The Phase Rule
From Soft-Matter
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> |