Optimizing low-dissipation Carnot-like thermal devices with heat leak

Abstract

Delimiting the bounds of optimal performance for heat engines (HEs), refrigerators (REs), and heat pumps (HPs) is a central goal in thermodynamics. While low-dissipation (LD) models have proven valuable for this purpose, the role of heat leak in such models has received limited attention. Here, we present a unified framework for LD Carnot-like (CL) HEs, REs, and HPs that incorporates heat leaks, and derive new results for the efficiency at maximum power and the power at maximum efficiency. We further investigate the relationship between the bounds of power at fixed efficiency and efficiency at fixed power, demonstrating that these bounds coincide and are described by identical curves across all thermal devices. Finally, we show that the optimal performance of all three devices can be achieved by optimizing the average entropy production rate over the cycle, a result that holds for any CL device and extends beyond the LD assumption.

12 pages, 7 figures

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