Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model

• URL: http://arxiv.org/abs/2012.08748v1
• Date: Wed, 16 Dec 2020 05:08:02 GMT
• Title: Self-consistency of optimizing finite-time Carnot engines with the low-dissipation model
• Authors: Yu-Han Ma, C. P. Sun, and Hui Dong
• Abstract summary: We show that the optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. The exact EMP is found to surpass the well-known bound $eta_mathrmC/ (2-eta_mathrmC/(2-eta_mathrmC/(2-eta_mathrmC/ (2-eta_mathrmC/(2-eta_mathrmC/ (2-eta_mathrmC
• Score: 0.1274452325287335
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: The efficiency at the maximum power (EMP) for finite-time Carnot engines established with the low-dissipation model, relies significantly on the assumption of the inverse proportion scaling of the irreversible entropy generation $\Delta S^{(\mathrm{ir})}$ on the operation time $\tau$, i.e., $\Delta S^{(\mathrm{ir})}\propto1/\tau$. The optimal operation time of the finite-time isothermal process for EMP has to be within the valid regime of the inverse proportion scaling. Yet, such consistency was not tested due to the unknown coefficient of the $1/\tau$-scaling. In this paper, using a two-level atomic heat engine as an illustration, we reveal that the optimization of the finite-time Carnot engines with the low-dissipation model is self-consistent only in the regime of $\eta_{\mathrm{C}}\ll1$, where $\eta_{\mathrm{C}}$ is the Carnot efficiency. In the large-$\eta_{\mathrm{C}}$ regime, the operation time for EMP obtained with the low-dissipation model is not within the valid regime of the $1/\tau$-scaling, and the exact EMP is found to surpass the well-known bound $\eta_{+}=\eta_{\mathrm{C}}/(2-\eta_{\mathrm{C}})$

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