Nonequilibrium thermodynamics uses a terminology and provides tools to conveniently analyze transport and relaxation processes characteristic of steady-state out-of-equilibrium situations. These are important features of the theory since thermodynamic potentials may be well defined and the relationship between heat and entropy variations can be extended and assume a flux form.
This formalism also rests on the hypothesis of minimal entropy production, which allows analyses in terms of quasi-static processes. One corner stone of the theory is the assumption of local equilibrium. The building of nonequilibrium thermodynamics has also benefited from a phenomenological approach, which resulted in the force-flux formalism and Lars Onsager’s recriprocal relations Onsager in the early 1930s. The object of the article is thus to cover some of the milestones of thermodynamics, and show through the illustrative case of thermoelectric generators, our model heat engine, that the shift from Carnot’s efficiency to efficienc ies at maximum power explains itself naturally as one considers continuity and boundary conditions carefully indeed, as an adaptation of Friedrich Nietzche’s quote, we may say that the thermodynamic demon is in the details. The favorable comparison of the CA efficiency to actual values led many to consider it as a universal upper bound for real heat engines, but things are not so straightforward that a simple formula may account for a variety of situations. The notion of finite rate explicitly introduced time in thermodynamics, and its significance cannot be overlooked as shown by the wealth of works devoted to what is now known as finite-time thermodynamics since the end of the 1970’s. Yvon’s first analysis of a model of engine producing power, connected to heat source and sink through heat exchangers, went fairly unnoticed for twenty years, until Frank Curzon and Boye Ahlborn published their pedagogical paper about the effect of finite heat transfer on output power limitation and their derivation of the efficiency at maximum power, now known as the Curzon-Ahlborn (CA) efficiency. In the 1950’s, Jacques Yvon published a conference paper containing the necessary ingredients for a new class of models, and even a formula, not so different from that of Carnot’s efficiency, which later would become the new efficiency reference. Although it was derived from Carnot’s unrealistic model, the upper bound on the thermodynamic conversion efficiency, known as the Carnot efficiency, became a paradigm as the next target after the failure of the perpetual motion ideal. As a matter of fact, one result of Sadi Carnot’s work was precisely that the heat-to-work conversion process is fundamentally limited as such, it is considered as a first version of the second law of thermodynamics. By the beginning of the 20th century, the principles of thermodynamics were summarized into the so-called four laws, which were, as it turns out, definitive negative answers to the doomed quests for perpetual motion machines.
Classical equilibrium thermodynamics is a theory of principles, which was built from empirical knowledge and debates on the nature and the use of heat as a means to produce motive power.
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