On the efficiency at maximum cooling power

¹ Institut d'Electronique Fondamentale, Université Paris - Sud, CNRS, UMR 8622 - F-91405 Orsay, France, EU
² Laboratoire CRISMAT, UMR 6508 CNRS, ENSICAEN et Université de Caen Basse Normandie 6 Boulevard Maréchal Juin, F-14050 Caen, France, EU
³ Université Paris Diderot, Sorbonne Paris Cité, Institut des Energies de Demain (IED) URD 0001 F-75205 Paris, France, EU

Received: 23 June 2013
Accepted: 6 August 2013

Abstract

The efficiency at maximum power (EMP) of heat engines operating as generators is one corner stone of finite-time thermodynamics, the Curzon-Ahlborn efficiency being considered as a universal upper bound. Yet, no valid counterpart to has been derived for the efficiency at maximum cooling power (EMCP) for heat engines operating as refrigerators. In this letter we analyse the reasons of the failure to obtain such a bound and we demonstrate that, despite the introduction of several optimisation criteria, the maximum cooling power condition should be considered as the genuine equivalent of maximum power condition in the finite-time thermodynamics frame. We then propose and discuss an analytic expression for the EMCP in the specific case of exoreversible refrigerators.