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The Many Avatars of Curzon-Ahlborn Efficiency

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Abstract

Efficiency at maximum power output of irreversible heat engines has attracted a lot of interest in recent years. Curzon-Ahlborn (CA) efficiency is a well-known result in this field, given by the expression \(1 - \sqrt {{T_c}/{T_h}}\), where Tc and Th are the cold and hot reservoir temperatures. We discuss the occurence of this particularly simple and elegant formula in different models and contexts.

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  1. F L Curzon and B Ahlborn, Efficiency of a Carnot engine at maximum power output, Am. J. Phys., Vol.43, 22, 1975, https://doi.org/10.1119/1.10023.

    Article  Google Scholar 

  2. A Bejan, Advanced Engineering Thermodynamics, p.377, Wiley, New York, 1997.

    Google Scholar 

  3. M Esposito, R Kawai, K Lindenberg and C Van den Broeck, Efficiency at maximum power of low-dissipation Carnot engines, Phys. Rev. Lett., Vol.105, 150603, 2010, https://doi.org/10.1103/PhysRevLett.105.150603.

    Article  Google Scholar 

  4. R S Johal, Efficiencies of power plants, quasi-static models and the geometric-mean temperature, The European Physical Journal Special Topics, Vol.226, 489, 2017, https://doi.org/10.1140/epjst/e2016-60265-9.

    Article  Google Scholar 

  5. A Vaudrey, F Lanzetta and M Feidt, H. B. Reitlinger and the origins of the efficiency at maximum power formula for heat engines, J. Noneq. Therm., Vol.39, 199, 2014, https://doi.org/10.1515/jnet-2014-0018.

    Google Scholar 

  6. G Lebon, D Jou and J Casas-Vázquez, Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers, Springer-Verlag, Berlin Heidelberg, 2008.

    Book  Google Scholar 

  7. L Onsager, Reciprocal relations in irreversible processes — I, Phys. Rev., Vol.37, 405, 1931, https://doi.org/10.1103/PhysRev.37.405.

    Article  Google Scholar 

  8. B Bagchi, Onsager’s reciprocal relations, Resonance: Journal of Science Education, Vol. 23, No. 10 pp. 1073–1075, 2018, https://doi.org/10.1007/s12045-018-0714-z.

    Article  Google Scholar 

  9. C Van den Broeck, Thermodynamic efficiency at maximum power, Phys. Rev. Lett., Vol.95, 190602, 2005, https://doi.org/10.1103/PhysRevLett.95.190602.

    Article  Google Scholar 

  10. M Esposito, K Lindenberg and C Van den Broeck, Universality of efficiency at maximum power, Phys. Rev. Lett., Vol.102, 130602, 2009, https://doi.org/10.1103/PhysRevLett.102.130602.

    Article  Google Scholar 

  11. H B Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed, John Wiley, New York, 1985.

    Google Scholar 

  12. R S Johal and R Rai, Near-equilibrium universality and bounds on efficiency in quasi-static regime with finite source and sink, Europhys. Lett., Vol.113, 10006, 2016, https://doi.org/10.1209/0295-5075/113/10006

    Article  Google Scholar 

  13. R S Johal, R Rai and G Mahler, Reversible heat engines: Bounds on estimated efficiency from inference, Foundations of Physics, Vol.45, 158, 2015, https://doi.org/10.1007/s10701-014-9856-3.

    Article  Google Scholar 

  14. R S Johal, Universal efficiency at optimal work with Bayesian statistics, Phys. Rev. E., Vol.82, 061113, 2010, https://doi.org/10.1103/PhysRevE.82.061113.

    Article  Google Scholar 

  15. A Calvo Hernández, J M M Roco, A Medina, S Velasco, and L Guzman-Vargas, The maximum power efficiency \(1 - \sqrt \tau\): Research, education, and bibliometric relevance, The European Physical Journal Special Topics, Vol.224, 809, 2015, DOI: https://doi.org/10.1140/epjst/e2015-02429-4.

    Article  Google Scholar 

  16. M Feidt, The history and perspectives of efficiency at maximum power of the Carnot engine, Entropy, Vol.19, 369, 2017, https://doi.org/10.3390/e19070369.

    Article  Google Scholar 

  17. N Sánchez-Salas, L López-Palacios, S Velasco and A Calvo Hernández, Optimization criteria, bounds, and efficiencies of heat engines, Phys. Rev. E., Vol.82, 051101, 2010, https://doi.org/10.1103/PhysRevE.82.051101.

    Article  Google Scholar 

  18. H Ouerdane, Y Apertet, C Goupil and P Lecoeur, Continuity and boundary conditions in thermodynamics: From Carnot’s efficiency to efficiencies at maximum power, The European Physical Journal Special Topics, Vol.224, 839, 2015, DOI: https://doi.org/10.1140/epjst/e2015-02431-x.

    Article  Google Scholar 

  19. H B Reitlinger, Sur l’utilisation de la chaleur dans les machines á feu (On the use of heat in steam engines in French), Vaillant-Carmanne, Liége, Belgium, 2008.

    Google Scholar 

  20. P Chambadal, Les Centrales Nuclearis, Armand Colin, Paris, France, Vol.4, 1, 1957.

    Google Scholar 

  21. I Novikov, The efficiency of atomic power stations, J. Nucl. Energy II., Vol.7, 125, 1958.

    Google Scholar 

  22. B Andresen, Current trends in finite-time thermodynamics, Ange. Chem., Vol.50, 2690, 2011, https://doi.org/10.1002/anie.201001411.

    Article  Google Scholar 

  23. A Bejan, Entropy generation minimization: The new thermodynamics of finite-size devices and finite-time processes, J. Appl. Phys., Vol.79, 1191, 1996, https://doi.org/10.1063/L362674.

    Article  Google Scholar 

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Acknowledgement

Arun M. Jayannavar thanks Department of Science and Technology, India for the grant of J.C. Bose National Fellowship.

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Correspondence to Ramandeep S. Johal or Arun M. Jayannavar.

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Ramandeep Johal works on the foundations of thermodynamics, including nonequilibrium and information-theoretic aspects of thermodynamics and its extensions to the quantum regime. He is a faculty in the Department of Physical Sciences, IISER Mohali.

Arun M Jayannavar is a senior scientist at Institute of Physics, Bhubaneswar. He is interested in general condensed matter physics and emergent phenomena.

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Johal, R.S., Jayannavar, A.M. The Many Avatars of Curzon-Ahlborn Efficiency. Reson 26, 211–225 (2021). https://doi.org/10.1007/s12045-021-1120-5

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