https://doi.org/10.1140/epjp/s13360-024-05811-x
Regular Article
Thermodynamic self-consistence of equations of state of gases with first to third laws: Dieterici equation, a peculiar case
1
Departamento de ciencias, Escuela de ingeniería y ciencias, Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Estado de México, Av. Lago de Guadalupe Km. 3.5, C. P. 52926, Atizapán de Zaragoza, México
2
Departamento de Ciencias, Escuela de ingeniería y ciencias, Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Santa Fe, Av. Carlos Lazo 100, C.P. 01389, Álvaro Obregón, Ciudad de Mexico, Mexico
3
Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional, Edif. 9, 2º. Piso, UP Zacatenco, CP 07738, Ciudad de México, México
Received:
30
September
2024
Accepted:
6
November
2024
Published online:
23
November
2024
As is well-known, equations of state of macroscopic thermodynamic systems can be obtained by using empirical, semi-empirical or theoretical procedures. However, any equation of state must be compatible with the three laws of thermodynamics. In 1973, Tykodi and Hummel (TH) proposed a noteworthy criterion to establish if a given equation of state is consistent or not with the first and second laws of thermodynamics. Nevertheless, in the TH paper, it is shown that the Dieterici equation of state, deduced from empirical and theoretical basis at the end of nineteenth century, did not fulfill their criterion. Hence, it could not be considered as a thermodynamically valid equation of state. In the present article, we generalize the TH criterion; with the generalized criterion, it is shown that the Dieterici equation is, in fact, consistent with the first and second laws of thermodynamics. Furthermore, we extend the TH criterion through the incorporation of the third law to embrace the study of quantum gases which are usually found at temperatures near to absolute zero. We show that the equations of state of quantum gases such as the photon, Fermi and Bose–Einstein gases fulfill such an extended criterion.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
