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A method for constructing the equation of state of a liquid and gas based on the Migdal phenomenological theory and the Benedek hypothesis

DOI: 10.17586/1606‑4313‑2020‑19‑3-83-90
UDC 536.71

A method for constructing the equation of state of a liquid and gas based on the Migdal phenomenological theory and the Benedek hypothesis

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

For citation: Rykov S. V., Sverdlov A. V., Rykov V. A., Kudryavtseva I. V., Ustyuzhanin E. E. A method for constructing the equation of state of a liquid and gas based on the Migdal phenomenological theory and the Benedek hypothesis. Vestnik Mezhdunarodnoi akademii kholoda. 2020. No 3. p. 83–90.

Abstract
A method is proposed for constructing the fundamental equation of state (FEoS) of a liquid and gas that takes into account the features of a thermodynamic surface in the vicinity of a critical point.The structure of the equation of state is chosen in accordance with the new representation of the scale hypothesis in the form of an expression for the Helmholtz free energy F = Fr + Fs, where Fr is the regular function of density ρand temperatureT; Fs = Fs(ρ, T, δ, a(x)) is a singular component Fthat describes in the asymptotic neighborhood of the critical point the behavior of the equilibrium properties of the liquid in accordance with the scale theory (MT) of critical phenomena. Here δ is the critical index of the critical isotherm; a0(x) isthe large-scale free-energy function of Kudryavtseva–Rykov, which is developed on the basis of Migdal's phenomenological theory, the Benedek hypothesis, and the Scofield–Lister–Ho linear model; xis a scale variable. When calculating the individual parameters of the Helmholtz free energy scale function a0(x), a similarity theory relation is used, which relates the lattice gas and the real fluid. Based on the proposed method, an equation of state for sulfur hexafluoride has been developed, which, in accordance with MT, describes the behavior of equilibrium properties of theSF6. A comparison is made of experimental data, data on isochoric heat capacity and isobaric heat capacity, density values p-ρ-T of saturated steam and saturated liquid with the corresponding data calculated on the basis of the developed FEoS of SF6.

Keywords: equation of state, sulphur hexafluoride, critical point, Benedek hypothesis, dimensional analysis.

All references

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