Abstract
In the literature second virial coefficients are calculated by series expansions or by direct numerical integration. For thermodynamic quantities such as thermodynamic functions, analytical expressions are wanted. This paper gives closed formulas for the second virial coefficient for a convex-body Kihara potential of the type U(ρ)= U 0[(ρ 0/ρ)2m -2(ρ 0/ρ)m], where m can be a rational number n>3. Furthermore, a number of related problems such as dielectric virial coefficients and Buckingham-Pople integrals are reduced to the same Laplace-transformation-type technique.
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References
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1964).
M. Edalat, S. S. Lan, F. Pang, and G. A. Mansoori, Int. J. Thermophys. 1:177 (1980).
G. C. Maitland, M. Rigby, E. B. Smith, and W. A. Wakeham, Intermolecular Forces (Clarendon, Oxford, 1981), App. 1.
E. A. Mason and T. H. Spurling, The Virial Equation of State (Pergamon Press, Oxford, 1969).
J. S. Rowlinson, Mol. Phys. 9:197 (1965).
A. E. Sherwood and J. M. Prausnitz, J. Chem. Phys. 41:429 (1964).
T. Kihara, Chem. Phys. Lett. 92:175 (1982).
E. A. Guggenheim and M. L. McGlashan, Proc. Roy. Soc. A 225:456 (1960).
A. N. Dufty, G. P. Matthews, and E. B. Smith, Chem. Phys. Lett. 26:108 (1974).
T. H. Spurling and G. DeRocco, J. Chem. Phys. 47:231 (1967).
T. Kihara, Prog. Theor. Phys. Suppl. 40:177 (1967).
T. Kihara, Rev. Mod. Phys. 25:831 (1955).
T. Kihara, Adv. Chem. Phys. 5:147 (1963).
A. Koide and T. Kihara, Chem. Phys. 5:34 (1974).
T. Kihara, Intermolecular Forces (Wiley, New York, 1976).
H. H. Michels, Phys. Fluids 9:1352 (1966).
W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Special Functions of Mathematical Physics (Springer, Berlin, 1966), p. 442.
A. J. M. Garrett, J. Phys. A 13:379 (1980).
F. Röscheisen and W. Witschel, J. Mol. Struct. Theochem 87:301 (1982).
B. Wetzel and W. Witschel, Chem. Phys. Lett. 119:543 (1985).
H. W. Connolly and G. A. Kandalic, Phys. Fluids 3:463 (1960).
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1965), Chap. 19.
L. F. Epstein and G. M. Roe, J. Chem. Phys. 28:874 (1958).
J. H. Dymond and E. B. Smith The Virial Coefficient of Gases, 2nd ed. (Clarendon, Oxford, 1980).
A. D. Buckingham, in The World of Quantum Chemistry, R. Daudel and B. Pullman, eds. (D. Reidel PC, Dordrecht, 1974).
A. D. Buckingham and J. A. Pople, Trans. Faraday Soc. 51:1173 (1955).
J. S. Gallagher and M. Klein, J. Res. Natl. Bur. Std. 75A:337 (1971).
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Witschel, W. Second virial coefficients in closed form for a Kihara (2m-m)-potential. Int J Thermophys 11, 1075–1085 (1990). https://doi.org/10.1007/BF00500561
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DOI: https://doi.org/10.1007/BF00500561