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In each phase chemical potential is a function of P and T. Phase equilibrium condition:
This determines a line in P-T plane. Two lines can intersect--there three phases meet! (Triple point).
have one isolated solution!
Binary mixtures: we add a new variable--concentration c and have two chemical potentials and . What is the largest number of phases to coexist?
If there are r phases, we have r+2 variables (P, T, cI, cII,...). There are 2r chemical potentials--2(r-1) equations. They have unique solution, if r+2=2(r-1), or r=4. In binary solutions four phases can coexist in a special point!
General case: n-component mixture, r phases. We have 2+r(n-1) variables for n(r-1) equations. Maximal value for r is 2+r(n-1)=n(r-1), or
r=n+2This is Gibbs Phase Rule. The maximum number of phases in equilibrium is two plus the number of components.