# The Phase Rule

 Consider the general case: C components and P phases. At equilibrium all pressures, temperatures, and each chemical potential is constant: \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} The number of unknowns is the number of intensive variables in each phase: (C+1) intensive variables in each phase: p, T, and (C-1) mole fractions times the number of phases P or $=\left( C+1 \right)P$] The number of equations: $=\left( P-1 \right)\left( C+2 \right)$ Therefore the degrees of freedom are: $F=\left( C+1 \right)P-\left( P-1 \right)\left( C+2 \right)=C+2-P$ $F=C+2-P$]