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arXiv · 2012.14787

The uniqueness of the integration factor associated with the exchanged heat in thermodynamics

Yu-Han Ma·Hui Dong·H. T. Quan·C. P. Sun
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Abstract

State functions play important roles in thermodynamics. Different from the process function, such as the exchanged heat $\delta Q$ and the applied work $\delta W$, the change of the state function can be expressed as an exact differential. We prove here that, for a generic thermodynamic system, only the inverse of the temperature, namely $1/T$, can serve as the integration factor for the exchanged heat $\delta Q$. The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat, and in turn, reveals the incorrectness of defining the entransy $E_{vh}=C_VT^2 /2$ as a state function by treating $T$ as an integration factor. We further show the errors in the derivation of entransy by treating the heat capacity $C_V$ as a temperature-independent constant.

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Yu-Han Ma, Hui Dong, H. T. Quan, C. P. Sun. 2020-12-29. The uniqueness of the integration factor associated with the exchanged heat in thermodynamics. https://doi.org/10.1016/j.fmre.2020.11.003

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