Homogeneity as a bridge between Carathéodory and Gibbs

In this paper we show that the homogeneity of the Pfaffian form representing the infinitesimal heat exchanged reversibly $δQ_{rev}$ by a thermodynamic system allows to find immediately and explicitly an integrating factor. An interesting bridge between Carathéodory's approach to thermodynamics and Gibbs' approach is established.

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