2. Postulates of Thermodynamics

In this chapter, postulates are announced in the form taken from the book of Herbert B. Callen, ready for actual thermodynamic calculations. The explanation of what a phenomenological or macroscopic treatment means is followed by the specification of equilibrium. Postulate 1 exactly defines thermodynamic equilibrium. Its important consequence – the measurability of internal energy – is described in details. Postulate 2 – the criterion of equilibrium, and the existence of entropy – is formulated in connection with composite systems and internal constraints. Postulate 3 specifies mathematical properties of the entropy function, like additivity, differentiability, and monotonity with respect to energy. An important consequence of these properties is the homogeneous first-order nature of this function. Extensive and intensive properties are also defined here. Euler relation and Gibbs–Duhem equation is derived and explained. There is a first mention of the fundamental equation which describes all possible states of a thermodynamic system. Postulate 4 specifies the scale of entropy and the possibility to completely determine its value. The second part of the chapter explains the relation of equations of state and the fundamental equation, followed by two model systems to demonstrate these relations; the ideal gas and the ideal van der Waals fluid.