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Journal of Non-Equilibrium Thermodynamics

Founded by Keller, Jürgen U.

Editor-in-Chief: Hoffmann, Karl Heinz

Managing Editor: Prehl, Janett / Schwalbe, Karsten

Ed. by Michaelides, Efstathios E. / Rubi, J. Miguel

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Volume 43, Issue 2


From Finite Time to Finite Physical Dimensions Thermodynamics: The Carnot Engine and Onsager’s Relations Revisited

Michel Feidt / Monica Costea
  • Corresponding author
  • Department of Engineering Thermodynamics, 195061 University POLITEHNICA of Bucharest, 060042 Bucharest, Romania
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  • Other articles by this author:
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Published Online: 2018-03-07 | DOI: https://doi.org/10.1515/jnet-2017-0047


Many works have been devoted to finite time thermodynamics since the Curzon and Ahlborn [1] contribution, which is generally considered as its origin. Nevertheless, previous works in this domain have been revealed [2], [3], and recently, results of the attempt to correlate Finite Time Thermodynamics with Linear Irreversible Thermodynamics according to Onsager’s theory were reported [4].

The aim of the present paper is to extend and improve the approach relative to thermodynamic optimization of generic objective functions of a Carnot engine with linear response regime presented in [4]. The case study of the Carnot engine is revisited within the steady state hypothesis, when non-adiabaticity of the system is considered, and heat loss is accounted for by an overall heat leak between the engine heat reservoirs.

The optimization is focused on the main objective functions connected to engineering conditions, namely maximum efficiency or power output, except the one relative to entropy that is more fundamental.

Results given in reference [4] relative to the maximum power output and minimum entropy production as objective function are reconsidered and clarified, and the change from finite time to finite physical dimension was shown to be done by the heat flow rate at the source.

Our modeling has led to new results of the Carnot engine optimization and proved that the primary interest for an engineer is mainly connected to what we called Finite Physical Dimensions Optimal Thermodynamics.

Keywords: Carnot engine; steady state modeling; linear irreversible thermodynamics; objective functions; optimization; Finite Time and Finite Physical Dimensions Thermodynamics


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    A. Vaudrey, F. Lanzetta and M. Feidt, H. B. Reitlinger and the origins of the efficiency at maximum power formula for heat engines, Journal of Non-Equilibrium Thermodynamics 39(4) (2014), 199–203.Google Scholar

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    A. Chisacof, S. Petrescu, B. Borcila, M. Costea, The History of Nice Radical and its Importance in the Optimization of Mechanical Work or Power Output of Reversible and Irreversible Cycles, in: Proceedings of the COFRET’16 Colloquium, Bucharest, Romania, June 29–30, (2016), 155–160.Google Scholar

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About the article

Received: 2017-09-12

Revised: 2018-02-04

Accepted: 2018-02-13

Published Online: 2018-03-07

Published in Print: 2018-04-25

Citation Information: Journal of Non-Equilibrium Thermodynamics, Volume 43, Issue 2, Pages 151–161, ISSN (Online) 1437-4358, ISSN (Print) 0340-0204, DOI: https://doi.org/10.1515/jnet-2017-0047.

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