Continuity and boundary conditions in thermodynamics: From Carnot's efficiency to efficiencies at maximum power

[...] 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. 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. 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. 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. Yvon's first analysis [...] 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. 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. [...] 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 efficiencies at maximum power explains itself naturally as one considers continuity and boundary conditions carefully [...]

On the efficiency at maximum cooling power

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency $\eta_{\rm CA}$ being considered as a universal upper bound. Yet, no valid counterpart to $\eta_{\rm CA}$ has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this Letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators

Réflexions sur l'optimisation thermodynamique des générateurs thermoélectriques

Les phénomènes thermoélectriques sont un moyen de convertir directement l énergie thermique en énergie électrique ; ils sont à ce titre au cœur de nombreuses recherches dans le domaine de l énergétique. Au-delà de l optimisation des matériaux constituants les générateurs thermoélectriques, il est également nécessaire de mener une réflexion sur la manière dont ces générateurs sont utilisés. La contribution des contacts thermiques entre le générateur et les réservoirs thermiques est un facteur qui va modifier les conditions de fonctionnement optimales du générateur. En utilisant la notion de courant thermique convectif, développée par Thomson il y a plus de 150 ans, nous généralisons les expressions classiques du fonctionnement à puissance maximum pour le générateur pour ce cas de figure. Nous constatons toutefois que ces conditions se réduisent à une adaptation d impédance, à la fois thermique et électrique Outre son intérêt pratique, le générateur thermoélectrique est également un système modèle de choix pour étudier la théorie du transport couplé et des phénomènes irréversibles. En utilisant la description donnée par Ioffe de ce système, nous montrons que l efficacité à maximum de puissance, un coefficient de performance au cœur de la thermodynamique à temps fini, s exprime comme une fonction relativement simple des paramètres du système. La nouveauté de ce travail repose sur une prise en compte appropriée des dissipations internes associées au processus de conversion d énergie. Les résultats sont généralisés enfin aux cas d autres machines thermiques telle que la roue à rochet de Feynman.Thermoelectric phenomena are a way to directly convert thermal energy into electrical energy; they thus are at the heart of several researches in the field of energy conversion. The optimization of the thermoelectric generators includes materials improvement but a reflection on their working conditions is also mandatory. The contribution of the thermal contacts between the generator and the heat reservoirs is a factor that will change the optimum operating conditions of the generator. Using the concept of convective heat flow, developed by Thomson more than 150 years ago, we generalize the classical expression of maximum power conditions. Moreover, we note that these conditions may be reduced to impedance matching conditions, both thermal and electrical. In addition to its practical interest, the thermoelectric generator is also an ideal model system to study the theory of coupled transport and of irreversible phenomena. Using the description of this system given by Ioffe, we show that the maximum power efficiency, a coefficient of performance at the heart of finite time thermodynamics, expressed as a simple function of the system parameters. The novelty of this work is based on a proper consideration of internal dissipation associated with the energy conversion process. The results are then generalized to other thermal engines such as the Feynman ratchet.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Green thermoelectrics: Observation and analysis of plant thermoelectric response

Plants are sensitive to thermal and electrical effects; yet the coupling of both, known as thermoelectricity, and its quantitative measurement in vegetal systems never were reported. We recorded the thermoelectric response of bean sprouts under various thermal conditions and stress. The obtained experimental data unambiguously demonstrate that a temperature difference between the roots and the leaves of a bean sprout induces a thermoelectric voltage between these two points. Basing our analysis of the data on the force-flux formalism of linear response theory, we found that the strength of the vegetal equivalent to the thermoelectric coupling is one order of magnitude larger than that in the best thermoelectric materials. Experimental data also show the importance of the thermal stress variation rate in the plant's electrophysiological response. Therefore, thermoelectric effects are sufficiently important to partake in the complex and intertwined processes of energy and matter transport within plants

Reflections on the thermodynamic optimization of thermoelectric generators

Les phénomènes thermoélectriques sont un moyen de convertir directement l’énergie thermique en énergie électrique ; ils sont à ce titre au cœur de nombreuses recherches dans le domaine de l’énergétique. Au-delà de l’optimisation des matériaux constituants les générateurs thermoélectriques, il est également nécessaire de mener une réflexion sur la manière dont ces générateurs sont utilisés. La contribution des contacts thermiques entre le générateur et les réservoirs thermiques est un facteur qui va modifier les conditions de fonctionnement optimales du générateur. En utilisant la notion de courant thermique convectif, développée par Thomson il y a plus de 150 ans, nous généralisons les expressions classiques du fonctionnement à puissance maximum pour le générateur pour ce cas de figure. Nous constatons toutefois que ces conditions se réduisent à une adaptation d’impédance, à la fois thermique et électrique Outre son intérêt pratique, le générateur thermoélectrique est également un système modèle de choix pour étudier la théorie du transport couplé et des phénomènes irréversibles. En utilisant la description donnée par Ioffe de ce système, nous montrons que l’efficacité à maximum de puissance, un coefficient de performance au cœur de la thermodynamique à temps fini, s’exprime comme une fonction relativement simple des paramètres du système. La nouveauté de ce travail repose sur une prise en compte appropriée des dissipations internes associées au processus de conversion d’énergie. Les résultats sont généralisés enfin aux cas d’autres machines thermiques telle que la roue à rochet de Feynman.Thermoelectric phenomena are a way to directly convert thermal energy into electrical energy; they thus are at the heart of several researches in the field of energy conversion. The optimization of the thermoelectric generators includes materials improvement but a reflection on their working conditions is also mandatory. The contribution of the thermal contacts between the generator and the heat reservoirs is a factor that will change the optimum operating conditions of the generator. Using the concept of convective heat flow, developed by Thomson more than 150 years ago, we generalize the classical expression of maximum power conditions. Moreover, we note that these conditions may be reduced to impedance matching conditions, both thermal and electrical. In addition to its practical interest, the thermoelectric generator is also an ideal model system to study the theory of coupled transport and of irreversible phenomena. Using the description of this system given by Ioffe, we show that the maximum power efficiency, a coefficient of performance at the heart of finite time thermodynamics, expressed as a simple function of the system parameters. The novelty of this work is based on a proper consideration of internal dissipation associated with the energy conversion process. The results are then generalized to other thermal engines such as the Feynman ratchet

Réflexions sur l’optimisation thermodynamique des générateurs thermoélectriques

Thermoelectric phenomena are a way to directly convert thermal energy into electrical energy; they thus are at the heart of several researches in the field of energy conversion. The optimization of the thermoelectric generators includes materials improvement but a reflection on their working conditions is also mandatory. The contribution of the thermal contacts between the generator and the heat reservoirs is a factor that will change the optimum operating conditions of the generator. Using the concept of convective heat flow, developed by Thomson more than 150 years ago, we generalize the classical expression of maximum power conditions. Moreover, we note that these conditions may be reduced to impedance matching conditions, both thermal and electrical. In addition to its practical interest, the thermoelectric generator is also an ideal model system to study the theory of coupled transport and of irreversible phenomena. Using the description of this system given by Ioffe, we show that the maximum power efficiency, a coefficient of performance at the heart of finite time thermodynamics, expressed as a simple function of the system parameters. The novelty of this work is based on a proper consideration of internal dissipation associated with the energy conversion process. The results are then generalized to other thermal engines such as the Feynman ratchet.Les phénomènes thermoélectriques sont un moyen de convertir directement l’énergie thermique en énergie électrique ; ils sont à ce titre au cœur de nombreuses recherches dans le domaine de l’énergétique. Au-delà de l’optimisation des matériaux constituants les générateurs thermoélectriques, il est également nécessaire de mener une réflexion sur la manière dont ces générateurs sont utilisés. La contribution des contacts thermiques entre le générateur et les réservoirs thermiques est un facteur qui va modifier les conditions de fonctionnement optimales du générateur. En utilisant la notion de courant thermique convectif, développée par Thomson il y a plus de 150 ans, nous généralisons les expressions classiques du fonctionnement à puissance maximum pour le générateur pour ce cas de figure. Nous constatons toutefois que ces conditions se réduisent à une adaptation d’impédance, à la fois thermique et électrique Outre son intérêt pratique, le générateur thermoélectrique est également un système modèle de choix pour étudier la théorie du transport couplé et des phénomènes irréversibles. En utilisant la description donnée par Ioffe de ce système, nous montrons que l’efficacité à maximum de puissance, un coefficient de performance au cœur de la thermodynamique à temps fini, s’exprime comme une fonction relativement simple des paramètres du système. La nouveauté de ce travail repose sur une prise en compte appropriée des dissipations internes associées au processus de conversion d’énergie. Les résultats sont généralisés enfin aux cas d’autres machines thermiques telle que la roue à rochet de Feynman

Continuum theory of TE elements

This chapter on optimization process of thermoelectric elements devices and elements begins with a discussion on Domenicali's heat balance equation, and then looks at a descriptive method that is often used in the corresponding calculation, the so-called constant properties model (CPM). The CPM is a widespread and adequate reference for comparing both TE materials and devices, and is sometimes denoted as Ioffe CPM approximation. The chapter proposes a detailed analysis of the maximum power (density) and efficiency of a thermogenerator element. A key factor of the overall performance of a TE module is the contact or the installation of the TE material in the modules and the corresponding contact resistances. The chapter also provides an overview of the influence of the leg geometry on the performance of a TE element. For this purpose, the representative literature references are discussed

Green thermoelectrics: Observation and analysis of plant thermoelectric response

Plants are sensitive to thermal and electrical effects; yet the coupling of both, known as thermoelectricity, and its quantitative measurement in vegetal systems never were reported. We recorded the thermoelectric response of bean sprouts under various thermal conditions and stress. The obtained experimental data unambiguously demonstrate that a temperature difference between the roots and the leaves of a bean sprout induces a thermoelectric voltage between these two points. Basing our analysis of the data on the force-flux formalism of linear response theory, we found that the strength of the vegetal equivalent to the thermoelectric coupling is one order of magnitude larger than that in the best thermoelectric materials. Experimental data also show the importance of the thermal stress variation rate in the plant’s electrophysiological response. therefore, thermoelectric effects are sufficiently important to partake in the complex and intertwined processes of energy and matter transport within plants