A nonparametric scaling equation of state for fluids with inclusion of asymmetry

Abstract

A nonparametric scaling equation of state in the explicit form is proposed for real fluids with inclusion of their asymmetry. This equation in reduced variables of the density (ρ − ρ c )/ρ c and temperature (T − T c )/T c adequately describes the P-ρ-T data in the vicinity of the critical points of fluids. The approximation of the P-ρ-T data for 4He, SF6, and isobutane in the critical region by the new equation has demonstrated that it is quite sufficient to take into account the asymmetry of the density in the terms of the equation of state. The calculation of the asymmetry of the boundary curve from constants of the asymmetric equation of state leads to close agreement with the “law of rectilinear diameter” for experimental curves of saturation in these fluids not only in the asymptotic region but also in the region located sufficiently far from the critical point of the density (|(ρ − ρ c )/ρ c | < 0.5). The proposed asymmetric equation of state describes the P-ρ-T data in the critical region (|(T − T c )/T c |, |(ρ − ρ c )/ρ c | < 0.1) with an error that does not exceed the experimental error. Explicit expressions are also derived for the entropy and the heat capacity with allowance made for the asymmetry of the density in their calculation with the use of constants of the equation of state. The new equation of state retains the advantages of the simplicity in the application to the description of the P-ρ-T data and the heat capacity in contrast to the parametric equations of state within the Schofield linear model.