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The figure of merit for refrigerators performing finite-time Carnot-likecycles between two reservoirs at temperature $T_h$ and $T_c$ ($<T_h$) isoptimized. It is found that the coefficient of performance at maximum figure ofmerit is bounded between 0 and $(\sqrt{9+8\varepsilon_c}-3)/2$ for thelow-dissipation refrigerators, where $\varepsilon_c =T_c/(T_h-T_c)$ is theCarnot coefficient of performance for reversible refrigerators. These boundscan be reached for extremely asymmetric low-dissipation cases when the ratiobetween the dissipation constants of the processes in contact with the cold andhot reservoirs approaches to zero or infinity, respectively. The observedcoefficients of performance for real refrigerators are located in the regionbetween the lower and upper bounds, which is in good agreement with ourtheoretical estimation.

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