Power–effectiveness and power–entropy transfer efficiency tradeoffs for Carnot heat engines with external and internal irreversibilities

To reveal the irreversibility mechanism for any irreversible cycle, measure the energy utilization quality of real heat engines and seek the most efficient engine at an arbitrary power produced in finite time, the concepts of weighted temperature and equivalent endoreversible reservoir temperature are introduced such that partial entropy productions are quantified by transforming an internally irreversible heat engine into an equivalent tandem construction with two engines or “standard” endoreversible model, which extends the Clausius inequality to the second law equality. The entropy transfer efficiency is defined as the ratio of the net entropy transfer into and out of a heat engine, and the effectiveness–entropic efficiency method for evaluating the relative quantity and quality of energy transfer in heat engines is developed, from which the Carnot efficiency, the Curzon–Ahlborn (CA) efficiency, and the bounds of effectiveness at maximum power or maximum ecological function for low-dissipation (LD) engines are recovered. According to different definitions of power, the maximum power effectiveness and entropic efficiency for CA and LD engines, the optimum effectiveness and entropic efficiency at maximum ecological function for LD engines, and general power–effectiveness and power–entropic efficiency tradeoffs for the LD engine and the externally and internally irreversible engine are obtained. These performance extrema constitute the key design criteria for achieving the most efficient engines for a given power produced in finite time and provide new insight into the energy utilization of optimal heat engines.