On the Interpretation of Near-Critical Gas–Liquid Heat Capacities

  • Leslie V. WoodcockEmail author


This comment is in response to a comment by Sengers and Anisimov on the article “Gibbs density surface of fluid argon” that contradicts prevailing theory. It has not “been established experimentally that the thermodynamic properties of fluids satisfy scaling laws with universal critical exponents asymptotically close to a single critical point of the vapor–liquid phase transition.” Here we explain why an apparent divergence of \(\hbox {C}_{\mathrm{v}}\), in historical experimental “evidence,” is based upon a misinterpretation of near-critical gas–liquid heat capacity measurements in the two-phase coexistence region. The conclusion that there is no “singular critical point” on Gibbs density surface still stands.


Argon Critical point Isochoric heat capacity Vapor–liquid coexistence 



I wish to thank (i) Dr. John F. Maguire of Scientific Simulation Systems Inc. for bringing the misinterpretations of “\(\hbox {C}_\mathrm{{v}}\)” to my attention, (ii) my colleague Prof. Igor Khmelinskii of University of Algarve, for help in obtaining the original Russian “\(\hbox {C}_\mathrm{{v}}\)” papers cited, and (iii) Prof. Richard Sadus, Swinburne University, Australia for providing the original “\(\hbox {C}_{ss}\)” dataset (plotted in Fig. 2) that were publicly distributed by the space shuttle authors [6].


  1. 1.
    L.V. Woodcock, Int. J. Thermophys. 35, 1770 (2014)ADSCrossRefGoogle Scholar
  2. 2.
    J.V. Sengers, M.A. Anisimov, Int. J. Thermophys. 36, 3001 (2015)ADSCrossRefGoogle Scholar
  3. 3.
    M.A. Anisimov, A.T. Berestov, L.S. Veksler, B.A. Koval’chuk, V.A. Smirnov, Sov. Phys. JETP 39, 359 (1972)ADSGoogle Scholar
  4. 4.
    A.V. Voronel, V.A. Smirnov, YuR Chashkin, JETP Lett. 9, 229 (1969)ADSGoogle Scholar
  5. 5.
    M.A. Anisimov, B.A. Koval’chuk, V.A. Smirnov, Thermophysical Properties of Substances and Materials, in Russian (Izd-vo Standartov, Moscow, 1978)Google Scholar
  6. 6.
    A. Haupt, J. Straub, Phys. Rev. E 59, 1975 (1999)CrossRefGoogle Scholar
  7. 7.
    A. Michels, J.M. Levelt, W. de Graaff, Physica 24, 659 (1958)ADSCrossRefGoogle Scholar
  8. 8.
    A. Michels, J.M. Levelt, G.J. Wolkers, Physica 24, 769 (1958)ADSCrossRefGoogle Scholar
  9. 9.
    NIST Thermo-physical Properties of Fluid Systems (2017),
  10. 10.
    M.A. Anisimov, Int. J. Thermophys. 32, 2003 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    M.I. Bagatskiǐ, A.V. Voronel, V.G. Gusak, Zh Exp, Teor Fiz, Sov. Phys. JETP 43, 728 (1962). [Sov. Phys. JETP, 16, 517 (1963)]Google Scholar
  12. 12.
    A.K. Wyczalkowska, J.V. Sengers, J. Chem. Phys. 111, 1551 (1999)ADSCrossRefGoogle Scholar
  13. 13.
    I. Traube, Trans. Faraday Soc. 34, 1234 (1938)CrossRefGoogle Scholar
  14. 14.
    O.K. Rice, in Thermodynamics and Physics of Matter, Section E Critical Phenomena, vol. 1, ed. by F.D. Rossini (Oxford University Press, London, 1955), pp. 419–500Google Scholar
  15. 15.
    L.V. Woodcock, Int. J. Thermophys. 37, 24 (2016)CrossRefGoogle Scholar
  16. 16.
    L.V. Woodcock, Percolation transitions and fluid state boundaries, in Proceedings of W. G. Hoover 80th Birthday Symposium, Sheffield, 2016 (CMST, in press, published online 7th April 2017). doi: 10.12921/mst.2016.0000070
  17. 17.
    M.S. Green, J.V. Sengers (eds.), in Critical Phenomena: Proceedings of a Conference Washington DC 1965, See e.g. (i) J. S. Rowlinson, Critical states of fluids and fluid mixtures: a review of the experimental position, 9–12 (ii) M. E. Fisher, Notes, definitions and formula for critical-point singularities, pp. 21–25. (National Bureau of Standards, Washington DC, 1966)Google Scholar
  18. 18.
    C. Tegeler, R. Span, W. Wagner, A new equation of state for argon covering the fluid region for temperatures from the melting line to 700 K at pressures up to 1000 MPa. J. Phys. Chem. Ref. Data 28, 779–850 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    L.V. Woodcock, Thermodynamic fluid equations-of-state: new science-based functional forms, in Proc. JETC Budapest May 2017 (to be published in journal Entropy).

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of AlgarveFaroPortugal

Personalised recommendations