# The Phase Rule

From Soft-Matter

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: | (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> |

<math>F=C+2-P</math>] |