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Analytical treatment of the critical properties of a generalized van der Waals equation

  • Magdy E Amin EMAIL logo
Veröffentlicht/Copyright: 14. Mai 2021
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 76 Heft 7

Abstract

The two-parameter van der Waals (vdW) equation of state is generalized, by adding another two parameters to the attractive term. General relations between thermodynamic functions of the generalized vdW equation and the hard sphere gas are derived. The cubic equation of the generalized vdW is solved and the critical points (Pc, Vc, Tc) are obtained for general k. The critical properties of the vdW real gas such as the isothermal compressibility KT, the isobaric expansion coefficient α and the isobaric heat capacity CP are calculated exactly. The temperature dependence of KT, α and CP is investigated close to the critical point on the critical isobar path Pr = 1(P = Pc). Numerical calculations for KT and CP are presented above and below Pr.

Keywords: critical exponents; critical point phenomena; generalized van der Waals equation of state; thermodynamic functions and equation of state
Pacs: 05.20.-y; 05.70.Ce; 05.70.jk; 64.60.Fr
Corresponding author: Magdy E Amin, Mathematics Department, Faculty of Science, Minia University, 61915El-Minia, Egypt, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/zna-2021-0002).

Received: 2021-01-03
Revised: 2021-03-29
Accepted: 2021-04-10
Published Online: 2021-05-14
Published in Print: 2021-07-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

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https://doi.org/10.1515/zna-2021-0002
Schlagwörter für diesen Artikel
critical exponents; critical point phenomena; generalized van der Waals equation of state; thermodynamic functions and equation of state

Artikel in diesem Heft

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Simultaneous effects of Brownian motion and thermophoretic force on Eyring–Powell fluid through porous geometry
  4. Gravitation & Cosmology
  5. A cyclic non-singular universe from Gauss–Bonnet and superstring corrections
  6. Hydrodynamics
  7. Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
  8. Solid State Physics & Materials Science
  9. Enhancement of thermal conductivity and ultrasonic properties by incorporating CdS nanoparticles to PVA nanofluids
  10. Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic
  11. Thermodynamics & Statistical Physics
  12. Analytical treatment of the critical properties of a generalized van der Waals equation
  13. Thermodynamic equilibrium of a fluid column under the influence of gravity
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