Coexisting phases are in thermal & mechanical equilibrium.
They can also exchange matter.
Hence, they have the same T, Y, and μ.
The condition for the coexistence of 2 phases I and II is
where, according to the Gibbs-Duhem equation (2.62), μ is a function of intensive variables only.
Eq(3.1) can be solved to give the coexistence curve of the 2 phases
in the Y-T plane.
The conditions for the coexistence of 3 phases I , II and III are
which can be solved to give the locations of triple points in the Y-T plane.
There cannot be a coexistence of more than 3 phases because the coexistence conditions will be over-determined.
For a mixture of m different types of particles in a YXT system, the
where is the molar fraction of particles of type i.
's are independent and the system itself has
The conditions for the coexistence of r phases are
… … …
… … …
where is the chemical potential of the i-type particles in the sth phase whose composition is .
The number of
The number of unknowns is .
The maximum number R of phases that can coexist simultaneously is therefore given by