Equation of state for compressed liquids from surface tension

A method for predicting an analytical equation of state for liquids from the surface tension and the liquid density at the freezing temperature (yi, pi) as scaling constants is presented. The reference temperature, T-ref, is introduced and the product (TrefTf1/2) is shown to be an advantageous corresponding temperature for the second virial coefficients, B-2(T), of spherical and molecular fluids. Thus, B-2(T) follows a promising corresponding-states principle and then calculations for alpha(T) and b(T), the two other temperature-dependent constants of the equation of state, are made possible by scaling. As a result, (gamma(f), rho(f)) are sufficient for the determination of thermophysical properties of fluids from the freezing line up to the critical temperature. The present procedure has the advantage that it can also be used in cases where T-c and P-c are not known or the vapor pressure is too small to allow accurate measurements. We applied the procedure to predict the density of Lennard-Jones liquids over an extensive range of temperatures and pressures. The results for liquids with a wide range of acentric factor values are within 5%.