A universal expression for optimum specific work of reciprocating heat engines having endoreversible Carnot efficiencies

Irreversible heat transfer (finite time) analysis is used to obtain the opt imum thermodynamic specific work potential at maximum power for various pra ctical reciprocating cycles having endoreversible Carnot efficiencies. The theory of finite-time thermodynamics for reciprocating endoreversible cycle s with heat transfer irreversibilities gives rise to an optimum efficiency at maximum power output, of eta = 1 - (T-L/T-H)(0.5) for Carnot-like cycles in contrast to the upper limit for Carnot-like cycles of eta = 1 - (T-L/T- H) Obtained from infinite-time thermodynamics. It is shown here that, addit ionally, for this same general family of regenerative reciprocating cycles which includes the Stirling, the Ericsson and the reciprocating Carnot cycl e, the finite-time optimum specific work output at maximum power, (w(opt)), is exactly half of that obtained for infinite-time reversible cycles (Carn ot work, w(rev)) operating between the same temperature limits (i.e., w(opt ) = 1/2 w(rev)). To accomplish this, the analysis makes use of time symmetr y to minimize overall cycle time and to thus optimize net cycle power. Base d on linear heat transfer laws, the expression for optimum specific work is shown to be independent of heat conductances. Moreover, this optimum speci fic work output is the same expression for all of the members of this famil y of cycles. This analysis makes use of the ideal gas model with constant s pecific heats, though the results are shown to be universal for the Carnot cycle for vapours and real gases. A sample calculation is given which shows that while operating under the same optimized conditions, the endoreversib le Stirling engine will have the same thermal efficiency as the endoreversi ble Ericsson, but will have a higher optimum power output. The optimum powe r of the reciprocating endoreversible Carnot engine will be superior to bot h. Copyright (C) 1999 John Wiley & Sons, Ltd.