Homogeneity as a bridge between Carath\'eodory and Gibbs

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