Zwanzig’s perturbation method applied to the thermodynamic properties of dense noble gases

Zwanzig’s perturbation method leads to power series in 1/T for the thermodynamic properties and the compressibility of simple gases or liquids. To check the convergence of these series, the precision of limited 1/T expansions is obtained by comparison with the experimental results for argon and xenon. The expansion coefficients are determined by minimizing the relative mean square deviations. The expansions for the thermodynamic functions have a remarkable precision, even when restricted to three terms (two for the internal energy). The relative deviation is typically of the order of 10−4 to 10−3 for the whole range explored experimentally (from normal conditions to rather far in the liquid state). The coefficients obtained by this procedure are functions of the density. The dependence is very smooth. It is shown that this dependence can be approximated by an expansion in powers of the density, restricted to two or three terms. Analytical expressions are obtained for these terms by means of a cluster type analysis. Three of these coefficients, the expression of which is rather simple, are calculated using the Lennard-Jones potential as an a priori potential, and compared to the results of the fitting. For each coefficient the comparison gives a value of the hard-sphere diameter which is an arbitrary parameter in Zwanzig’s method. The three values obtained in this way are in reasonable agreement.