A Simple Approach to Heat Engine Efficiency

Abstract

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.

Coefficient of performance of Stirling refrigerators

“…Returning to figure 1, only the heat transfers denoted Q H and Q C are with the external temperature reservoirs (connected to the ambient surroundings at temperature T H and to the cooling load at T C ). The regenerator has obviated the need for other reservoirs at intermediate temperatures between T H and T C during the isochoric processes [12]. Therefore, calculating the COP as the ratio of the 'energy transfer wanted' to the 'energy transfer paid for' gives…”

A note on the use of the temperature–entropy diagram in the proof of the second carnot theorem

“…To show the importance of the clarification made by this proof, one example of a relevant interpretation which may lead to misunderstanding or errors is reviewed here. The example is a comparison between the thermal efficiency of Carnot and Stirling engines using the T-S diagram studied in [5]. In the 'Graphical Efficiency' section of this investigation, Salter presents a proof of the statement on the first page of the paper as 'Stirling cycles and other reversible cycles cannot have an efficiency equaling the Carnot efficiency'.…”

A simple, all-purpose nonlinear algorithm for univariate calibration

“…Let b represent the variables in question. Then the variance in some function f(b) is given by [10][11][12][13][14] s f 2 = g T V g, (2) in which the elements of g are g i = ∂f/∂b i , and V is the variance-covariance matrix of the variables b. For example, in the calculation of the error in the linear calibration fit function itself (f = a + bx), g 1 = 1 and g 2 = x if b 1 is taken to be a and b 2 is b.…”