The Consequences of Extensivity

While not all thermodynamic systems are extensive, those that are homogeneous satisfy the useful postulate of extensivity. In this chapter we return to the thermodynamic postulates and consider the consequences of extensivity. The Euler equation can be derived from extensivity, and the Gibbs–Duhem equation can be derived from the Euler equation. The Gibbs–Duhem equation shows that changes in the chemical potential are not arbitrary, but are determined by changes in the temperature and pressure for. That in turn simplifies the reconstruction of the fundamental equation from the equations of state. The Euler equation also allows the various thermodynamic potentials to be rewritten in terms of other functions.