Total views : 42

Joule – Thomson Inversion Curves for Van Der Waals Gas from a Mathematical Point of View


  • Department of Applied Mathematics and Physical Sciences, National Technical University of Athens (NTUA), Zografou Campus 9, Iroon Polytechniou street, Zografou – 15780, Greece


A continuation of our ongoing investigation into Joule - Thomson inversion curves for van der Waals gas, is performed from a mathematical viewpoint. The methodology basis of our analysis is the quadratic polynomial theory. In this context, focusing on the parametric equation of inversion curves in a P - V frame of reference we obtain a qualitative illustration of variables T, V by means of two inequality relations. However, we should elucidate that these inequalities are valid only for the intersection points between the family of Joule - Thomson inversion curves and the isothermal spinodal lines, provided that they are both sketched in a common P - V coordinate system. The mathematical treatment of the parametric equation of these curves has been carried out in a rigorous manner and no further restriction is introduced for the variables T, V. Thus, the proposed inequalities have a wider range of validity when compared with those that had been previously presented by the author and therefore their possible applications to P - V - T surfaces of van der Waals gas, are also wider.


J – T Inversion Curves, P – V System, Quadratic Polynomial, Spinodal Lines, Van Der Waals Gas.

Full Text:

 |  (PDF views: 28)


  • Colazo A, da Silva F, Müller E, Olivera F. Joule-Thomson inversion curves and the supercritical cohesion parameters of cubic equations of state. 1992; 22:135.
  • Smith EB. Basic chemical thermodynamics. 3rd Edition, Clarendon Press, Oxford; 1982. p. 119.
  • Caldin EF. An introduction to chemical thermodynamics. Clarendon Press, Oxford; 1958. p. 424.
  • Mc Glashan ML. Chemical thermodynamics. Academic Press, London; 1979. p. 94.
  • Vrabec J, Kedia GK, Hasse H. Prediction of Joule–Thomson inversion curves for pure fluids and one mixture by molecular simulation. Cryogenics. 2005; 45(4):253–8. Crossref
  • Vrabec J, Kumar A, Hasse H. Joule–Thomson inversion curves of mixtures by molecular simulation in comparison to advanced equations of state: natural gas as an example. Fluid Phase Equilibria. 2007; 258:34–40.
  • Escobedo FA, Chen Z. Simulation of isoenthalps and Joule-Thomson inversion curves of pure fluids and mixtures. Molecular Simulation. 2006 Sep 23; 26(6):395–416. Crossref
  • Colina C, Lisal M, Siperstein F, Gubbins K. Accurate CO2 Joule–Thomson inversion curve by molecular simulations. Fluid Phase Equilibria. 2002 Nov 15; 202(2):253–62.
  • Castro-Marcano F, Olivera-Fuentes CG, Colina CM. Joule Thomson inversion curves and third virial coefficients for pure fluids from molecular-based models. Industrial Engineering Chemical Research. 2008 Sep 27; 47(22):8894–905.
  • Matin NS, Haghighi B. Calculation of the Joule-Thomson inversion curves from cubic equations of state. Fluid Phase Equilibria. 2000 Oct 1; 175(1–2):273–84. Crossref.
  • Haghighi B, Laee MR, Husseindokht MR, Matin NS. Prediction of Joule-Thomson inversion curves by the use of equation of state. Journal of Industrial and Engineering Chemistry. 2004; 10(2):316–20.
  • Nichita DV, Leibovici CF. Calculation of Joule–Thomson inversion curves for two-phase mixtures. Fluid Phase Equilibria. 2006; 246(1–2):167–76.
  • Bessieres D, Randzio SL, Pineiro M, Lafitte T, Daridon J. A combined pressure-controlled scanning calorimetry and monte carlo determination of the Joule−Thomson inversion curve: application to methane. Journal of Physics and Chemistry B. 2006 Feb 23; 110(11):5659–64. Crossref
  • Venetis J. The effect of the spinodal curve condition on J – T inversion curves for van der Waals real gas. Scientific Research and Essays. 2015 Oct; 10(19):610–4.
  • Adkins CJ. Equilibrium thermodynamics. Cambridge University Press, United Kingdom; 1968.
  • Prasolov VV. Polynomials. Algorithms and Computation in Mathematics, Springer –Verlag, Berlin, Heidelberg. 2004; 11:301.
  • Borwein P, Erdelyi T. Polynomials and polynomial inequalities. Graduate Texts in Mathematics, Spinger. 1995; 161:1–482. Crossref
  • Jafari M, Salarian H, Bazrafshan J. Study on entropy generation of multi – stream plate fin heat exchanger with use of changing variables thermodynamic and fluids flow rate between plates and provide an optimal model. Indian Journal of Science and Technology. 2016 Feb; 9(7):1–7. DOI: 10.17485/ijst/2016/v9i7/87736.
  • He X, Doolen G. Thermodynamic foundations of kinetic theory and lattice boltzmann models for multiphase flows. Journal of Statistical Physics. 2002 Apr; 107(1):309–28. Crossref
  • Kalanov TZ. The correct theoretical analysis of the foundations of classical thermodynamics. Indian Journal of Science and Technology. 2009 Jan; 2(1):12–7. DOI: 10.17485/ijst/2009/v2i1/29364.


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.