Entropy equation and absolute temperature

In this paper we consider the equivalence between the heat and the entropy balance laws. These two equations are related by an integrating factor, which defines the absolute temperature. This result is obtained applying the thermodynamic laws to a perfect fluid. So that, by means of the entropy equation we introduce the Second Law of Thermodynamics. Two particular cases of constitutive equations, both for the internal energy and for the heat flux, are considered and their corresponding differential equations, useful to study the behaviour of these materials, are also given