On the efficiency at maximum cooling power

TL;DR

This paper investigates the efficiency at maximum cooling power (EMCP) in heat engines functioning as refrigerators, highlighting the lack of a universal bound like the Curzon-Ahlborn efficiency and proposing an analytic expression for exoreversible refrigerators.

Contribution

It demonstrates that EMCP should be regarded as the true finite-time thermodynamics counterpart to maximum power and provides an analytic formula for exoreversible refrigerators.

Findings

No universal EMCP bound analogous to $\\eta_{CA}$ exists.

Maximum cooling power condition is fundamental in finite-time thermodynamics.

An explicit expression for EMCP in exoreversible refrigerators is proposed.

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 $\eta_{\rm CA}$ being considered as a universal upper bound. Yet, no valid counterpart to $\eta_{\rm CA}$ 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.