The fundamental equations derived in the previous chapter can only be applied to closed systems (i.e. to systems that do not exchange mass) that are homogeneous (i.e. they involve just one phase). In such cases we do not need to specify how thermodynamic functions depend on the composition of the system. Only two independent variables (T and p, or p and V, or p and T) need to be known. Since the total mass (m) remains constant, if we know the values of the extensive variables per unit mass we can extend the equations to any mass by multiplying by m or by n (the number of moles).

A heterogeneous system involves more than a single phase. In this case we are concerned with the conditions of internal equilibrium between the phases. Even if the heterogeneous system is assumed to be (as a whole) a closed system the phases constitute homogeneous but open “subsystems” which can exchange mass between them. In this case the fundamental equations must be modified to include extra terms to account for the mass exchanges. These extra terms involve a function μ called the chemical potential, μ = μ(T, p). We will not go into the details of defining μ; we will only accept that in the case of open systems something else must be included to account for the heterogeneity of the system. In this book we are concerned with a heterogeneous system that involves dry air (N2, O2, CO2, Ar) and water, with the water existing in vapor and possibly one of the condensed phases (water or ice).