The thermodynamic efficiency of heat engines with friction

The presence of the work done against friction is incorporated into the analysis of the efficiency of heat engines based on the first and second laws of thermodynamics. We obtain the efficiencies of Stirling and Brayton engines with friction and recover results known from finite-time thermodynamics. We show that ηfric/η ≈ (1 − Wfric/W), where ηfric/η is the ratio of the efficiencies with and without friction and Wfric/W is the fraction of the work W performed by the working fluid which is spent against friction forces.