Integral equation and perturbation method of calculating thermodynamic functions for a square-well fluid

Abstract

The pressure of a classical simple fluid of particles interacting with square-well potentials is computed by a method combining the use of a parametric integral equation with first-order perturbation theory. This method leads to a simple expression for the pressure of the fluid. In contrast to the usual choice, the reference part of the potential energy is taken to be a square well itself. The results are in good agreement with pressure values from molecular dynamics and are relatively insensitive to the choice of the reference-well depth, provided that that well is shallow. Based on these findings, fine-meshed tables giving (reduced) pressure, internal energy, and Helmholtz free energy are constructed for ranges in reduced density and temperature of ${n}^{*}\ensuremath{\le}0.85$, $1.4\ensuremath{\le}{T}^{*}\ensuremath{\le}4.0$. These tables should provide reliable estimates of the thermodynamic variables for a square-well gas at any (${n}^{*}$, ${T}^{*}$) within the given ranges; they also help to lay the basis for comparative studies of the applicability of perturbation theory to the square-well gas.