International audienceEven if not so ancient, the history of the heat engine efficiency at maximum power expression has been yet turbulent. More than a decade after the publication of the seminal article by Curzon and Ahlborn in 1975, two older works by Chambadal and Novikov were rediscovered, both dating from 1957. Then, some years ago, the name of Yvon arose from a textual reference to this famous relation in a conference article published in 1955. Thanks to a historical study of French-written books not published for a long time, and since never translated into other languages, we bring to light in this paper that this relation was actually first proposed by Henri B. Reitlinger in 1929

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This paper reviews how ideas have evolved in this field from the pioneering work of CARNOT right up to the present. The coupling of thermostatics with thermokinetics (heat and mass transfers) and entropy or exergy analysis is illustrated through study of thermomechanical engines such as the Carnot heat engine, and internal combustion engines. The benefits and importance of stagnation temperature and irreversibility parameters are underlined. The main situations of constrained (or unconstrained) optimization are defined, discussed and illustrated. The result of this study is a new branch of thermodynamics: Finite Dimensions Optimal Thermodynamics (FDOT).

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Nowadays the importance of thermomechanical engines is recognized worldwide. Since the industrial revolution, physicists and engineers have sought to maximize the efficiency of these machines, but also the mechanical energy or the power output of the engine, as we have recently found. The optimization procedure applied in many works in the literature focuses on considering new objective functions including economic and environmental criteria (i.e., ECOP ecological coefficient of performance). The debate here is oriented more towards fundamental aspects. It is known that the maximum of the power output is not obtained under the same conditions as the maximum of efficiency. This is shown, among other things, by the so-called nice radical that accounts for efficiency at maximum power, most often for the endoreversible configuration. We propose here to enrich the model and the debate by emphasizing the fundamental role of the heat transfer entropy together with the production of entropy, accounting for the external or internal irreversibilities of the converter. This original modeling to our knowledge, leads to new and more general results that are reported here. The main consequences of the approach are emphasized, and new limits of the efficiency at maximum energy or power output are obtained.

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