Efficiency at maximum power of thermochemical engines with near-independent particles

Abstract

Two-reservoir thermochemical engines are established in by using near-independent particles (including Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein particles) as the working substance. Particle and heat fluxes can be formed based on the temperature and chemical potential gradients between two different reservoirs. A rectangular-type energy filter with width $\Gamma$ is introduced for each engine to weaken the coupling between the particle and heat fluxes. The efficiency at maximum power of each particle system decreases monotonously from an upper bound $\eta^+$ to a lower bound $\eta^-$ when $\Gamma$ increases from 0 to $\infty$. It is found that the $\eta^+$ values for all three systems are bounded by $\eta_{\mathrm{C}}/2 \leq \eta^+ \leq \eta_{\mathrm{C}}/(2-\eta_{\mathrm{C}})$ due to strong coupling, where $\eta_{\mathrm{C}}$ is the Carnot efficiency. For the Bose-Einstein system, it is found that the upper bound is approximated by the Curzon-Ahlborn efficiency: $\eta_{\mathrm{CA}}=1-\sqrt{1-\eta _{\mathrm{C}}}$. When $\Gamma\rightarrow\infty$, the intrinsic maximum powers are proportional to the square of the temperature difference of two reservoirs for all three systems, and the corresponding lower bounds of efficiency at maximum power can be simplified in the same form of $\eta^{-}=\eta_{\mathrm{C}}/[1+a_0(2-\eta_{\mathrm{C}})]$.