Coefficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators

TL;DR

This paper derives bounds for the coefficient of performance at maximum figure of merit for low-dissipation Carnot-like refrigerators, aligning theoretical limits with observed real-world data.

Contribution

It establishes theoretical bounds for the performance of low-dissipation refrigerators and compares these bounds with experimental data.

Findings

Bounds for COP at maximum figure of merit are between 0 and a specific function of Carnot COP.

Extremely asymmetric dissipation cases reach these bounds.

Real refrigerator COPs fall within the theoretical bounds.

Abstract

The figure of merit for refrigerators performing finite-time Carnot-like cycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) is optimized. It is found that the coefficient of performance at maximum figure of merit is bounded between 0 and $(\sqrt{9+8\varepsilon_c}-3)/2$ for the low-dissipation refrigerators, where $\varepsilon_c =T_c/(T_h-T_c)$ is the Carnot coefficient of performance for reversible refrigerators. These bounds can be reached for extremely asymmetric low-dissipation cases when the ratio between the dissipation constants of the processes in contact with the cold and hot reservoirs approaches to zero or infinity, respectively. The observed coefficients of performance for real refrigerators are located in the region between the lower and upper bounds, which is in good agreement with our theoretical estimation.