A Two-Potential Model for the Equations of State of Gases at Moderate and High Densities

The isothermal compression, up to nearly half the liquid densities, of argon, nitrogen, and methane at three different temperatures ranging from 0–150 deg C are investigated by using the cell method originally developed by Lennard-Jones and Devonshire. A two-potential model is adopted in the evaluation of the classical partition function to partially take into account the contributions arising from the correlations of molecular motions. The Lennard-Jones 6–12 potential and the Kihara hard core model are used, respectively, for the calculation of the energy of the geometrically symmetric lattice and the energy of augmentation arising from molecular motions. The potential parameters used in the calculations are those derived from fitting the second virial coefficient of dilute gases. The resulting calculated isotherms are compared with experimental measurements; agreement obtained is good for the range of density considered. The Kihara hard-core model with parameters determined for dilute gases is found to be ineffective at very high densities. This agrees with the conclusion derived from the Monte Carlo and molecular dynamics calculations that the Lennard-Jones 12–6 potential is tolerably good in representing the effective pair potential at liquid densities.