Efficiency at Maximum Power of Low-Dissipation Carnot Engines

Abstract

We study the efficiency at maximum power, ${\ensuremath{\eta}}^{*}$, 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 ${\ensuremath{\eta}}_{C}=1\ensuremath{-}{T}_{c}/{T}_{h}$ in the reversible limit (long cycle time, zero dissipation), we find in the limit of low dissipation that ${\ensuremath{\eta}}^{*}$ is bounded from above by ${\ensuremath{\eta}}_{C}/(2\ensuremath{-}{\ensuremath{\eta}}_{C})$ and from below by ${\ensuremath{\eta}}_{C}/2$. 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 ${\ensuremath{\eta}}_{\mathrm{CA}}=1\ensuremath{-}\sqrt{{T}_{c}/{T}_{h}}$ is recovered.