The Fermi-Dirac distribution as a model of a thermodynamically ideal liquid. Phase transition of the first kind for neutral gases (corresponding to nonpolar molecules)

Mathematical notes. 2017. Vol. 101. No. 1. P. 100–114.

In this paper, we introduce the notions of enlarged number theory and of thermodynamically ideal liquid and calculate the temperature below which it appears. This temperature is T = 0.84Tc, where Tc is the critical temperature of a gas whose molecules are nonpolar. For such a gas, in a sufficiently wide neighborhood of the binodal, the isotherms of a gas and of a thermodynamically ideal liquid coincide with those of a van der Waals gas for the critical value of the compressibility factor Zc = 3/8. In this sense, for T ≤ 0.84Tc and the particular case Zc = 3/8, the developed theory is a generalization of the van der Waals model. A new phase transition of the second kind at the point of zero activity is described. 

Ключевые слова: Phase transition, spinodal, binodal, the van der Waals gas, Fermi–Dirac distribution, Bose statistics, critical parameters, thermodynamically ideal liquid, tropical analysis, virial expansion