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 \\ 


The number of unknowns: (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions, times the number of phases.

<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>


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