by O. F . Furukawa pieces, (B ), (E), and (0 ), are held toget her b,'~ long at the N a.tional Bureau of Standards with an adia machine screws fastened in the bottom of the sur batic calorimeter showed liquid-soluble solid-in rounding press ure vessel. These four pieces are all solubJe impurities to be about 10 ppm. The conduc electricall,- insulated from one another. tivity cell was filled with this nitrogen, which had The eA:ective operation of the thermal-co nductivity been passed through a sili ca-gel dryer a nd a filter a pparatus depended upon th e proper temperature made of glass wool. co nt rol of the various components. For this pur pose, five automat ic thermoregulators were used to 3 .3 . Procedure cont rol the temperatures of the coldplate, guard, a uxiliar.\T guard, fUl'nace, and t he furnace neck. The general procedure was to set the furnace co n These thermoreg ulators were actuated by thermo trols to the desired temperature, fill the conductivity couples or res istance thermometers (not the meas" cell with gas at the desired pressure, and put in a uring resistance thermometers), a nd they consisted chosen electric power in the hotplate. "With the eold essentially of "chopper-amplifiers" operat ing satur plate automatically regul ated to a constant tempera able reactors in th e heater circuits. The guard was ture and the guard temperature automaticall y (,O ll maintained at the same temperature as that of the trolled to the temperature of the hotplate, the hot- 273 plate temperature b ecam e constant. After the The constan t B was evaluated in preliminary experi capacitance between the two plates was m easured, m en ts over the en tire temperature range with the a lternate m easuremen ts of electric power (H') a nd conductivity cell evacuated . The gas pressure in the temperature differ ence ( L'1t) between the plates were cell in these experimen ts was estimated to be less m ade until the constancy of their values indicated than 10 - 5 mm of mercury . During the progress of that a steady state had b een r each ed . The power in the experimen ts with gas, the constant B was check ed t he hotplate' was then changed so that similar m ea,s p eriodically at tempera tures of 350° C and belm\- to urements were made at three or more powers. The test for possible changes in emissivity with time. (Tas pressure was then changed and m easurem ents Higher temper atures wer e not r echeck ed for reasons ~r er e repeated for each of the pressures 0.7, 50, and to b e discussed la ter with temperature m easurem en t. 100 atm, All of these m easurem ents were made at The direct capacitance (0) between the hot pla t e o .'iO , 100°, 200°, 300°, 400°, and 500°. and coldplate was m easured by flo substitution m ethod According to eq (2), the three quan t it ies needed to using a calibrated sta ndard and a Sylvania typ e 125 d etermine the thermal-conductivity coeffi cient, k , capacitance bridge. The precision of the bridge are the rate of heat flow , Q, the temperature differ readi ng was better than the certified accuracy of th e ence L'1t and the direct rapacitan ce, 0, between the standard capacitor. ho t pl a t ~ and coldpla te. E ach of th ese quantities is The capacitance, 0, in eq (2) is tha t m easured in discussed in de tail below. vacuum. For m easurements wi t h gas in the cell, In order to obtain Qfro m H ', the m easured electr ic correction must be made for the di electric constant . power in the hotplate, it is neeessary to account fo r E, of the gas. E was determined by using the all hrat flo w from the hotpla te other than b.\- conduc Clausius-Mosotti equa tion tion through the gas. The possible pat hs of this heat flow are (1) to the surrounding guard by conduction E- l and convection through gas, conduction through E+ 2=Dp, (6) lead wires and radiation, (2) to the coldplate by con- vection, a ~d (3) to the coldplate by radia tion . . where D is a constant independ ent of temperature Preliminar y experiments were m ade to determ1l1 e for nonpolar gases, and p is the gas density . The the heat-transfer coeffi cien t b etween the guard and value used fo r D was 1953 X 10- 7 [1] 2 when p is ill hotplate. R esults of th ese experimcnts showed that Amagat units [2]. Although the correction for the an un cer tainty in conductivity of less tha n 0.1 per dielectric constant of t he nitrogen may amount t,o cen t would be caused by a temperature difference 1 or 2 p ercen t at the hig hest densities, it is believed between the guard and the hotplate of 0.001 ° C . .It t hat the uncer tain ties in k due to this correction ar e was found possible to control the temperature chf less than 0.01 percen t. ference au tom atically to about this value. T empera ture m easuremen ts were m ade with the The conductivity cell was d es ign e ~ to elimin ~ t e any convection curren ts. If convectlOll does eXI st, r esistan ce t hermometers in t he coldpla te and t he it ,,,ill cause an apparen t cha nge in the value of k guard, together wi th the four-junction thermopile with change in power input. At the lower gas between the gua rd and the hotpla te. These r esist densities, no such change was observed, and con ance thermometers were ca libra ted by the N BS vection effects seem ed absen t. However , at the T emperatUl' e M easuremen ts Section before assembly higher gas densities, k appear ed to vary with power . of the cell. I t was found, however , t hat when the The apparen t k values were corrected by extrap system was k ep t under high vacuum at temperatures ola ting to zero power input . This apparen t change above 400° C, the t hermometer char acteristirs in k with power is believed to be due to a "chimney" changed slig htly . This was probably due to con type con vection r esulting from gas f1owin ~ into the tamination of t he platinum by other metals in the space b etween the guard and colclpla te and out of the holes (no t shown in fig , 2) provided for electri c leads system . Such a change took place during the deter in the top of the guard. It is expected that blocking mination of radiation corrections a t 500° C. Rath er of these sp aces would have elim inated this effect. t han dismantle t he apparatus to reca1ibrate the The heat transfer by radiat ion was accounted for t hermometers, it was thoug h t t hat suffi :;ien t aecura c.\· bY m easurem en ts with the cell cvacuated . This could be r etained if the two thermometers wer e power (H 'r) transferred between two p arallel plates compared ill place. In this way, the temperature can b e expressed as differ ence would be known more accurately than the Wr=e AO"(T~- T 1), (4) absolute temperature. This procedure is valid only because the evaluatiolI of t he temperature d~ffe rence, where e is an eff ective emissiv ity of the smfaces, A is L'1 t, is t he important factor, wller eas the cll ange in an effective area, 0" is the Stefa n-Boltzm ann con stant, thermal conductiv ity with temperature is sm all. I t and Tl and T2 are the ab solute temperatures. If the is estima ted t hat after t hi s procedure, t he accuracy temperature differ ence, L'1t , is small compa red to the of th e m easurem en t of L'1 t was 0.002 c1 eg C a nd of average temperature, T = 0.5 (T 2 + T j ), then the average temperature Twas 0.01 cle:b C. tr ansfer equation can be simplified to
(5) Z Figu res in brackets ind icate the Ii tetatl1J'c refc l' f'llces 3t the end of t h is paper.
274 4. Results 'fA BI, I" J . E.rpel' £lI!entall'eslills on nitrogen
T he results of the measurements arc given in T l'IllIJ(' r· rL'cmpcr Capaci API H.I.rl' 1ll table 1. The first column gives tbe temperature of atu re, ai ure tance, conctu C' t '''itil W ith clifl'crcn cc, C lh'ih+ th e ex periment, which is the mean of the hotplate ni t rogrn, I ytiClIUl11 , At I:" , and coldplate temperatmes. The second column lI' IV, gives the power (TV) put into the hotplate (as meas Pn '~S llJ'(\, 0.7 aLm med electrically) with nitrogen in the conductivity ------
cell. Values of power Wr , given in the third column, /0- 1 iF/ f lit arc based on experiments with the conductivity cell w w deg evacua ted and are calculated from eq (5). These 51. 03 0.05107 0. 00027 I. 647 9.781) 2.790 52. 75 .1039 .OOO5fl :l.3:l2 9.7S!! 2.80·1 valu es are subtracted from the cOlTesponding valu es 57.85 . 2630 .0015 8. :J06 9.797 2. 841i
of liT' to give Q, as used in eq (2). Over 40 experi 100.1:l . 058% .00042 1. 664 9.975 3.122 ments were made to determine the value of B in 101. 87 . 1202 .0000 3. 371 10. 049 :l.120 106.68 .2927 .0022 8. 117 10.017 3. 16.5 this equaLion. A value of B = 4.90 X IO- 12 w/deg4 in 200.09 . 07569 .00088 1. 696 10.450 3. liST this equation was found to fit the results best. The 201. 50 · l3S7 · DOW 3.101 10.4 55 3.74·1 values of B calculated from the individual vacuum 205.02 .2981 .0035 r,.614 10. '163 3. ,tin experiments deviated on the average about 4 per 204.86 .2971 .0035 6.615 10.435 3. , 0, :l00.48 .09072 .0148 1. 704 10. 80 4.29:l cellt from the above value, and seemed to be inde 302. 17 . 1818 . 0030 3.404 10.82 4.2!l9 pendent of tempemLure. Because the maximum :l04.25 . 2972 . 0049 5.5:l4 10. ~.\ 4. :1 12 :l06. (\4 · ·1:l08 .0072 7.991 10. R3 4. :l:lli values of TVr arc onl~r 3 percent of Lhe cOl'l'esponding 306. 56 .:HW .00uG G.891 10. 8,\ 4.326
values of lV, an enor of 4 percent in B would cause JOl. 02 .106-1 .002(1 1. 706 II. 17 4. ~2 2 a maximum elTor of only about 0.1 percent ill 402. (;,\ .2177 .0fl5:l :l.4R4 II . 1 ~ 4. Q29 conduc tiviLy lc. -106.4:l · 4702 .01t0 7.539 11 .20 4.84l 50 1.(>0 .1311 .0010 1. 770 ll. 71 .'.408 The valu es of tempel'aLme difference l1t given in 502.0:1 . 2:Jr,9 .oon 3.205 11.71 5. 410 column 4 arc based Oll measurements wi Lh the two 506.46 .524 8 .0](\4 7.04!1 11 . 77 :'.430 " resistance Lhermometers and Lite Lhennopile, which was used only as a "llull" indicator. Column 5 Pl'(' ~~ u n'. 50 atlll
gives the values of capacitance C (as used in eq (2» 50.59 O.Il~4 1 0 o 0002 1 I. 200 9.llil 0.0911 between the hotplate and coldplate as determined .,1. 02 .0.\9:l8 .OOOZO 1. 718 H.7fi:l 3.120 02 .4(1 . 11 :l8 · ()()05 3. l79 9. ii2 3. 22~ at the same time and under the same conditions of ,S5. in .25 11 .0011 (i. 519 9.78X :l. 1;0
the condu ctivity experiment. These values have 09. fiH .04'157 . 00030 1. 172 O. 9~7 :l. :l 18 been conecLed for the dielectric constant of the 100.31 . 0(1805 . 00045 I. 7Rl 9. 9 ~ 0 :1.3fiX 101. 94 · 1:l·I.> . 0009 3.4:l4 9.90(; J.44fi nitrogen. lOS. 1.\ . 27'18 .00 lS 0.711\ 10.02 1 a. 59:!
The values of "apparen t" thermal conductivity, 200.2(i . 09 102 .00 10 1 1. 937 1O . 4.\ii :l.9:37 201. 6 1 · I.\()9 · (){) 17 3.322 10.
t~T pe convection, it should diminish at lower power 001. 57 · 13:l1 .0039 1. 720 11.7'2 .5.67'1 inputs. Therefore, the values of lc* were extrapo 502.98 . 2575 .0076 3.316 11 .74 .5.68.\ .6426 .0191 8. 195 11 .77 .1, 721 lated to zero power to give "true" conductivities, k. 1_50 7.42 In the worst case, at 100-atm pressure and 50° C, Pressure, 100 atm the extrapolation is over a large range of values of lc *. However, it is believed that this extrapolation 50. 12 o 03336 0. 000 14 0. 8:l5 9.809 J.5Yl 50. S:l . 06738 . 00025 1. 57G 9.81:l :l.84:l should introduce only a relatively small error. The 51. 82 . 1210 .0005 2.615 9.821 .1. 158 results from the three experiments at different powers 99.86 .0597 .0004 L 423 10. 007 :l.6R9 were fitted by the method of least squares to a 101. 10 . 1195 .0007 2. fi75 10. 014 3.921\ linear equation in power. Tbe maximum deviaLion 104.06 . 3421 .0018 6.539 1O.031i 4.490 of the observed values of k* in this linear equation 199. 70 .07(\64 .0008:l 1. 003 10.41 4.023 201.08 · 1502 .0010 3.02J 10. -I:l 4. 177 was only 0.28 percent, so that it is believed that the 204.51 . 347:l .00:l5 6.556 10. -I(i 4.440
lineal' extrapolation was adequate. 299. (12 . IH7:l2 . 00082 0. 889 1O.8:l 4. 271) :100.79 . 11 50 · DO l O 2.048 1O. 8:l 4.511) At low pressures the effect of temperature discon 302.7'i . 236fi .0038 4.079 10. R-I 4.662 tinuity near the walls may become significant. This 305.30 .401i8 .00n5 6.811 10. 84 4.802 has been taken into account for the 0.7-atm data by 400.79 · 1059 .0024 1. .\70 11. 17 5.231 402. fi8 .2468 .0055 3.641 11. 19 5. 244 use of the equation 405.56 . 4(;50 . 0104 6.778 I I. 20 5.303
501. 21 · 1342 . 0039 1. 698 II. 69 5.8 1fi 502.66 . 2612 . 0075 3.290 II. 70 5.831i (7) 506.68 .6218 .0180 7.727 11. 75 5.890
41 883:>- 57--4 275 • •
Tlte,,"temperatur ~ -jump di~tance ", g, is related to taincd from NBS Circular 564 (Nov. 1955), which the accommodatIOn coeffiClent ", a, by the relation tabulates heat-transport properties for a number of [16]: ga se~. The constants of these equations were 2- a, ~ 0.5 k obtalI~ed by the m ethod of least squares. 'i-alues
g=----a:-,27rRT) Cr+ l )Cy P' (8) of lc given 111 column 3 of table 2 are calculated from these equations. Column 4 gives the deyiations in which R is the gas constant, T the absolute tem of the observed results from these calculated values. p erature, k the thermal conductivity, Oy the con Thel results are also given in figure 3, where the stant-volume specific heat, 'Y the specifi c-heat ratio, ClI'C es represent observed values and the solid lines and P the pressure of the gas. Values of a for nitro the values from the above equations. gen on silver vary from about 0.8 at room tempera The empirical eq (10) and (11) fit the obserYCd t Ut'e to 0.4 at 800° C [6] . The value of 0.5 was values at 50- and 100-atm pressure respectivelY chosen as the most probable for the temperatLlre a.h:l0st 3;s well as would be expected 'from t he pr'c~ range of these experiments. C1SlOn of the data. The averaO'e deviation of eq Values of observed conductivit), k, corrected to (10) (which is linear in t) from th~ observed cOllCluc eyen temperatures, are listed in column 2 of table 2. t i',"ities is only 0.1 percent, with f1 maximum deYi In order to facilitate interpolation of the results be atlOn of 0. 3 ,Percent. The deviations from eq (11 ) tween the observed points, empirical equations were are also qUite small except below 200 °C where derived to give conductivity as a function of tem ther~ was .increased difficulty, both. experi~entall y perature at each of the three pressures. These and 111 fi~tll:g the observed POll1ts WIth an equation. equations are as follows: The devlatlOI1S of eq (9) from the observed values seem to be larger than can be attributed to experi mental enol's. Equation (9) is the same semi k= 1.0591) ( Cv+~ R) (pressure, 0.7 atm) , (9) empirical equation proposed by Eucken [3], except for the con stant factor. A factor of 1.059 was 104lc = 2.714+ 0.005897t (pressure, 50 atm) , (JO) found t? fit the present data, as compared to a factor of 1. o['JgIn ally proposed by Eucken. 1101'e recell t modlficatlOns of Eucken's equation by other in J 0·llc = 3 .161 + 2.9 317 X 10 - 3t+ 9.0761 X 1O - 6t2- vestigators generally h ave predicted a value slio'hth~ (pressure, 100 atm) (ll) greater .than 1. An alternative equation fo~ 0.7 atn:, wInch ftts well up to 400°C, and which may he In these equations, lc is in watts cm- I deg- I, t is in eaS ler for use in llumerical interpolatioll in < tllis d.eg 0, 1) is viscosity (poise), Cy is heat capacity region, is (J g-I deg- I ), at constant volume, and R is the gas constant (8.317/28.016 j g- I deg- I). The values of lc = 2.495 X 10- 4 + 6.366 X l 0- 7t - 1.065 X 1O - 10t". (12) yiscosity and heat capacity used in eq (9) were ob-
TAIlLE 2. Thermal condllclivily oj n-itrogen 65 ,----,----,-----,------~--~ -
Conductivity, k Observed U') 'remper- mj nus o ature calculated x 60 P=IOO aIm Observed I Calculated T 104 k=3.161 + 2.9317 X 1O- 3 t _. 0> +9.0761 X 10-St2 Pressure, 0.7 atm '0'" 55 -8.8318 X 10- 9 t 3 -- T I P=50alm ]O-j wlc", j E I lO- 11"/C'" u 4 o C dey dey % 10 k=2 .714+0.005897 t 50 2.794 2.818 - 0.9 ~ 50 ]00 3.129 3.131 -.1 '0 200 3.750 3.727 +.6 ~ 300 4.308 4.308 .0 400 4.836 4.857 -.4 245 500 5.430 5. 38 1 +.9 > I f- Pressure, 50 atm > t; 40 ~ P=0.7olm 50 3. 003 3.009 -0.2 o 100 3.303 3. 304 .0 z - - k= 1.059T)(Cv+~R ) 200 3.905 3.893 +.3 35 300 4.477 4.483 -.1 8 400 5.075 5.073 .0 ..J 500 5.660 5.662 .0 3.340 3.329 + 0.3 50 25~--~------~ 100 3.513 3.536 -.6 200 4.060 4. 040 +.5 o 100 200 300 400 500 600 300 4.612 4.619 -.1 TEMPERATURE (t) , °C 400 5.218 5.221 .0 500 5.794 5.792 . 0 FIG VR E 3. Thermal conductivity of nitrogen. 276 • ------ where le is-in w cm-I deg-\ a nd t is in deg C. AI- capacitance belween electric leads and the relatively though all of these equations are suitable for inter large capaciL a nce to ground (the guard is grounded) polation at their respective pressures, they may not of the hotplate and coldplates. The electric leads be valid for extrapolation beyond the experimental were cm·cfu ll.\- shield ed to avoid significant error range. Equation (9) is probabl:l- the most suitable from this source. The cHect of t he ground capae for extrapolation to higher temperatures. itance is largel.\" eliminated by the design of the bridge used in its measurernent. Use of a substitu tion method that compares the conductivit.\"-cell 5. Discussion of Results capacitance with that of a standard capacitor minimizes a number of possible errors. B.\- usin g 5.1. Accuracy this method, it is believed that this comparison is aeeurate to better than 0.1 pereent. The absolute In order to estimate the accuraCI" of the final value of the standard capacitor is certified b~- t he res ults, it is necessar.l" to consider the eHect of each NBS (with a high probability) to only 0. 3 percent. of the terms in the conductivit:l" equation In the experiments with nit rogen, the effect of the dielectrie constant of the gas must be co n sid ered. It is estimated that un certainty in the le= 0.0885516Q. value of the dielectric constant of nitrogen is less O!:::,. t than 0.01 percent, giving the same unccrtaint:\" in o and le . The total uncertainty in th e capacit anC't' The constanL 0.0885516 is a co nv ersion facLor to measurement is believed to be about 0.3 perce nt. . allow for the system. of units. IL has negli gible This is the largest un cerLa int:I' in most of the meas uncertainty in its use here. Some poss ible sources urement s, and it is based on 1 chance in ] 0 that of elTor ill the measured capacit a nce , 0, are the the elTOr will he larger than O.:~ perce nt. . ~ N as ( EQ UAT IO N III · 0 - 5 0 0 - 10 PR ESSURE· 100 olm ;' V> Z 0 ~ @ 0" ~ 00 V> V + "'z • ~ NBS (EOUAT IO N 10j -3 PRE SSU RE · 50 o lm '"0 ~ G @ . • ' '''---NBS @ G • (EOU ATION 9) Xa> as x«> • x e • • ·0 • ~ e - 5 e e e e PRESSU RE · 101m - 10 100 200 300 4 00 500 600 700 BOO 900 1000 TEMPERATURE , °c FIG L' m } 4. Comparisons with others. e, ~B ~ ; 0, SloJ)·arov, 1p"t'e\', and 'L'eodoJ'ov icb; (), K eyes; {), Vargaft ik; 8 . Frank ; 278