Phenomenological Theory of the Critical Point and the Fundamental Equation of State in Physical Variables

The linear Scofield–Litster–Ho (LM) model is used to obtain a representation of the scaling hypothesis (SH) similar in structure to the SH representation. The new representation follows from the phenomenological theory of the Migdal critical point and allows the construction of an equation of state in physical variables, in accordance with the requirements of the scale theory. As in the Berestov critical point model, isochoric heat capacity reduced to absolute temperature ( $${{C}_{{v}}}$$ /T) is used as a scale factor in the proposed critical point model. Based on Benedek’s hypothesis, scale functions of Helmholtz free energy in density–temperature variables not inferior to the corresponding LM scale functions can be calculated using the proposed SH model. In contrast to scale functions calculated on the basis of Migdal’s SH representations, free energy scale functions calculated within the proposed critical point model do not contain integrals of differential binomials. A unified fundamental equation of state in the context of the new SH concept is proposed and tested by describing the equilibrium properties of methane in the 90.6941–620 K range of temperatures at pressures up to 600 MPa.