Wang Yang, Li Mingxing, Tu Z C, Hernández A Calvo, Roco J M M
Department of Physics, Beijing Normal University, Beijing 100875, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jul;86(1 Pt 1):011127. doi: 10.1103/PhysRevE.86.011127. Epub 2012 Jul 24.
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+8ε(c)] - 3)/2 for the low-dissipation refrigerators, where ε(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.
对在温度(T(h))和(T(c))（(T(c)<T(h))）的两个热源之间进行有限时间类卡诺循环的冰箱的品质因数进行了优化。结果发现，对于低耗散冰箱，品质因数最大时的性能系数在(0)到((\sqrt{9 + 8\varepsilon(c)} - 3)/2)之间，其中(\varepsilon(c) = T(c)/(T(h) - T(c)))是可逆冰箱的卡诺性能系数。当与冷热源接触的过程的耗散常数之比分别趋近于零或无穷大时，对于极端不对称的低耗散情况，可以达到这些界限。实际冰箱的观测性能系数位于上下限之间的区域，这与我们的理论估计非常吻合。
