The Phase Rule

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Consider the general case:	C components and P phases.
At equilibrium all pressures, temperatures, and each chemical potential is constant:	<math>\begin{align} & p_{a}=p_{b}=\ldots =p_{P} \\ & T_{a}=T_{b}=\ldots =T_{P} \\ & \mu _{ia}=\mu _{ib}=\ldots =\mu _{iP};\text{ }i=1,2,\ldots C \\ \end{align}</math>
The number of unknowns in each phase is (C+1):	p, T, and (C-1) mole fractions
times the number of phases	P
or	<math>=\left( C+1 \right)P</math>]
The number of equations:	<math>=\left( P-1 \right)\left( C+2 \right)</math>
Therefore the degrees of freedom are:	<math>F=\left( C+1 \right)P-\left( P-1 \right)\left( C+2 \right)=C+2-P</math>
The phase rule: the number of degrees of freedom is:	<math>F=C+2-P</math>

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