Efficiency at maximum power output of an irreversible Carnot-like cycle with internally dissipative friction

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 η_C/2 and η_C/(2-η_C), with η_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 η_CA=1-T_c/T_h is derived.