Abstract
A new method for obtaining the well-known Karnahan-Starling equation for systems of hard spheres and its generalization for the case of any number of precisely known virial coefficients is proposed. The efficiency of the method for the construction of the statistical thermodynamics of a system of soft spheres, where an analytical expression for free energy and equations of state that agree well with the data of the computer experiment are found, is shown. The considered approach is generalized for systems with a positive definite potential of interaction between particles.
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