Equations of state for a square-well gas from a parametric integral equation

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Abstract
A parametric integral equation is used to compute radial distribution functions for a classical gas whose particles interact pairwise with a square-well potential function. The parameter is fixed at one value for an isotherm by adjusting it to provide good agreement with available ’’exact’’ (Monte Carlo or molecular dynamics) pressure at a high density. Six isotherms in the gas region are studied and thermodynamic functions (pressure, internal energy, Helmholtz free energy, Gibbs free energy, entropy, and enthalpy) are computed from the radial distribution functions. Comparisons with available ’’exact’’ calculations indicate that these results are good for the higher isotherms but that for temperatures nearer the critical temperature, larger errors appear. These calculations, when considered with previous results, indicate that the parametric integral equation gives excellent results for a single value of the parameter along an isotherm for high temperature gases, but that a more complex determination of the parameter is needed for low temperature gases and for liquids.