Nonparametric scaling equation of state for description of critical behavior of liquid

Abstract

A new nonparametric scaling equation of state is suggested for the description of equilibrium thermodynamic properties of liquids in the vicinity of the critical point. The equation contains three system-dependent fitting constants. This equation is used to perform approximation of experimental P-ρ-T data for He4 in the range of reduced densities of −0.45 < (ρ−ρ c )ρ c < 0.37 with mean-square error with respect to pressure of 18% for the values of critical exponents adopted for the three-dimensional Ising model. The behavior of isochoric heat capacity of He4 in the critical region is calculated using the fitting constants obtained as a result of approximation of P-ρ-T data. The error of calculation by the new equation of the experimental data with respect to C V for He4 in the ranges of reduced temperatures (T−T c /T c from −0.3 to −0.001 and from 0.001 to 0.2 does not exceed 4%.