The European Physical Journal Special Topics

, Volume 226, Issue 3, pp 489–498 | Cite as

Efficiencies of power plants, quasi-static models and the geometric-mean temperature

  • Ramandeep S. JohalEmail author
Regular Article
Part of the following topical collections:
  1. Nonlinearity, Nonequilibrium and Complexity: Questions and Perspectives in Statistical Physics


Observed efficiencies of industrial power plants are often approximated by the square-root formula: 1 − √T /T +, where T +(T ) is the highest (lowest) temperature achieved in the plant. This expression can be derived within finite-time thermodynamics, or, by entropy generation minimization, based on finite rates for the processes. In these analyses, a closely related quantity is the optimal value of the intermediate temperature for the hot stream, given by the geometric-mean value: √T +/T . In this paper, instead of finite-time models, we propose to model the operation of plants by quasi-static work extraction models, with one reservoir (source/sink) as finite, while the other as practically infinite. No simplifying assumption is made on the nature of the finite system. This description is consistent with two model hypotheses, each yielding a specific value of the intermediate temperature, say T 1 and T 2. The lack of additional information on validity of the hypothesis that may be actually realized, motivates to approach the problem as an exercise in inductive inference. Thus we define an expected value of the intermediate temperature as the equally weighted mean: (T 1 + T 2)/2. It is shown that the expected value is very closely given by the geometric-mean value for almost all of the observed power plants.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)ADSCrossRefGoogle Scholar
  2. 2.
    A. Bejan, in Advanced Engineering Thermodynamics (Wiley, New York, 1997), p. 377Google Scholar
  3. 3.
    M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)ADSCrossRefGoogle Scholar
  4. 4.
    G.B. Moreau, M.L.S. Schulman, Phys. Rev. B 85, 021129 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    H.B. Reitlinger, Sur l’utilisation de la chaleur dans les machines à feu (“On the use of heat in steam engines”, in French) (Vaillant-Carmanne, Liége, Belgium, 1929)Google Scholar
  6. 6.
    P. Chambadal, in Les Centrales Nucléaires (Armand Colin, Paris, France, 1957), pp. 41–58Google Scholar
  7. 7.
    I. Novikov, J. Nucl. Energy II 7, 125 (1958)Google Scholar
  8. 8.
    A. Vaudrey, F. Lanzetta, M. Feidt, J. Noneq. Therm. 39, 199 (2014)Google Scholar
  9. 9.
    G. Lebon, D. Jou, J. Casas-Vázquez, Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers (Springer-Verlag, Berlin, Heidelberg, 2008)Google Scholar
  10. 10.
    B. Andresen, Angew. Chem. 50, 2690 (2011)CrossRefGoogle Scholar
  11. 11.
    A. Bejan, J. Appl. Phys. 79, 1191 (1996)ADSCrossRefGoogle Scholar
  12. 12.
    M. Borlein, Kerntechnik (Vogel Buchverlag, Wurzburg, Germany, 2009)Google Scholar
  13. 13.
    W. Thomson, Phil. Mag. 5, 102 (1853)Google Scholar
  14. 14.
    M.J. Ondrechen, B. Andresen, M. Mozurchewich, R.S. Berry, Am. J. Phys. 49, 681 (1981)ADSCrossRefGoogle Scholar
  15. 15.
    H.S. Leff, Am. J. Phys. 55, 602 (1986)ADSCrossRefGoogle Scholar
  16. 16.
    B.H. Lavenda, Am. J. Phys. 75, 169 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    R.S. Johal, R. Rai, Europhys. Lett. 113, 10006 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    R.S. Johal, Phys. Rev. E 94, 012123 (2016)ADSCrossRefGoogle Scholar
  19. 19.
    Y. Izumida, K. Okuda, Phys. Rev. Lett. 112, 180603 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    M.J. Moran, H.N. Shapiro, D.D. Boettner, M.B. Bailey, in Fundamentals of Engineering Thermodynamics, 7th edn. (Wiley, New York, 2010), Chap. 7Google Scholar
  21. 21.
    H. Jeffreys, Theory of Probability, 2nd edn. (Clarendon Press, Oxford, 1948)Google Scholar
  22. 22.
    E.T. Jaynes, Probability Theory: The Logic of Science (Cambridge University Press, Cambridge, 2003)Google Scholar
  23. 23.
    P.S. Laplace, Memoir on the Probabilities of the Causes and Events, Stat. Sc. 1, 364 (translated by S.M. Stigler, 1986)CrossRefGoogle Scholar
  24. 24.
    E.T. Jaynes, The evolution of Carnot’s principle, in Maximum-Entropy and Bayesian Methods in Science and Engineering, edited by G.J. Erickson, C.R. Smith (Kluwer, Dordrecht, 1988)Google Scholar
  25. 25.
    J. Yvon, The Saclay Reactor: Two years experience in heat transfer by means of compressed gas as heat transfer agent, in Proceedings of the International Conference on Peaceful Uses of Atomic Energy (Geneva, Switzerland, 1955)Google Scholar
  26. 26.
    R.S. Johal, Phys. Rev. E 82, 061113 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    G. Thomas, R.S. Johal, J. Phys. A: Math. Theor. 48, 335002 (2015)CrossRefGoogle Scholar
  28. 28.
    P. Aneja, R.S. Johal, J. Phys. A: Math. Theor. 46, 365002 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    R.S. Johal, R. Rai, G. Mahler, Found. Phys. 45, 158 (2015)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Department of Physical SciencesIndian Institute of Science Education and Research Mohali, Sector 81, S.A.S. NagarPunjabIndia

Personalised recommendations