~~-
CORRESPONDENCE
Unit Compressibility Curve
Sir: In issue no. 3 of 1974, Holleran (1974) presents an argument that the temperature a t which the unit compressibility curve intersects the Joule-Thomson inversion curve is equal to one-half of the Boyle point temperature. In the immediately following article, Bursik (1974) shows that a test of this on data for helium-4 produces an inconclusive result, quoting values for the Boyle temperature, taken from Keyes (1941) and Glasstone (1946), of 24.06 K and 33 K, respectively. His value for the intersection temperature, 12.58 K, is found from the equations of McCarty (1972), and these equations also yield a value for the Boyle temperature of 22.5 K. A recent analysis of the second virial coefficient of helium by Dymond and Smith (1969) gives, on interpolation, a value of 25 K , and another by Levelt Sengers et al. (1971) gives a value of 22.64 K. Since these estimates are based on analyses of substantially the same bodies of data, though with different systems of weighting, it appears that the present uncertainty in the Boyle temperature is such that Holleran's argument cannot as yet be proven or disproven for helium. Bursik also draws attention to the wide ranges of values which are to be found for the Boyle temperatures of various other fluids. Of those mentioned, we have recently completed an analysis of the data on carbon dioxide (Angus et al., 1975). Our value for the Boyle temperature is 712.5 K and a rough estimate of the intersection temperature is 358 K . Our earlier correlation of the data on argon (Angus et al., 1972) gives a value for argon of 206 K. We did not include values of the second virial coefficient, but the Levelt Sengers et al. compilation gives the Boyle temperature as 411.52 K . This apparent agreement must be qualified by the errors present in the estimation of both T I and TB. The largest error is that in T , due to the error in B, and considering this alone, if we write 6T =
~
6B dB/dT
where iiT is the error in the Boyle temperature, 6B the error in the second virial coefficient, and dB/dT the slope a t the Boyle temperatl.;e, then we obtain Table I.
Sir: The zero-density intercept of the unit-compressibility (UC) line is the Boyle temperature, T,; the extrapolated zero-temperature intercept is designated do. If the UC line is straight then its intersection with the IC is a t T = TB/2, d = do/2, and P = d o R T ~ / 4 .This result is mathematicallv rigorous (Holleran. 1974). ExDerimental disagreements with these relations may be due either to a curvature in the UC line or to the difficulty of determining accurately the quantities involved, especially TH,from "
142
Y
Ind. Eng. Chem., Fundam., Vol. 14, No. 2, 1975
Table I (d B/d T ) /
T,/K Helium Carbon dioxide Argon
22.51 25.0' 22.6* 712.5" 411.52d
5B/cm3 mol''
cm3 mo1-lK-l
GT/K
11.0"
0.8O
*1.2
i0.5'
0.6" 0.7" 0.084" 0.097O
i0.8 il.8
11.25" 12.W *0.95a
k24.0 59.8
a = Our estimate. L e v e l t Sengers e t a l . (1971). D y m o n d a n d Smith (1969). A n g u s e t a l . (1972). e Angus e t al. (1974). f M c C a r t y
(1972).
These errors make it impossible to confirm that Holleran's suggestion holds for these fluids, but it cannot be regarded as disproven. Incidentally, the large error in 6T due to uncertainties in 6B probably accounts for the discrepancies in the Boyle point noted by Bursik. Literature Cited Angus, S., Armstrong, B., de Reuck, K. M., "International Thermodynamic Tables of the Fluid State-Ethylene, 1972," Butterworths. London, 1973. Angus, S., Armstrong, B., de Reuck, K. M.. et al., "international Thermodynamic Tables of the Fluid State-Carbon Dioxide, 1973," Butterworths. London, in press, 1975. Bursik. J. W . , Ind Eng. Chern.. Fundam, 1 3 , 298 (1974). Dymond, J. H., Smith, E 6.."The Virial Coefficients of Gases-A Critical Compilation," Oxford Science Research Papers 2, p 172, Clarendon Press, Oxford, 1969. Glasstone, S.,"Textbook of Physical Chemistry,' 2nd ed, p 247, Van Nostrand. Princeton, N.J., 1946. Holleran, E., I n d Eng Chern . Fundarn.. 1 3 , 297 (1974). Keyes. F. G., "Temperature, Its Measurement and Control in Science and Industry," p 59, Reinhold, New York, N.Y., 1941 Levelt Sengers, J. M. H., Klein. M., Gallagher, J. S., "Pressure-VolumeTemperature Relationships of Gases: Virial Coefficients." American Institute of Physics Handbook, 3rd ed, 4i, pp 204-221, McGraw-Hill. New York, N.Y., 1971. McCarty, R . D., Nat Bur Stand ( U S . ) Tech. Note. 631 (1972).
D e p a r t m e n t of Chemistry I.U.P.A.C.T h e r m o d y n a m i c Tables t3.ojwt Centre Imperial College o f S c i e n c e & Technology South Kensington, L o n d o n SW72A Y , England
S . Angus
experimental data, as confirmed by Bursik (1974) and Angus (1975). Literature Cited Angus, s , Ind. Chern.,
F u n d a m , ,4 142 (,975) Bursik. J. W . . Ind Eng. Chem., F u n d a m . . ' l 3 , 298 (1974) Holleran, E., /nd. Eflg. Chem.. Fundam.. 13, 297-298 (1974).
C h e m i s t q Department S t John's Uniaersity Jamaica, New York I1439
Eugene M. Holleran
