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 Mat. Zametki, 2017, Volume 101, Issue 1, paper published in the English version journal (Mi mz11529)

Papers published in the English version of the journal

The Fermi–Dirac Distribution as a Model of a Thermodynamically Ideal Liquid. Phase Transition of the First Kind for Neutral Gases (Corresponding to NonpolarMolecules)

V. P. Maslov

National Research University Higher School of Economics, Moscow, Russia

Abstract: In this paper, we introduce the notion of a thermodynamically ideal liquid and calculate the temperature below which it appears. This temperature is $T=0.84 T_c$, where $T_c$ 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 $Z_c=3/8$. In this sense, for $T\leq 0.84 T_c$ and the particular case $Z_c=3/8$, 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.

Keywords: thermodynamically ideal liquid, van der Waals gas, binodal, spinodal, critical parameters, tropical analysis, Fermi–Dirac distribution, Bose statistics, virial expansion, phase transition.

English version:
Mathematical Notes, 2017, 101:1, 100–114

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Citation: V. P. Maslov, “The Fermi–Dirac Distribution as a Model of a Thermodynamically Ideal Liquid. Phase Transition of the First Kind for Neutral Gases (Corresponding to NonpolarMolecules)”, Math. Notes, 101:1 (2017), 100–114

Citation in format AMSBIB
\Bibitem{Mas17} \by V.~P.~Maslov \paper The Fermi–Dirac Distribution as a Model of a Thermodynamically Ideal Liquid. Phase Transition of the First Kind for Neutral Gases (Corresponding to NonpolarMolecules) \jour Math. Notes \yr 2017 \vol 101 \issue 1 \pages 100--114 \mathnet{http://mi.mathnet.ru/mz11529} \crossref{https://doi.org/10.1134/S0001434617010102} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3635288} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000396392700010} \elib{http://elibrary.ru/item.asp?id=29482164} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014751663} 

• http://mi.mathnet.ru/eng/mz11529

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. V. P. Maslov, “The Relationship between the Fermi–Dirac Distribution and Statistical Distributions in Languages”, Math. Notes, 101:4 (2017), 645–659
2. V. P. Maslov, T. V. Maslova, “A generalized number theory problem applied to ideal liquids and to terminological lexis”, Russ. J. Math. Phys., 24:1 (2017), 96–110