Temperature-entropy (TS) diagrams are introduced as a way to simplify the calculation of
efficiency for reversible heat engines. The equation for the efficiency of the Stirling cycle
is derived from its TS diagram. The conflict over the efficiency of the Stirling cycle is
thereby resolved; the standard Stirling cycle does not have an efficiency equal to the Carnot
cycle efficiency. The historical confusion about the efficiency of the Stirling cycle is shown
to arise from two sources: a careless definition of heat input into the cycle, and the unclear
role of the regenerator when used with a Stirling cycle. The Stirling cycle with a reversible
regenerator is shown to be a Carnot cycle.
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