New Comment on Gibbs Density Surface of Fluid Argon: Revised Critical Parameters, L. V. Woodcock, Int. J. Thermophys. (2014) 35, 1770–1784

  • I. H. Umirzakov


The author comments on an article by Woodcock (Int J Thermophys 35:1770–1784, 2014), who investigates the idea of a critical line instead of a single critical point using the example of argon. In the introduction, Woodcock states that “The Van der Waals critical point does not comply with the Gibbs phase rule. Its existence is based upon a hypothesis rather than a thermodynamic definition”. The present comment is a response to the statement by Woodcock. The comment mathematically demonstrates that a critical point is not only based on a hypothesis that is used to define values of two parameters of the Van der Waals equation of state. Instead, the author argues that a critical point is a direct consequence of the thermodynamic phase equilibrium conditions resulting in a single critical point. It is shown that the thermodynamic conditions result in the first and second partial derivatives of pressure with respect to volume at constant temperature at a critical point equal to zero which are usual conditions of an existence of a critical point.


Coexistence Critical point First-order phase transition Liquid Phase equilibrium Vapor 


  1. 1.
    L.V. Woodcock, Comment on Gibbs density surface of fluid argon, revised critical parameters. Int. J. Thermophys. 35, 1770–1784 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    J.D. van der Waals, Ph.D. thesis, Leiden, The Netherlands (1873)Google Scholar
  3. 3.
    J.O. Hirschfelder, C.F. Curtiss, C.F. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)MATHGoogle Scholar
  4. 4.
    R. Balescu, Equilibrium and Non-equilibrium Statistical Mechanics (Wiley, New York, 1975)MATHGoogle Scholar
  5. 5.
    L.D. Landau, E.M. Lifshitz, Statistical Physics. Part 1 (Nauka, Moscow, 1976). [in Russian] Google Scholar
  6. 6.
    J.V. Sengers, M.A. Anisimov, Comment on Gibbs density surface of fluid argon, L. V. Woodcock, Int. J. Thermophys. (2014) 35, 1770–1784. Int. J. Thermophys. 36, 3001–3004 (2015)ADSCrossRefGoogle Scholar
  7. 7.
    F.G. Donnan, A. Haas, A Commentary on the Scientific Writings of J. Willard Gibbs, vol. 1 (Yale University, New Haven, CN, 1936), p. 41Google Scholar
  8. 8.
    J. Lekner, Parametric solution of the van der Waals liquid–vapor coexistence curve. Am. J. Phys. 50, 161–163 (1982)ADSCrossRefGoogle Scholar
  9. 9.
    M.N. Berberan-Santos, E.N. Bodunov, L. Pogliani, The van der Waals equation: analytical and approximate solutions. J. Math. Chem. 43, 1437–1457 (2008)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    D.C. Johnston, Advances in Thermodynamics of the van der Waals Fluid (Morgan and Claypool, San Rafael, CA, 2014)CrossRefGoogle Scholar
  11. 11.
    D.C. Johnston, Thermodynamic Properties of the van der Waals Fluid. ArXiv preprint arXiv:1402.1205 (2014)
  12. 12.
    G.A. Korn, T.M. Korn, Mathematical Handbook (McGraw-Hill Book Company, New York, 1968)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institute of ThermophysicsNovosibirskRussia

Personalised recommendations