Fundamental equation of state developed on basis of Migdal’s phenomenological theory of critical point

Abstract

In this work a fundamental equation of state (FEoS) with account taken of requirements of the scale theory of the critical point has been developed. The behavior of the FEOS in the asymptotic vicinity of the critical point is determined by the characteristics of the scaling function a(x) of the Helmholtz scale free energy F. The structure of the function a(x) is calculated on the basis of Migdal’s phenomenological theory and the hypothesis about the identical behavior of the isothermal compressibility coefficient at the critical and near-critical isohors near the critical point (Benedek’s hypothesis). The parameters of the singular component of the FEOS are calculated using the similarity theory. The proposed FEoS has been approved on the example of description of equilibrium properties of the refrigerating agent R1234yf in the range of state parameters: by a temperature from 220 K to 440 K and by pressure up to 40 MPa. The obtained results are discussed.