Gibbs Phase Rule for One- and Two-Component Systems

number of components

C

1

2

J. Willard Gibbs (ca. 1870) derived a simple rule that determines the number of degrees of freedom for a heterogeneous system. If a system in thermodynamic equilibrium contains

P

phases and

C

components, then the phase rule states that the number of degrees of freedom is given by

F=C-P+2

. Degrees of freedom

F

represents the number of intensive variables (such as pressure, temperature, and composition) that can be varied arbitrarily over some finite range without changing the number of phases. The phase rule has been described as "pretty but powerful, qualitative yet exact".

This Demonstration considers only the simplest cases of one- and two-component systems. Omitted are such phenomena as multiple crystal structures, solid solutions, partial miscibility of liquids, and azeotrope formation. You can drag the locator over various regions of the phase diagrams. For one-component systems, this selects values for the pressure and temperature. For two-component systems, this selects the temperature and composition. The two-component phase diagram should actually be three-dimensional, with pressure providing an additional degree of freedom.