The efficiency of reversible heat engines: The possible misinterpretation of a corollary to Carnot's theorem

Seidman, Kurt; Michalik, Thomas R.

doi:10.1021/ed068p208

Cited by 7 publications

(9 citation statements)

References 1 publication

(1 reference statement)

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“…This result conforms to the second half of Carnot's theorem stating that any irreversible cycle will have lower efficiency than a reversible cycle if both cycles operate between exactly two external reservoirs of the same temperatures [13]. Just as the COP of a Stirling fridge is reduced if it is operated irreversibly without its regenerator, so too the efficiency of a Stirling heat engine is reduced if it is run irreversibly without a regenerator [16].…”

Section: Fully Irreversible Stirling Refrigeratorsupporting

confidence: 79%

“…This result matches the COP of a Carnot refrigerator operating between the same pair of hot and cold temperature reservoirs. That agreement is consistent with the first half of Carnot's theorem which states that all reversible cycles operating between exactly two external reservoirs of given temperatures have the same efficiency [13].…”

supporting

confidence: 87%

“…after substituting equation (13). Finally, instead of an infinite set of such infinitesimal fridges, suppose that a single auxiliary fridge is used whose cold temperature and cooling energy are continuously varied in just this manner.…”

Section: Hybrid Stirling-carnot Refrigeratormentioning

confidence: 99%

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Coefficient of performance of Stirling refrigerators

Mungan

2017

Eur. J. Phys.

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Stirling coolers transfer heat in or out of the working fluid during all four stages of their operation, and their coefficient of performance depends on whether the non-isothermal heat exchanges are performed reversibly or irreversibly. Both of these possibilities can in principle be arranged. Notably, if the working fluid is an ideal gas, the input of energy in the form of heat during one isochoric step is equal in magnitude to the output during the other isochoric step in the cycle. The theoretical performance of the fridge can then attain the reversible Carnot limit if a regenerator is used, which is a high heat capacity material through which the gas flows. Various Stirling refrigerator configurations are analysed in this article at a level of presentation suitable for an introductory undergraduate thermodynamics course.

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Section: Fully Irreversible Stirling Refrigeratorsupporting

confidence: 79%

supporting

confidence: 87%

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Coefficient of performance of Stirling refrigerators

Mungan

2017

Eur. J. Phys.

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“…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'. He then confirmed the same conclusion obtained by Seidman and Michalik in [6], in spite of the challenge on this conclusion made by Liley in [7]. In fact, in the calculation of the heat transfer absorbed from the high temperature heat reservoir, Salter has taken the path ABC in figure 2 into account for the Stirling engine.…”

Section: Lemma 2 For a Cycle Which Operates Totally Reversibly Betwee...supporting

confidence: 71%

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

Morad

2014

Eur. J. Phys.

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A general graphical proof for the second Carnot principle is presented using the temperature–entropy diagram. This proof is simple and is independent of the proof of the first Carnot principle. The Carnot relation for thermal efficiency is also obtained simultaneously for all totally reversible heat engines between the same two reservoirs. The concept of reversibility in heat transfers and the role of environments in heat engine cycles will be further clarified and could be better understood using the proof presented here, which will be useful both for teaching and performing research in thermodynamics.

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“…Many articles in this Journal during the last four decades examine various aspects of the Carnot cycle, from the true shape of the cycle on a PV diagram (1) to its historical impact on the derivation of Maxwell's relations (2). Recently Seidman and Michalik carried out a detailed analysis of the efficiency of reversible heat engines operating on cycles other than the Carnot cycle (3); they concluded that only the Carnot cycle has the efficiency given by the classic equation…”

mentioning

confidence: 99%

A Simple Approach to Heat Engine Efficiency

Salter

2000

J. Chem. Educ.

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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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The efficiency of reversible heat engines: The possible misinterpretation of a corollary to Carnot's theorem

Abstract: Clarifying a common misinterpretation.

Cited by 7 publications

References 1 publication

Coefficient of performance of Stirling refrigerators

Coefficient of performance of Stirling refrigerators

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

A Simple Approach to Heat Engine Efficiency

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