Читать книгу Geochemistry - William M. White - Страница 99

Another significant aspect of the Gibbs–Duhem equation is that the phase rule can be derived from it. We begin by recalling that the variance of a system (the number of variables that must be fixed or independently determined to determine the rest) is equal to the number of variables minus the number of equations relating them. In a multicomponent single-phase system, consisting of c components, there are c +2 unknowns required to describe the equilibrium state of the system: T, P, μ₁, μ₂, ...μ_c. But in a system of φ phases at equilibrium, we can write φ versions of eqn. 3.23, which reduces the independent variables by φ. Thus, the number of independent variables that must be specified to describe a system of c components and φ phases is:

which is the Gibbs phase rule.

Specification of ƒ variables will completely describe the system, at least with the qualification that in thermodynamics we are normally uninterested in the size of the system, that is, in extensive properties such as mass and volume (though we are interested in their intensive equivalents), and outside forces or fields such as gravity, electric, or magnetic fields. Nevertheless, the size of the system is described as well, provided that only one of the ƒ variables is extensive.