Analysis of the second virial coefficient, and application to rare gas mixtures

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Abstract The second virial coefficients characterize the real-gas non-ideality caused by the interaction between molecular pairs and ensure a link between macroscopic thermodynamic properties and microscopic molecular interactions because they depend on intermolecular interaction energy and temperature. Therefore, the second virial coefficients that are suitable for calculating the thermodynamic properties of gases used in the many fields in this work are preferred. In this study, a semi-analytic representation for the second virial (SV) coefficient over exponent–spline-Morse-spline-van der Waals potential (ESMSV), investigating the thermodynamic properties of rare gases, is presented. In the study the series formulae of the hypergeometric function, exponential function, gamma function, Meijer function, and binomial expansion have used in the suggested method. The numerical approach has been used mostly to evaluate the SV coefficient with ESMSV potential in literature. This unified formula can be applied and tested for rare gases. The obtained results for the SV coefficient over ESMSV potential of 4He–4He, 4He–Ne, 4He–Ar, 4He–Kr, 4He–Xe, Ne–Ne, O2–O2, and Ar–O2 rare gases have been compared with alternative experimental data and numerical calculations and shown that semi-analytical expression can be successfully applied to evaluate simple fluids.