A nonparametric scaling equation of state, developed on the basis of the Migdal's phenomenological theory and Benedek's hypothesis

A new nonparametric scaling equation with density and temperature as variables is proposed using the phenomenological theory of critical phenomena and the experimentally confirmed Benedek's hypothesis, on the basis of which we assume that the behavior of a number of thermodynamic functions for the critical and near-critical isochores in the neighborhood of an asymptotic critical point is similar. In comparison to Scofield's linear model (LM), the proposed scale equation is not inferior to known nonparametric equations of the same type; in contrast to the latter, however, its physical grounds are just as valid as the LM equation.