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 eta(fric)/eta approximate to (1 - W-fric/W), where eta(fric)/eta is the ratio of the efficiencies with and without friction and W-fric/W is the fraction of the work W performed by the working fluid which is spent against friction forces. (C) 2012 American Association of Physics Teachers. [DOI: 10.1119/1.3680168]