Saturation line of methane in the renormalization group theory in the range from the triple to the critical point

A new model of the phase equilibrium line (PEL) of methane has been developed on the basis of the Clapeyron–Clasius equation and the relations of the renormalization group (RG) theory. In contrast to the known PEL, when describing the density of a saturated liquid ρ⁺, density ρ⁻, and pressure p_s of saturated methane vapor, a system of mutually consistent equations (CE) including those describing the saturation density line and saturation vapor line is used. These equations have a number of common parameters: critical indices, critical pressure, critical temperature T_c, critical density, as well as a series of coefficients of the average diameter model, d_f, coefficient D_2β, complexes D_2β/D_1−α and D_2β/D_τ, calculated within the framework of modern RG theory for asymmetric systems. Based on the proposed approach, a methane saturation line has been developed; its average diameter in a wide vicinity of the critical point is described in accordance with the RG theory by the dependence: d_f = D_2βτ^2β + D_1−ατ^1−α + D_ττ, where τ = (1 − T/T_c). It has been established that d_f = d_f(T) within the framework of the proposed approach is a strictly decreasing function of temperature in the range from the triple point to the critical point. It has also been found that the derivative of the vaporization heat with respect to temperature, in accordance with the principles of thermodynamics, has a minimum in the vicinity of the triple point. Within the framework of the proposed PEL model, experimental data on ρ⁺, ρ⁻, and p_s published by R. Kleinrahm and W. Wagner in 1986 are provided with standard deviation 0.0011 %, 0.0072 %, and 0.0012 %, respectively, that is, with greater accuracy than the international equations of U. Setzmann and W. Wagner derived in 1991.