The thermodynamic principles developed in Chaps. 2 and 3 apply to a homogeneous system, which can involve only a single phase. For it to be in thermodynamic equilibrium, a homogeneous system must be in thermal equilibrium: At most, an infinitesimal temperature difference exists between the system and its environment. It must also be in mechanical equilibrium: At most, an infinitesimal pressure difference exists between the system and its environment.

A heterogeneous system can involve more than one phase. For such a system, thermodynamic equilibrium imposes an additional constraint. The system must also be in chemical equilibrium: No conversion of mass occurs from one phase to another. Analogous to thermal and mechanical equilibrium, chemical equilibrium requires a certain state variable to have, at most, an infinitesimal difference between the phases present.

DESCRIPTION OF A HETEROGENEOUS SYSTEM

For a homogeneous system, two intensive properties describe the thermodynamic state. Conversely, only two state variables may be varied independently. A homogeneous system therefore has two thermodynamic degrees of freedom. For a heterogeneous system, each phase may be regarded as a homogeneous subsystem, one that is “open” due to exchanges with the other phases present. Consequently, the number of intensive properties that describe the thermodynamic state of a heterogeneous system is proportional to the number of phases present. Were they independent, those properties would constitute additional degrees of freedom for a heterogeneous system. However, thermodynamic equilibrium between phases introduces additional constraints.