Thermodynamical properties of nitrogen as functions of density and temperature between −125° and +150°C and densities up to 760 Amagat

Physica X V I I , no 9

September 1951

T H E R M O D Y N A M I C A L P R O P E R T I E S OF N I T R O G E N AS FUNCTIONS OF D E N S I T Y AND T E M P E R A T U R E B E T W E E N --125 ° AND + 150°C AND D E N S I T I E S U P TO 760 AMAGAT b y A. MICHELS, R. J. L U N B E C K and G. J. W O L K E R S 115th publication of the Van der Waals Fund Van der Waals Laboratorium, Gemeente-Universiteit, Amsterdam

Synopsis F o r some recent experiments t h e r m o d y n a m i c a l data on nitrogen were required over as wide a t e m p e r a t u r e and pressure range as possible. The experiments carried out in the Van der Waals L a b o r a t o r y supplied these d a t a only between 0 ° and 150°C for pressures up to 3000 atmospheres. Compressibility d a t a overlapping those mentioned, b u t extending in t e m p e r ature down to --185°C and in pressure up to 6000 atmospheres, have been published elsewhere. F r o m these data t h e r m o d y n a m i c a l functions have been calculated for temperatures between --125°C and + 150°C and densities up to 760 A m a g a t (pressure about 5500 atmospheres).

§ 1. Introduction. In a previous publication 7) thermodynamical properties of nitrogen have been given for pressures up to 3000 atmospheres and temperatures between 0 ° and 150°C. For recent experiments these properties were required over a wider region. To obtain these use has been made of the compressibility data published by Benedict2) for pressures up to 5800 atmospheres and temperatures between --185 ° and +200°C. Since this region overlaps that investigated in this laboratory it was possible to obtain information on the mutual agreement of the results. Calculation showed this agreement to be within 0.2% ,an accuracy claimed by B e n e d i c t for his measurements. The greatest deviations were found at a pressure of 3000 atmosoheres; they decrease gradually for lower pressures. To obtain continuity throughout the whole P - V - T region it was decided to apply a graduation technique to B e n e d i c t s' data for pressures higher than 3000 atmospheres. The smoothing procedure involved small changes being made in the data of B e n e d i c t --

Physica XVII

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A. ~~MICHELS, R. J. L U N B E C K A N D G. J. W O L K E R S

above 0°C, the correction being 0.2% at 3000 atm. and increasing to 1.5% at the highest pressure of 6000 atmospheres. T h e d a t a below 0°C were not altered. Although B e n e d i c t e x t e n d e d his m e a s u r e m e n t s down to - - 183 °, only the dat:a for t e m p e r a t u r e s above the critical t e m p e r a t u r e of nitrogen (126.0°K) were used, as calculations of t h e r m o d y n a m i c a l functions in the critical region w o u l d require a knowledge of the h e a t of evaporation. , § 2. T h e determination o[ a consistent see o / P V - v a l u e s .

T e m p e r-

atures below 0°C ". B e n e d i c t gives a formula for P V as a function of the density between 200 and 760 Amagat, so t h a t the calculation of P V for r o u n d values of t h e d e n s i t y is easy for this t e m p e r a t u r e region. F o r zero density the value of P V is R T , whilst f r o m m e a s u r e m e n t s of K a m e r l i n g h Onnes and U r k 3 ) and from H o 1 b o r n and 0 t. t o 4) t h e value of t h e ~ e c o n d virial coefficient is known. W i t h this information it was possible to derive P V - v a l u e s for the Whole density range up to 760 A m a g a t between 0 ° and - - 1 5 0 ° with an e s t i m a t e d a c c u r a c y of iI o}/o for the lowest temperature. T e m p e r a t u r e s a b o v e 0°C. The d a t a ,s this t e m p e r a t u r e region and at pressures up to 3000 atmospheres as given b y M ic h e 1,s et al. 1), can be expressed b y a power series P V = A + B d + Cd 2 27 Z d 3 27 D d 4 27 Y d 5 + E d 6 + F d 7

(1)

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815

B e n e d i c t published densities as a function of pressure and temperature. As slight scattering in the experimental data makes the calculation of thermodynamical functions less reliable, it was therefore advisable to graduate, and this was carried out b y a graphical method. Instead of taking for this purpose the P V values directly, it was found more practicable to use a graphical representation of APV/Ad (where 3 P V is the difference in the PV-values of two consecutive points and zld the corresponding density difference) vs. the averaged density (of the two points). B y plotting on the same graph the data of B e n e d i c t, and of M i c h e 1 s e t al., it was possible to obtain one set of P - V - T data which is given in table II.

§ S. Thermodynamical /unctions. With the computing technique described previously 6),thermodynamical properties*) were calculated from the coml3ressibility data of table II and the zero specific heat data of G o f f and G r ~ t c h e). The results for energy, entropy,

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*) Since this p a p e r was s u b m i t t e d for p u b l i c a t i o n , it has been found t h a t a R u s s i a n a u t h o r carried o u t s i m i l a r c a l c u l a t i o n s (P. E. B o 1 s h a k o w, J. phys. Chem. U.S.S.R. 18 (1945) 121). Since this a u t h o r did not g r a d u a t e B e n e d i c t d a t a and used older zero pressure d a t a for the specific h e a t his results do not c o m p l e t e l y agree w i t h those presented h'ere.

B 16

THERMODYNAMICAL PROPERTIES OF NITROGEN

enthalpy, free energy, free enthalpy and internal kinetic energy are given in tables III to VII.I. The accuracy of the data depends on the reliability o f t h e P V values and thus varies for the different r.egions. It can be estimated to be of the order of 0.2% in the region where P V is reliable to within 0.02% and to decrease in the other regions to roughly 2%.

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As the specific heats and the sound velocity, given in tables IX, X and XI, are derived from second derivatives the corresponding accuracy for these properties m a y vary from 1 to 10%. This m a y be responsible for the fact that the Cv~ isothermals intersect in the low temperature region, as can be seen from fig. 1, a phenomenon not observed in the corresponding data of carbon dioxide s). A comparision of figs. 1 and 2 shows, however, that the general behaviour of the two gases shows a great similarity. Received 23-5-51. REFERENCES 1) M i c h e l s , A., W o u t e r s , H. and B o e r , J. de, Physica | (1934)587; 3 (1936) 585. 2) B e n e d i c t , M., J. Am. chem. Soc.59 (1937) 2224, 2233. 3) K a m e r l i n g h Onnes, H. and U r k , A. Th. v a n , Comm. Leiden (1924) no. 169d. 4) H o l b o r n , L. and Otto, j., z. c Physik 33 (1925) I. 5) M i c h e l s , A., G e l d e r m a n s , M. and G r o o t , S. R. de, Physica 12 (1946) 10S. 6) G o l f , J . A . and G r a t c h , S . , T r a n s . Am. Soc. Mech. Eng. 72(1950) 741. 7) M i c h e l s , A., W o u t e r s , H. and B o e r , J. d e , Physica 3 (1936) 597. 8) M i c h e l s , A., B i j l , A. and M i c h e l s , C.,Proc. roy. Soc. A 1 6 0 (1937) 376; M i c h e l s , A. and G r o o t , S. R. de, Appl. sci. Res. A I (1948) 94.