Efficiency at Maximum Power of Low-Dissipation Carnot Engines

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 ${\eta }_{\mathrm{CA}}=1-\sqrt{T_c/T_h}$ is recovered.

Figure 1

Efficiency at maximum power as a function of ${\eta }_C$. The upper and lower bounds of the efficiency given by Eq. (11) are denoted by a black solid line and a (blue) dotted line, respectively. The Curzon-Ahlborn efficiency is the (red) dashed line. The dots represent the observed efficiencies of the various thermal power plants reported in Table . Observed efficiencies above and below the bounds could result from power plants not operating at maximum power.