We investigate the efficiency at the maximum power output (EMP) of an irreversible Carnot engine performing finite-time cycles between two reservoirs at constant temperatures $T_h$ and $T_c$ $(<T_h)$, taking into account the internally dissipative friction in two “adiabatic” processes. The EMP is retrieved to be situated between ${\eta }_{{}_C}/2$ and ${\eta }_{{}_C}/(2-{\eta }_{{}_C})$, with ${\eta }_{{}_C}=1-T_c/T_h$ being the Carnot efficiency, whether the internally dissipative friction is considered or not. When dissipations of two “isothermal” and two “adiabatic” processes are symmetric, respectively, and the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation, the Curzon-Ahlborn (CA) efficiency ${\eta }_{{}_{CA}}=1-\sqrt{T_c/T_h}$ is derived.

• Received 30 July 2012

DOI:https://doi.org/10.1103/PhysRevE.86.051112