Reversible Performance of Cycles with Variable Temperature Heat Transfer Interactions

Abstract

The reversible performance of cycles with variable temperature heat transfer interactions is examined. The cycles considered operate at steady state with heat input and heat rejection occurring over a range of temperatures. A Carnot-style thermodynamic analysis is performed based on an average temperature associated with the variable temperature processes. The average temperature is termed an entropic average since it is defined in terms of the entropy flowing with the heat. In terms of this entropic average temperature, it is possible to prove that the reversible performance of two cycles operating between the same entropic average temperatures must be equal. This general result collapses to the Carnot conclusion, that all reversible cycles operating between the same two fixed temperatures have the same performance, for cycles with fixed temperature heat transfer interactions. The significance of the result is in the way we interpret the performance of real cycles. The thermodynamic conclusions obtained from the Carnot analysis can be extended to variable temperature cycles directly. The ideas presented in this paper allow the student to readily apply the concept of a reversible process to a real, variable temperature process and to readily calculate the performance of reversible cycles containing such processes.