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Nonparametric equation of state on the basis of the phenomenological theory of a critical point with the use of similarity theory

DOI: 10.17586/1606-4313-2020-19-2-79-85
UDC 536.71

Nonparametric equation of state on the basis of the phenomenological theory of a critical point with the use of similarity theory

Rykov S.V. , Kudryavtseva I.V. , Rykov V.A., Sverdlov A.V.

For citation: Rykov S.V., Kudryavtseva I.V., Rykov V.A., Sverdlov A.V. Nonparametric equation of state on the basis of the phenomenological theory of a critical point with the use of similarity theory. Vestnik Mezhdunarodnoi akademii kholoda. 2020. No 2. p.79-85

Abstract
One of the options for constructing a scaled equation with the use of Migdal’s phenomenological theory is analyzed. In the framework of this option, the hypothesis of the relationship between critical indices βand equality γis considered the equation γ= 4β, in addition to Griffith's equalities: 2 – α = βδ + β and γ = βδ – β. A variant of constructing a scale equation using the similarity relation between a lattice gas model and a real liquid is proposed. That allowed us to reduce the number of individual parameters of the scale function to one. The proposed approach is tested on the example of constructing the scale equation of argon. A comparative analysis is carried out with the scale equations of state of argon, where the critical indices are specified in accordance with the Griffith equalities and the condition γ= 3β justified by Bondarev V.N. in the framework of the statistical theory of a critical point.

Keywords: critical indices, lattice gas, similarity relations, scale function, Migdal's phenomenological theory, linear model.

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