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Derivation of a General Uid Equation of State Based on the Quasi-gaussian Entropy Theory: Application to the Lennard-jones Uid

In this article we present an equation of state for uids, based on the quasi-Gaussian entropy theory. The temperature dependence along iso-chores is described by a connned Gamma state, previously introduced, combined with a simple perturbation term. The eleven parameters occurring in the free energy and pressure expressions along the isochores are obtained from molecular dynamics simulation data. The equation of state has been parametrized for the Lennard-Jones uid in the (reduced) density range 0-1.0 and (reduced) temperature range 1.0-20.0 using (partly new) NV T molecular dynamics simulation data. An excellent agreement for both energy and pressure was obtained. 1 To test the ability to extrapolate to unknown state points, the parametriza-tion was also performed on a smaller set of data in the temperature range 1.0-6.0. The results in the two cases are remarkably close, even in the high temperature range, and are often almost indistinguishable, in contrast to a pure empirical equation of state, like for example the modiied Benedict-Webb-Rubin equation. The coexistence line agrees in general very well with Gibbs ensemble and NpT simulation results, and only very close to the critical point there are deviations. Our estimate of the critical point for both parametrizations is somewhat diierent from the best estimate based on Gibbs ensemble simulations, but is in excellent agreement with other estimates based on NV T simulations and integral equations.