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# What Is the Real Clausius Statement of the Second Law of Thermodynamics?

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Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
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Entropy 2019, 21(10), 926; https://doi.org/10.3390/e21100926
Received: 19 August 2019 / Revised: 10 September 2019 / Accepted: 19 September 2019 / Published: 24 September 2019
(This article belongs to the Special Issue Carnot Cycle and Heat Engine Fundamentals and Applications)
In this paper, we first analyze the difference between the second law of thermodynamics and the laws in other disciplines. There are some phenomena in other disciplines similar to the Clausius Statement of the second law, but none of them has been accepted as the statement of a certain law. Clausius’ mechanical theory of heat, published in the nineteenth century, is then introduced and discussed in detail, from which it is found that Clausius himself regarded “Theorem of the equivalence of the transformation of heat to work, and the transformation of heat at a higher temperature to a lower temperature”, rather than “Heat can never pass from a colder to a warmer body without some other change”, as the statement of the second law of thermodynamics. The latter is only laid down as the fundamental principle for deriving the theorem of the equivalence of transformations. Finally, based on the theorem of the equivalence of transformations and the average temperature method, a general quantitative relation among the heat, the work, and the temperatures is obtained for arbitrary cycles, which is thus recommended as an alternative mathematic expression of the second law. Hence, the theorem of the equivalence of transformations is the real Clausius Statement of the second law of thermodynamics. View Full-Text
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Xue, T.-W.; Guo, Z.-Y. What Is the Real Clausius Statement of the Second Law of Thermodynamics? Entropy 2019, 21, 926.