Analytic Equation of State for Lennard-Jones Fluids Based on the Ross Variational Perturbation Theory

By using a previously developed analytic expression for the radial distribution function of hard spheres, a simple analytic equation of state (EOS) for fluids with a continuous Lennard-Jones potential is established based on Ross's variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified, and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original Ross variational theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one, and their applicable range is believed identical. A comparison with the recently proposed mean-sphere-approximation theory shows that the analytic equation of state developed here has wider applicability and precision.