Optimal staging of endoreversible heat engines

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Abstract
One way to classify performance indices of irreversible heat engines is according to how the indices change when one engine is replaced by two (or more) of the same kind in series. We investigate the performance of two endoreversible engines (i.e., heat engines with the only irreversibility being heat resistance to the surroundings) which are put in series to form a single engine, whose power output is maximized. In this unconstrained optimization the interface between the two stages, which for the present model is the intermediate temperature and the relative timing of the two engines, is arbitrary and can be used to satisfy other, nonthermodynamic constraints. Adding any constraint on the volume of the working gas does not lift this indeterminacy. The optimum composite system is equivalent to a single endoreversible engine, thus displaying a sequencing property similar to Carnot engines.