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

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., $\Delta S^{(\mathrm{ir})}\propto 1/\tau$. 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 ${\eta }_{\mathrm{C}}\ll 1$, 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 ${\eta }_{+}={\eta }_{\mathrm{C}}/(2-{\eta }_{\mathrm{C}})$

6 pages, 4 figures, Comments are welcome

References in corpus (4)

• Quantum Thermodynamic Cycles and quantum heat engines
• An endoreversible quantum heat engine driven by atomic collisions
• Efficiency of molecular motors at maximum power
• Geometric optimisation of quantum thermodynamic processes

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