Evaluation of P-V-T differential properties of the Lennard-Jones fluid using radial distribution functions and molecular dynamics

Evaluation of P-V-T differential properties such as internal pressure, thermal pressure and isothermal compressibility, is a critical test for any equation of state. Certainly, pressure and internal energy equations obtained from RDF theory are not excepted from this rule either. Internal pressure, thermal pressure and isothermal compressibility for a Lennard-Jones (LJ) fluid have been calculated using three known analytical expressions for radial distribution function (RDF) at different temperatures and densities and compared with the corresponding values of these properties obtained from molecular dynamics (MD) and two accurate equations of state for the LJ fluid. Until now, this approach has not been utilized to estimate these quantities. To calculate these quantities, the variation of radial distribution function (RDF) with density and temperature is required. Therefore, we should have analytical expressions which explicitly present RDF as a function of temperature, density and interparticle distance. It is shown that some of these expressions evaluate the values of these quantities well.