Abstract
A new nonparametric scaling equation of state is suggested. The equation correctly describes the p-ρ-T data and heat capacities of liquids close to the critical vaporization points. It was obtained with the use of the S spinodal and the mixing of scaling fields as a first approximation (asymmetric and nonasymptotic terms were ignored). The new equation was used to approximate the data on 4He, C2H4, and H2O in the critical region. The results showed that it correctly described the critical behavior of thermodynamic functions, including isochoric heat capacity, not only in the asymptotic but also over a fairly wide density region at the critical point. The suggested equation of state describes the p-ρ-T data with the same error as the Schofield parametric equation of state. The new equation, however, better reproduces the behavior of heat capacities and is much simpler to use. As distinct from the Schofield equation, the new equation, like classic equations of state, allows the spinodal to be determined from the (ϖp/ϖv) T = 0 condition at T < T c .
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. B. Griffiths, Phys. Rev. 158, 176 (1967)
G. M. Avdeeva and A. A. Migdal, Pis’ma Zh. Eksp. Teor. Fiz. 16, 253 (1972).
E. Brezin, D. J. Wallace, and K. G. Wilson, Phys. Rev. B: Condens. Matter 7, 232 (1973)
P. Schofield, Phys. Rev. Lett. 22(12), 606 (1969).
P. Schofield, G. D. Litster, and G. T. Ho, Phys. Rev. Lett. 23(19), 1098 (1969).
V. A. Agayan, M. A. Anisimov, and J. V. Sengers, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 64, 026125-1 (2001).
A. G. Sartakov and V. G. Martynets, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Khim., No. 3, 14 (1982).
C. M. Sorensen and M. D. Semon, Phys. Rev. A: At., Mol., Opt. Phys. 21, 340 (1980).
I. M. Abdulagatov and B. G. Alibekov, in State Service of Standard Reference Data: Thermal Properties of Substances and Materials (Izd. Standartov, Moscow, 1985), Vol. 22, p. 97 [in Russian].
P. P. Bezverkhii, V. G. Martynets, and E. V. Matizen, Zh. Eksp. Teor. Fiz. 126(5), 1146 (2004) [J. Exp. Theor. Phys. 99 (5), 998 (2004)].
A. Z. Patashinskii and V. L. Pokrovskii, Fluctuation Theory of Phase Transitions (Nauka, Moscow, 1982) [in Russian].
J. Osman and C. M. Sorensen, J. Chem. Phys. 73, 4142 (1980).
Kh. I. Amirkhanov, G. A. Stepanov, I. M. Abdulagatov, and O. A. Bui, in Isochoric Specific Heat of Propyl and Isopropyl Alcohols, Ed. by V. V. Sychev (Dagestanskii Filial Akad. Nauk SSSR, Makhachkala, 1989), p. 86 [in Russian].
M. R. Moldover, Phys. Rev. 182(1), 342 (1969).
P. P. Bezverkhii, V. G. Martynets, E. V. Matizen, and V. F. Kukarin, Teplofiz. Vys. Temp. 26(4), 700 (1988).
V. F. Kukarin, V. G. Martynets, E. V. Matizen, et al., Fiz. Nizk. Temp. (Kiev) 6(5), 549 (1980).
S. L. Rivkin and T. S. Akhundov, Teploenergetika, No. 10, 66 (1963).
S. L. Rivkin, T. S. Akhundov, E. A. Kremenevskaya, and N. N. Asadullaeva, Teploenergetika, No. 4, 59 (1966).
S. L. Rivkin and T. S. Akhundov, Teploenergetika, No. 1, 57 (1962).
J. R. Hastings, J. M. H. Levelt Sengers, and F. W. Balfour, J. Chem. Thermodyn. 12(11), 1009 (1980).
V. V. Sychev, A. A. Vasserman, A. D. Kozlov, et al., State Service of Standard Reference Data: Thermodynamic Properties of Helium (Izd. Standartov, Moscow, 1984) [in Russian].
P. R. Roach, Phys. Rev. 170(1), 213 (1968).
Author information
Authors and Affiliations
Additional information
Original Russian Text © P.P. Bezverkhii, V.G. Martynets, E.V. Matizen, 2007, published in Zhurnal Fizicheskoi Khimii, 2007, Vol. 81, No. 6, pp. 978–984.
Rights and permissions
About this article
Cite this article
Bezverkhii, P.P., Martynets, V.G. & Matizen, E.V. A nonparametric scaling equation of state for liquids. Russ. J. Phys. Chem. 81, 847–853 (2007). https://doi.org/10.1134/S0036024407060039
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0036024407060039