Power optimized work limit for internally irreversible reciprocating engines

Abstract The theory of irreversible thermodynamics for reciprocating externally irreversible cycles gives rise to an optimum efficiency at maximum power output of η=1−(TL/TH)0.5 for internally reversible Carnot cycles, in contrast to the upper limit for Carnot cycles of η=1−(TL/TH) obtained from classical thermodynamics. It is shown here in addition, for the internally irreversible reciprocating Carnot cycle using linear heat transfer modes, that the optimum work output at maximum power (Wopt) is less than (and in the limit of no internal irreversibility is equal to) exactly one-half of the work potential of the externally reversible cycle operating at maximum thermal efficiency (Carnot work, Wrev) between the same temperature limits (i.e., W opt ⩽ 1 2 W rev ). To accomplish this the analysis goes one step further than earlier works to make use of time symmetry to minimize overall cycle time and thus better optimize overall cycle power. Because this novel procedure implies the concurrent use of first and second laws of thermodynamics, it automatically ensures optimal allocation of thermal conductances at the hot and cold ends while simultaneously achieving both minimization of internal entropy generation and maximization of specific cycle work. Based on linear heat transfer laws, this expression for optimum work is shown to be independent of heat conductances.