Statistical-mechanical basis for accurate analytical equations of state for fluids

Abstract

Abstract Theories of liquids have been developed over the past twenty years based on the recognition that the structure of a liquid is determined primarily by repulsive forces, so that fluids of hard bodies (spherical or nonspherical) can serve as useful reference states for perturbation theories. We show how these results can be extended to obtain simple analytical equations of state for real fluids, which include the low-density vapor and the supercritical fluid as well as the true liquid. These equations are quintic in the density (the van der Waals equation is cubic), and are very accurate (parts per thousand to a few percent in the density for nonpolar fluids). They are first-principles equations in the sense that the entire fluid p-v-T surface can be calculated if the intermolecular potential is known, but they can be used with much less input information. Because the parameters of the equations of state that depend only on the repulsion are insensitive to the detailed shape of the potential, knowledege of just the second virial coefficient as a function of temperature is sufficient to construct the p-v-T surface. Examples are given for a selection of fluids, including Ne, CH4 CO2, and H2O.