A method for constructing the equation of state of a liquid and gas based on the Migdal phenomenological theory and the Benedek hypothesis

A method is proposed for constructing the fundamental equation of state (FEoS) of a liquid and gas that takes into account the features of a thermodynamic surface in the vicinity of a critical point. The structure of the equation of state is chosen in accordance with the new representation of the scale hypothesis in the form of an expression for the Helmholtz free energy F = F r + F s , where F r is the regular function of density ρ and temperature T; F s = F s (ρ, T, δ, a (x)) is a singular component F that describes in the asymptotic neighborhood of the critical point the behavior of the equilibrium properties of the liquid in accordance with the scale theory (MT) of critical phenomena. Here δ is the critical index of the critical isotherm; a 0 (x) is the large-scale free-energy function of Kudryavtseva – Rykov, which is developed on the basis of Migdal’s phenomenological theory, the Benedek hypothesis, and the Scofield – Lister – Ho linear model; x is a scale variable. When calculating the individual parameters of the Helmholtz free energy scale function a 0 (x), a similarity theory relation is used, which relates the lattice gas and the real fluid. Based on the proposed method, an equation of state for sulfur hexafluoride has been developed, which, in accordance with MT, describes the behavior of equilibrium properties of the SF 6 . A comparison is made of experimental data, data on isochoric heat capacity and isobaric heat capacity, density values p-ρ-T of saturated steam and saturated liquid with the corresponding data calculated on the basis of the developed FEoS o SF 6 .