Besides, the Carathéodory Statement also occupies an important position in thermodynamics, which is “In the neighbourhood of any arbitrary state of a thermally isolated system, there are states which are inaccessible from that state”. The Clausius Statement is more in accord with experience and thus easier to accept, while the Kelvin–Planck Statement provides a more effective means for bringing out second law deductions related to a thermodynamic cycle. The Clausius Statement was expressed as “Heat can never pass from a colder to a warmer body without some other change, connected therewith, occurring at the same time”, and the Kelvin–Planck Statement as “It is impossible to construct a device that operates in a cycle and produces no other effect than the production of work and the transfer of heat from a single body”. The classic statements given in most of the literatures mainly include the Clausius Statement and the Kelvin–Planck Statement. The second law has different statements for different physical phenomena. Hence, the theorem of the equivalence of transformations is the real Clausius Statement of the second law of thermodynamics.Īs with the first law of thermodynamics, the second law of thermodynamics has been verified by countless natural facts. 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. The latter is only laid down as the fundamental principle for deriving the theorem of the equivalence of transformations. 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. 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. In this paper, we first analyze the difference between the second law of thermodynamics and the laws in other disciplines.
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