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Size dependence of efficiency at maximum power of heat engine

  • Y. IzumidaEmail author
  • N. Ito
Regular Article

Abstract

We perform a molecular dynamics computer simulation of a heat engine model to study how the engine size difference affects its performance. Upon tactically increasing the size of the model anisotropically, we determine that there exists an optimum size at which the model attains the maximum power for the shortest working period. This optimum size locates between the ballistic heat transport region and the diffusive heat transport one. We also study the size dependence of the efficiency at the maximum power. Interestingly, we find that the efficiency at the maximum power around the optimum size attains a value that has been proposed as a universal upper bound, and it even begins to exceed the bound as the size further increases. We explain this behavior of the efficiency at maximum power by using a linear response theory for the heat engine operating under a finite working period, which naturally extends the low-dissipation Carnot cycle model [M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The theory also shows that the efficiency at the maximum power under an extreme condition may reach the Carnot efficiency in principle.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    F. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)ADSCrossRefGoogle Scholar
  2. 2.
    I.I. Novikov, J. Nucl. Energy II 7, 125 (1958)Google Scholar
  3. 3.
    P.T. Landsberg, H.S. Leff, J. Phys. A 22, 4019 (1989)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    J.M. Gordon, Am. J. Phys. 57, 1136 (1989)ADSCrossRefGoogle Scholar
  5. 5.
    A. Benjamin, J. Appl. Phys. 79, 1191 (1996)ADSCrossRefGoogle Scholar
  6. 6.
    P. Salamon, J.D. Nulton, G. Siragusa, T.R. Andersen, A. Limon, Energy 26, 307 (2001)CrossRefGoogle Scholar
  7. 7.
    L. Chen, Z. Yan, J. Chem. Phys. 90, 3740 (1989)ADSCrossRefGoogle Scholar
  8. 8.
    S. Velasco, J.M.M. Roco, A. Medina, A. Calvo Hernández, J. Phys. D 34, 1000 (2001)ADSCrossRefGoogle Scholar
  9. 9.
    H. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edn. (Wiley, New York, 1985), Chap. 4Google Scholar
  10. 10.
    C. Van den Broeck, Phys. Rev. Lett. 95, 190602 (2005)CrossRefGoogle Scholar
  11. 11.
    A. Gomez-Marin, J.M. Sancho, Phys. Rev. E 74, 062102 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    T. Schmiedl, U. Seifert, Europhys. Lett. 81, 20003 (2008)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    M. Esposito, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 102, 130602 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    Y. Izumida, K. Okuda, Europhys. Lett. 83, 60003 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    Y. Izumida, K. Okuda, Phys. Rev. E 80, 021121 (2009)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Y. Izumida, K. Okuda, Europhys. Lett. 97, 10004 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    B. Gaveau, M. Moreau, L.S. Schulman, Phys. Rev. Lett. 105, 060601 (2010)ADSCrossRefGoogle Scholar
  18. 18.
    M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    U. Seifert, Phys. Rev. Lett. 106, 020601 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    Y. Apertet, H. Ouerdane, O. Glavatskaya, C. Goupil, Ph. Lecoeur, Europhys. Lett. 97, 28001 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    J. Hoppenau, M. Niemann, A. Engel, Phys. Rev. E 87, 062127 (2013)ADSCrossRefGoogle Scholar
  22. 22.
    V. Blickle, C. Bechinger, Nat. Phys. 8, 143 (2012)CrossRefGoogle Scholar
  23. 23.
    U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    B.J. Alder, T.E. Wainwright, J. Chem. Phys. 31, 459 (1959)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    R. Tehver, F. Toigo, J. Koplik, J.R. Banavar, Phys. Rev. E 57, R17 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    B.J. Alder, T.E. Wainwright, J. Chem. Phys. 27, 1208 (1958)ADSCrossRefGoogle Scholar
  27. 27.
    T. Shimada, T. Murakami, S. Yukawa, K. Saito, N. Ito, J. Phys. Soc. Jpn 69, 3150 (2000)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Applied PhysicsThe University of TokyoTokyoJapan

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