If the minerals of a rock have reached chemical equilibrium, the observed assemblage of minerals and the mineral compositions are constrained in various ways by thermodynamics. J. Willard Gibbs (1878), in his classic papers "On the equilibrium of hetergeneous substances", was the first to show that laws of thermodynamics limit the number of phases to the number of components plus two. This limit is known as

**Gibbs Phase Rule**, commonly stated as follows:

**f = c + 2 - p**

where

**c**is the number of chemical components,

**p**is the number of phases, and

**f**is the number of "degrees of freedom" (choices that remain). On the previous pages, most of the examples were for "a random T and P." This means that two choices (degrees of freedom) are used to "pick" a temperature and pressure. Therefore,

**p**must be less than or equal to

**c**at equilibrium

*at a random T and P*, which is the

**Mineralogical Phase Rule.**

Gibbs found the phase rule by identifying the variables among the properties and conditions of phases at equlibrium and then carefully identifying all the independent equations among those variables. He found that one additional equation comes with each additional phase. The number of "degrees of freedom,"

**f**, is simply the difference between the number of variables and the number of independent equations among those variables.