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

Abstract

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.

Classical Thermodynamics Revisited: A Systems and Control Perspective

“…Finally, let us close this section with a simple, but intriguing, re-interpretation of the fundamental equality (12) for a Carnot cycle (Q h , T h ; Q c , T c ); see also [18] for similar reasoning in the original work of Clausius. Rewrite (12) as…”

Proof of Equivalence of Carnot Principle to II Law of Thermodynamics and Non-equivalence to Clausius I and Kelvin Principles

“…The CI principle is ascribed to Clausius' publications from 1850, 1851 [17,18] and 1854, 1856 [19,20]. Contemporary work by Xue and Guo suggests that the above assignment is not strict [21]. These authors do not distinguish two Clausius principles (CI, CI I), so it is not surprising that their reference to later Clausius textbooks [22,23] has to do with the second version of the Clausius principle (CI I).…”

Thermodynamic Proof That the Thermal Energy of a Uniform Fluid Never Converts into Its Own Mechanical Energy

“…Energy conversion is an important subject of research in physical sciences from both theoretical and practical perspectives. Energy conversion between different materials (as in heat engines) has been actively studied thermodynamically (for such recent work, see, e.g., refs ( 1 ) and ( 2 )). Energy can also convert inside the same substance.…”