Analysis of the $\rm SF_6$ phase equilibrium line based on scale theory and the Clausius–Clapeyron equation

A system of mutually consistent equations describing the pressure $p_s$, vapor density $\rho^-$, and liquid density $\rho^+$ on the phase equilibrium line of technically important substances in the range from the triple to critical points has been proposed. At the stage of development of this system, the following have been considered: (a) the features of the behavior of a number of properties $(\rho^-{,}~\rho^+{,}~p_s{,}~d_f$ is the average diameter of the saturation line, and $d_s$ is the order parameter) in the critical region; (b) some concepts of the scale theory of critical phenomena and renormalization group theory, which was adapted by Wang L. et al. $(2013)$ for substances with a given molecular structure, including $\rm SF_6$; (c) the Clausius–Clapeyron equation, in which the “apparent” vaporization heat $r^*= r(1 - \rho^-/\rho^+)^{-1}$ is used instead of the vaporization heat $r$. At the stage of approbation of this system of equations, a method for calculating the adjustable coefficients included in this system using the example of $\rm SF_6$, for which precision data on the thermal properties including the experimental $(p_s{,}~\rho^-{,}~\rho^+{,}~T)$ data are available, has been proposed. Using the proposed technique, the coefficients of the system of equations have been determined using the precision data for $\rm SF_6$ and the calculated values of the $\rm SF_6$ properties in a given temperature range have been obtained. The uncertainty of the calculated data has been statistically analyzed; in particular, the average squared deviations of the experimental $(p_s{,}~\rho^-{,}~\rho^+{,}~T)$ data from the corresponding equations have been found. It has been shown that the proposed system describes the listed properties with less uncertainty than that of the properties corresponding to the original equations of Funke et al. $(2001)$. The temperature dependence $d_f(T)$ of the proposed model satisfactorily agrees with the model developed by Wang et al. $(2013)$ for the $\rm SF_6$ critical region.