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# The Gibbs Phase Rule

 (26-1)

The Gibbs phase rule is a very useful equation because it put precise limits on the number of phases that can be simultaneously in equilibrium for a given number of components.

What does Equation 26-1 mean? Consider the following example of a single component (pure) phase diagram .

Consider a single-phase region:

This implies that two variables ( and ) can be changed independently (i.e., pick any and ) and a single phase remains in equilibrium.

Consider where two phases are in equilibrium:
,
There is only one degree of freedom-for the two phases to remain in equilibrium, one variable can be changed freely (for instance, ) but then the change in the other variable (i.e., ) must depend on the change of the free variables:

Finally, consider where three phases are in equilibrium then:
.

There can be no change any variable that maintains three phase equilibrium.

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W. Craig Carter 2002-11-21