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Condensed Matter > Statistical Mechanics
Title: Optimizing Thermodynamic Cycles with Two Finite-Sized Reservoirs
(Submitted on 23 Jul 2021 (v1), last revised 6 Dec 2021 (this version, v3))
Abstract: We study the non-equilibrium thermodynamics of a heat engine operating between two finite-sized reservoirs with well-defined temperatures. Within the linear response regime, it is found that the uniform temperature of the two reservoirs at final time $\tau$ is bounded from below by the entropy production $\sigma_{\mathrm{min}}\propto1/\tau$. We discover a general power-efficiency trade-off depending on the ratio of heat capacities ($\gamma$) of the reservoirs for the engine. And a universal efficiency at maximum average power of the engine for arbitrary $\gamma$ is obtained. For practical purposes, the operation protocol of an ideal gas heat engine to achieve the optimal performance associated with $\sigma_{\mathrm{min}}$ is demonstrated. Our findings can be used to develop an general optimization scenario for thermodynamic cycles with finite-sized reservoirs in real-world circumstances.
Submission history
From: Yu-Han Ma [view email][v1] Fri, 23 Jul 2021 16:40:42 GMT (390kb,D)
[v2] Wed, 4 Aug 2021 07:47:09 GMT (390kb,D)
[v3] Mon, 6 Dec 2021 03:04:32 GMT (455kb,D)
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