On an ideal gas related to the law of corresponding states
type: Item
instance of: scholarly article
title: On an ideal gas related to the law of corresponding states
zbMATH Open document ID: 1267.82123
DOI: 10.1134/S1061920810020081
author: V. P. Maslov
published in: Russian Journal of Mathematical Physics
publication date: 2012-10-22T00:00:00Z
review text: Using old ideas of A. I. Bachinsky and a new mathematical apparatus, the author develops a method for the construction of the equation of state for real gases consisting of one or two atoms or molecules. This new method is based on the correspondence between the thermodynamics of real nonideal gases and thermodynamics of ideal Bose gases but in a space of fractional dimension. The thermodynamic potential of the ideal Bose gas is used in the form \[ \Omega^{\mathrm{real}}(V(\gamma) V^{-1}_0- C_\gamma)[\pi^{1+\gamma} T^{2+\gamma}/\Gamma(2+ \gamma)] \int^\infty_0 \Biggl[{1\over e^{\zeta-k}-1}- {N\over e^{(\zeta-k)/N}-1}\Biggr]\,\zeta^{1+ \gamma}\,d\zeta. \] Here, \(T\) is the temperature, \(N\) is the real full number of particles in a gas, \(\zeta= \varepsilon/k_B T\), \(\varepsilon\) is the energy, \(k= \mu/k_BT\), \(\Gamma(x)\) is the Euler gamma function, \(\gamma= d/2- 1\), \(d\) is the fractional dimension, \(V_0\) is the normalization volume. Thus, the new thermodynamic variable \(d\) or more conveniently \(\gamma\), is introduced The fractional dimension \(d\) is unknown and it is unknown how the volume \(V_\gamma\) depends on \(\gamma\), whereas the character of this dependence is not known at present. Now, all thermodynamical functions (the equation of state, the compressibility factor) can be expressed using this new thermodynamic variable. In this paper, the method for obtaining the new thermodynamical variable \(\gamma\) is presented. The fractional dimension can be determined using the hypothesis that the compressibility factor of the ideal Bose gas is equal to the compressibility factor of the real gas and the isotherms of pressure of the ideal Bose gas, in units reduced to the critical one, can be equal to the reduced critical isotherms of a real gas.
reviewed by: Oleg A. Sinkevich
Mathematics Subject Classification ID: 82D05
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 91B70
Mathematics Subject Classification ID: 82B27
Mathematics Subject Classification ID: 82B30
zbMATH DE Number: 6097042
zbMATH Keywords: thermodynamical properties
zbMATH Keywords: gas vapors
zbMATH Keywords: corresponding states
zbMATH Keywords: equation of state
zbMATH Keywords: Zenon line
zbMATH Keywords: isotherms
zbMATH Keywords: compressibility factor
zbMATH Keywords: critical point
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6097042