Molecular kinetic analysis of a finite-time Carnot cycle

Izumida, Yuki; Okuda, Koji

doi:10.1209/0295-5075/83/60003

Cited by 76 publications

(97 citation statements)

References 15 publications

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“…We found there that η max agrees with the CA efficiency in the limit of ∆T → 0. Our molecular kinetic theory also confirmed this property [4]:…”

Section: The Efficiency At the Maximal Powersupporting

confidence: 73%

“…From this figure, we can see that as u becomes larger, the cycle deviates from the theoretical quasistatic line and the temperatures during the isothermal processes (A) and (C) relax to the steady temperatures T and the steady part in the case of a finite-time cycle, where T (t) instantaneously changes from the initial temperature of the isothermal process to the steady temperature in the relaxational part and T (t) keeps the steady temperature in the steady part. These relaxational parts in the isothermal processes (A) and (C) are surely missed in the original model by Curzon and Ahlborn [1,4,14]. Moreover we note that the heat flow per unit time q i as shown in Eq.…”

Section: Molecular Kinetic Theorymentioning

confidence: 85%

“…We first introduce a theoretical model for a finite-time Carnot cycle of a two-dimensional weakly interacting gas which we can regard as a nearly ideal gas [4,5]. To mimic the weakly interacting nearly ideal gas, we confine a low dense N hard-disc particles with diameter d and mass m into a cylinder with rectangular geometry and let them collide with each other.…”

Section: Modelmentioning

confidence: 99%

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Onsager coefficients of a finite-time Carnot cycle

2009

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We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T h − Tc → 0 where T h and Tc are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linearresponse regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power ηmax of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.

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“…We found there that η max agrees with the CA efficiency in the limit of ∆T → 0. Our molecular kinetic theory also confirmed this property [4]:…”

Section: The Efficiency At the Maximal Powersupporting

confidence: 73%

Section: Molecular Kinetic Theorymentioning

confidence: 85%

Section: Modelmentioning

confidence: 99%

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Onsager coefficients of a finite-time Carnot cycle

2009

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“…The obtained result η CA = 1 − T c /T h for the efficiency at maximum power (EMP) seemingly exhibits the same degree of generality as the Carnot's formula and also it describes well the efficiency of some actual thermal plants [6][7][8]. Although it turned out that η CA is not a universal result, neither it represents an upper or lower bound for the EMP [9][10][11], its close agreement with EMP for several model systems [12][13][14][15][16][17][18][19][20][21][22][23][24] ignited search for universalities in performance of heat engines.…”

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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“…In the nonlinear regime, no general result is known. Efficiencies at maximum power, not only below but also above Curzon-Ahlborn efficiency, have been reported [5,6,7,8]. However, it was also found, again in several strong coupling models [7,8,9], that the efficiency at maximum power agrees with η CA up to quadratic order in η c , i.e., η = η c /2+η 2 c /8+O(η 3 c ), again raising the question of universality at least to this order.…”

mentioning

confidence: 83%

Universality of Efficiency at Maximum Power

Esposito

Lindenberg²,

Broeck³

2009

Phys. Rev. Lett.

406

447

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We investigate the efficiency of power generation by thermo-chemical engines. For strong coupling between the particle and heat flows and in the presence of a left-right symmetry in the system, we demonstrate that the efficiency at maximum power displays universality up to quadratic order in the deviation from equilibrium. A maser model is presented to illustrate our argument. The concept of Carnot efficiency is a cornerstone of thermodynamics. It states that the efficiency of a cyclic ("Carnot") thermal engine that transforms an amount Q r of energy extracted from a heat reservoir at temperature T r into an amount of work W is at most η = W/Q r ≤ η c = 1 − T l /T r , where T l is the temperature of a second, colder reservoir. The theoretical implications of this result are momentous, as they lie at the basis of the introduction by Clausius of the entropy as a state function. The practical implications are more limited, since the upper limit η c ("Carnot efficiency") is only reached for engines that operate reversibly. As a result, when the efficiency is maximal, the output power is zero. By optimizing the Carnot cycle with respect to power rather than efficiency, Curzon and Ahlborn found that the corresponding efficiency is given by η CA = 1 − T l /T r [1]. They obtained this result for a specific model, using in addition the so-called endo-reversible approximation (i.e., neglecting the dissipation in the auxiliary, work producing entity). Subsequently, the validity of this result as an upper bound, as well as its universal character, were the subject of a longstanding debate. In the regime of linear response, more precisely to linear order in η c , it was proven that the efficiency at maximum power is indeed limited by the Curzon-Ahlborn efficiency, which in this regime is exactly half of the Carnot efficiency,. The upper limit is reached for a specific class of models, namely, those for which the heat flux is strongly coupled to the work-generating flux. Interestingly, such strong coupling is also a prerequisite for open systems to achieve Carnot efficiency [3,4]. In the nonlinear regime, no general result is known. Efficiencies at maximum power, not only below but also above Curzon-Ahlborn efficiency, have been reported [5,6,7,8]. However, it was also found, again in several strong coupling models [7,8,9], that the efficiency at maximum power agrees with η CA up to quadratic order in η c , i.e., η = η c /2+η 2 c /8+O(η 3 c ), again raising the question of universality at least to this order. In this letter we prove that the coefficient 1/8 is indeed universal for strong coupling models that possess a left-right symmetry. Such a universality is remarkable in view of the fact that most explicit macroscopic relationships, for example the symmetry of Onsager coefficients, are limited to the regime of linear response. The interest in strong coupling is further motivated by the observation that it can naturally be achieved in nano-devices [10,11,12]. To complement our theoretical discussion, we also present a deta...

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Molecular kinetic analysis of a finite-time Carnot cycle

Cited by 76 publications

References 15 publications

Onsager coefficients of a finite-time Carnot cycle

Onsager coefficients of a finite-time Carnot cycle

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

Universality of Efficiency at Maximum Power

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