Analytical Equation of State for Solid-Liquid-Vapor Phases

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_r and T_r are reduced pressure and temperature with respect to the critical pressure (P_c) and temperature (T_c), respectively, while V_R is a reduced molar volume defined as V_R=P_cV/RT_c, 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, a_R, b_R, c_R, and d_R 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.