Work Output and Efficiency at Maximum Power of Linear Irreversible Heat Engines Operating with a Finite-Sized Heat Source

Izumida, Yuki; Okuda, Koji

doi:10.1103/physrevlett.112.180603

Cited by 65 publications

(101 citation statements)

References 34 publications

(55 reference statements)

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“…For thermochemical engines it was shown that the form of the EMP [25] is controlled by the symmetries of the underlying dynamics (see also [26] for a similar study, but with finite-sized reservoirs). This result was further precised [27] and recently a similar argumentation was successfully used for general thermodynamic devices [28].…”

Section: Introductionmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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A new universality in optimization of trade-off between power and efficiency for low-dissipation Carnot cycles is presented. It is shown that any trade-off measure expressible in terms of efficiency and the ratio of power to its maximum value can be optimized independently of most details of the dynamics and of the coupling to thermal reservoirs. The result is demonstrated on two specific trade-off measures. The first one is designed for finding optimal efficiency for a given output power and clearly reveals diseconomy of engines working at maximum power. As the second example we derive universal lower and upper bounds on the efficiency at maximum trade-off given by the product of power and efficiency. The results are illustrated on a model of a diffusion-based heat engine. Such engines operate in the low-dissipation regime given that the used driving minimizes the work dissipated during the isothermal branches. The peculiarities of the corresponding optimization procedure are reviewed and thoroughly discussed.

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Section: Introductionmentioning

confidence: 99%

Efficiency at and near maximum power of low-dissipation heat engines

Holubec

Ryabov

2015

Phys. Rev. E

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“…The seminal results of Carnot apply to the case of infinite reservoirs. However, in recent years, the study of the role of finite reservoirs has also caught attention [1][2][3][4][5][6][7]. This is motivated by practical considerations such as a limited supply of fuel (a finite heat source), or the working medium being in contact with a small environment (sink) which may be the case in small-scale devices, or even relevant for the design of modern cities.…”

Section: Introductionmentioning

confidence: 99%

Optimal performance of heat engines with a finite source or sink and inequalities between means

Johal

2016

Phys. Rev. E

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Given a system with a finite heat capacity and a heat reservoir, and two values of initial temperatures, T + and T − (< T + ), we enquire, in which case the optimal work extraction is larger: when the reservoir is an infinite source at T + and the system is a sink at T − , or, when the reservoir is an infinite sink at T − and the system acts as a source at T + ? It is found that in order to compare the total extracted work, and the corresponding efficiency in the two cases, we need to consider three regimes as suggested by an inequality, the so-called arithmetic mean-geometric mean inequality, involving the arithmetic and the geometric means of the two temperature values T + and T − . In each of these regimes, the efficiency at total work obeys certain universal bounds, given only in terms of the ratio of initial temperatures.The general theoretical results are exemplified for thermodynamic systems for which internal energy and temperature are power laws of the entropy. The conclusions may serve as benchmarks in the design of heat engines, where we can choose the nature of the finite system, so as to tune the total extractable work and/or the corresponding efficiency.

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“…Heat engines that attain their maximal power and maximal efficiency (which is either the Carnot efficiency or a lower value) at different working conditions are here defined as heat engines with a power-efficiency trade-off. The power-efficiency trade-off is the subject of many recent studies [3,[6][7][8][9][10][11].Less is known about the efficiency and power of cyclic heat engines, but a lot of research effort has been devoted to understanding them in recent years [12][13][14][15][16][17][18][19]. The operation of a cyclic engine is characterized by a protocol that describes the time dependence of key variables along the cycle -e.g.…”

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confidence: 99%

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confidence: 99%

Geometric Heat Engines Featuring Power that Grows with Efficiency

2016

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Thermodynamics places a limit on the efficiency of heat engines, but not on their output power or on how the power and efficiency change with the engine's cycle time. In this letter, we develop a geometrical description of the power and efficiency as a function of the cycle time, applicable to an important class of heat engine models. This geometrical description is used to design engine protocols that attain both the maximal power and maximal efficiency at the fast driving limit. Furthermore, using this method we also prove that no protocol can exactly attain the Carnot efficiency at non-zero power.Introduction Heat engines -machines that exploit temperature differences to extract useful work, are modeled as operating in either a non-equilibrium steadystate, e.g. thermoelectric [1,2] or chemical potential [3] driven engine, or as a cyclic engine, where external parameters and temperature are varied periodically in time, e.g. the Carnot, Otto, Stirling and the Diesel cycles [4]. Both types of engines are characterized by two main figures of merit: efficiency and power.In steady-state heat engines, currents generated by the temperature difference flow against some affinities (thermodynamical forces), e.g. electrical [1,2,5] or chemical potentials [3], generating useful work. From a practical standpoint, the interest in these engines is limited, since the majority of heat engines are better modeled as cyclic engines. One of the main motivations to study steady-state heat engines, however, is the hope that they share universal characteristics with cyclic engines, which are generically more difficult to analyze. An example for such a characteristic behavior is the relationship between power and efficiency: in all steady state heat engines, the affinity at maximal power does not equal to the affinity at maximal efficiency, unless one of the heat baths is at infinite or zero temperature. Heat engines that attain their maximal power and maximal efficiency (which is either the Carnot efficiency or a lower value) at different working conditions are here defined as heat engines with a power-efficiency trade-off. The power-efficiency trade-off is the subject of many recent studies [3,[6][7][8][9][10][11].Less is known about the efficiency and power of cyclic heat engines, but a lot of research effort has been devoted to understanding them in recent years [12][13][14][15][16][17][18][19]. The operation of a cyclic engine is characterized by a protocol that describes the time dependence of key variables along the cycle -e.g. piston position and temperature. The set of feasible protocols however, is strongly bounded by a set of engine specific and hence non-generic constraints. Maximizing power or efficiency is, therefore, a nontrivial constrained optimization problem. Nevertheless, there is a natural optimization problem in these engines which is both simpler and of practical importance: optimization with respect to overall cycle time. In most cyclic engines, the protocol is determined up to a rescaling of the cycle time. In...

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Work Output and Efficiency at Maximum Power of Linear Irreversible Heat Engines Operating with a Finite-Sized Heat Source

Cited by 65 publications

References 34 publications

Efficiency at and near maximum power of low-dissipation heat engines

Efficiency at and near maximum power of low-dissipation heat engines

Optimal performance of heat engines with a finite source or sink and inequalities between means

Geometric Heat Engines Featuring Power that Grows with Efficiency

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