Thermodynamic Functions at Liquid—Vapor Transition Range of the van der Waals, the Berthelot, and the Dieterici Equations of State

Abstract

The vapor pressure, the volumes of liquid and vapor at the liquid—vapor phase equilibrium, the heat of vaporization, the internal energy, and the entropy changes at the phase transition are obtained with the use of the van der Waals, the Berthelot, and the Dieterici equations of state by imposing the condition that the work done in an isothermal reversible cyclic process is zero. The results show that: (1) The vapor pressures obtained by using the van der Waals equation agree closely with the experimental data for Ar, Kr, and Xe from the triple point to the critical point, and there is an inflection point when the logarithms of the pressures are plotted against the reciprocal absolute temperatures as observed in saturated hydrocarbons; (2) Berthelot's equation of state describes fairly well the existing data of liquid and vapor densities at the liquid—vapor phase equilibrium for Ar, Kr, Xe, N₂, O₂, CO, and CH₄; (3) none of these equations describes properly the heat of vaporization of inert gases. Formulas for the above thermodynamic quantities are given as a function of temperature by fitting the numerical results to a certain set of equations.