Efficiency at maximum power of low dissipation Carnot engines

TL;DR

This paper analyzes the efficiency at maximum power of low dissipation Carnot engines, establishing bounds and conditions under which specific efficiencies like Curzon-Ahlborn are achieved.

Contribution

It derives bounds on the efficiency at maximum power for low dissipation Carnot engines and identifies conditions for reaching these bounds.

Findings

Efficiency at maximum power is bounded by $rac{ extit{η}_C}{2}$ and $rac{ extit{η}_C}{2- extit{η}_C}$.

Symmetric dissipation yields the Curzon-Ahlborn efficiency.

Bounds are attained when dissipation ratios tend to zero or infinity.

Abstract

We study the efficiency at maximum power, $\eta^*$, of engines performing finite-time Carnot cycles between a hot and a cold reservoir at temperatures $T_h$ and $T_c$, respectively. For engines reaching Carnot efficiency $\eta_C=1-T_c/T_h$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that $\eta^*$ is bounded from above by $\eta_C/(2-\eta_C)$ and from below by $\eta_C/2$. These bounds are reached when the ratio of the dissipation during the cold and hot isothermal phases tend respectively to zero or infinity. For symmetric dissipation (ratio one) the Curzon-Ahlborn efficiency $\eta_{CA}=1-\sqrt{T_c/T_h}$ is recovered.