Analytical Equation of State for Solid-Liquid-Vapor Phases

Abstract

A simple analytical equation of state has been proposed for describing the phase behavior of three thermodynamic states (solid, liquid, and vapor) of matter. In terms of reduced parameters, it can be written as: $$P_{\text{r}} = \frac{{T_{\text{r}} }}{{V_{\text{R}} - b_{\text{R}} }}\left( {\frac{{V_{\text{R}} - d_{\text{R}} }}{{V_{\text{R}} - c_{\text{R}} }}} \right) - \frac{{a_{\text{R}} }}{{V_{\text{R}}^{\text{2}} }}.$$ Pr and Tr are reduced pressure and temperature with respect to the critical pressure (Pc) and temperature (Tc), respectively, while VR is a reduced molar volume defined as VR=PcV/RTc, where R is the universal gas constant. This may be regarded as an extension of the classical van der Waals's equation of state for fluid (liquid and vapor) only states. The four parameters, aR, bR, cR, and dR in this equation are free adjustable constants, and can be variable with temperature. The basic physical idea underlining the model is presented, and examples applied successfully to actual pure substances and mixtures are demonstrated. Also, applications to the hard-sphere model are examined. Further improvements, limitations, and possible applications of the present model are discussed.