Application of the fractal state equation to calculate helium isobars at high temperatures and pressures
R.A. Magomedov, E.N. Akhmedov
Institute for Geothermal Research and Renewable Energy of the Joint Institute for High Temperatures of the RAS
DOI: 10.26456/pcascnn/2025.17.276
Original article
Abstract: The paper presents calculations of the state equation (isobars) of helium-4 in the pressure range from 10 to 100 MPa and the temperature range from 600 to 1500 K using the fractal state equation and the Fract EOS software. It was discovered that the temperature dependence of the fitting parameter α for the temperatures above 400 K weakens sharply and practically disappears approaching to 600 K. For helium-4, this allowed to approximate the dependence of α on density by a polynomial and to use it in calculations at temperatures above 600 K. For calculation of isobars, a set of isotherms with a small temperature step was calculated. Then, a point with the required pressure was selected on each isotherm. Obtained results show good agreement with literature data. In addition, for the specified temperatures and pressures, the isobars of the classical equation of state and the Redlich-Kwong equation of state were calculated. A comparison of the relative calculation error showed a significant advantage of the fractal equation of state.
Keywords: mathematical modeling, software for substance properties calculation, fractal state equation, Redlich-Kwong state equation, integral-differentiation of fractional order, Maxwell relations, Helmholtz potential, partition function, helium-4, isobar, thermophysical properties
- Ramazan A. Magomedov – Senior Researcher, Institute for Geothermal Research and Renewable Energy of the Joint Institute for High Temperatures of the RAS
- Enver N. Akhmedov – Researcher, Institute for Geothermal Research and Renewable Energy of the Joint Institute for High Temperatures of the RAS
For citation:
Magomedov R.A., Akhmedov E.N. Primenenie fraktalnogo uravneniya sostoyaniya dlya raschyota izobar geliya pri vysokikh temperaturakh i davleniyakh [Application of the fractal state equation to calculate helium isobars at high temperatures and pressures], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 276-283. DOI: 10.26456/pcascnn/2025.17.276. ⎘
Full article (in Russian): download PDF file
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