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A method is proposed to approximate the unlimited subcritical set of Mayer`sreducible cluster integrals (i.e., the power coefficients of the known virialexpansions for pressure and density in powers of activity) on the basis ofinformation about several irreducible integrals (virial coefficients) and thesaturation activity. For the Lennard-Jones fluid, the first four irreducibleintegrals are actually sufficient to reproduce gas isotherms (including theflat phase-transition region) with high accuracy at temperatures between thetriple and critical points. At low temperatures, even the usage of thefirst-order irreducible integral only (second virial coefficient) yields almostthe same accuracy that, in turn, makes the method applicable to the real fluidswith unknown interaction potential. In particular, the calculated waterisotherms are in good agreement with experiments.

A method to approximate cluster integrals and reproduce subcritical isotherms for model and real gases