A recent analysis of the Carnot's results has pointed out that natural systems may not convert all the inflow of energy to do work. Some energy will be used to maintain the systems' internal processes. These exergy flows appear as the heat exchanged with a second thermostat of a thermodynamic engine. In this Letter a calculus of this internal irreversibility is developed using the entropy generation approach. The obtained results are exemplified in the analysis of superconductivity. (C) 2013 Elsevier B.V. All rights reserved.