Universality of energy conversion efficiency for optimal tight-coupling heat engines and refrigerators

Aunified chi-criterion for heat devices (including heat engines and refrigerators), which is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by theworking substance (de Tomas et al 2012 Phys. Rev. E 85 010104), is optimized for tight-coupling heat engines and refrigerators operating between two heat baths at temperatures T-c and T-h(> Tc). By taking a new convention on the thermodynamic flux related to the heat transfer between two baths, we find that for a refrigerator tightly and symmetrically coupled with two heat baths, the coefficient of performance (i.e., the energy conversion efficiency of refrigerators) at maximum chi asymptotically approachesv root epsilon(C) when the relative temperature difference between two heat baths epsilon(-1)(C) equivalent to (T-h - T-c)/T-c is sufficiently small. Correspondingly, the efficiency atmaximum. (equivalent to maximum power) for a heat engine tightly and symmetrically coupled with two heat baths is proved to be eta(C)/2 + eta(2)(C)/8 up to the second order term of eta(C) equivalent to (T-h - T-c)/T-h, which reverts to the universal efficiency at maximum power for tight-coupling heat engines operating between two heat baths at small temperature difference in the presence of left-right symmetry