The Phase Rule

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The phase rule is a method to count the number of degrees of freedom (how many independent variables are sufficient to specify a multi-component, multi-phase system.

The idea is from Gibbs and the derivation of the equation is:

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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