Hello. In this video, we're going to talk
about Gibbs' Phase Rule. Gibbs' phase rule is a rule
that allows you to determine how many phases might be
present in a given substance. So if we define r as the number of components
or the number of species, and M the number of phases, then f is called the
thermodynamic degrees of freedom. It is also equal to the number of independent
intensive parameters. The rule is that f is
equal to r minus M plus 2. Since S is equal to
a function of U, V and the mole numbers, there are r plus 2
intensive parameters. Because of Gibbs-Duhem,
only r plus 2 minus 1 of the intensive parameters are
independent of each other. When there are two or
more phases present, fewer are independent by
the number of phases. So re-writing Gibbs'
phase rule equation from the previous slide and solving for the number
of co-existing phases, that would be equal
to r plus 2 minus f. So for a one component system, we'd have M is equal
to 1 plus 2 minus f. So if f is zero,
M would be three. If f is one, it would be two. If f is two, it would be one. If we look at the phase diagram for a simple
compressible substance, it looks like the plot here. We have, at high
temperatures, we have vapor. At low temperatures, at very
low temperatures, solid. We have a transition
between vapor and liquid, that's the vaporization
or condensation line. We have a transition
between liquid and solid, that's the melting line. We have a direct transition
between vapor and solid called the solidification
or sublimation line. Finally, when f is zero, we have the triple point where three phases
are present together; vapor, liquid and solid. If we add a component, go to a two components system, then r is equal to 2 and then M would be
equal to 4 minus f, so M can range from 4 if f is
zero to one if f is three. This plot shows a classic
binary system phase diagram for a liquid-solid system. You might have seen
something like this in Materials Science class. So you can have all
melted, or all crystal, or you can have a melt
and a phase A together, a melt and a phase B together, or you can have a quad point where f is equal to 0 and four phases are
present together. Finally, we should point
out the difference between thermodynamic versus
dynamic stability. Even though thermodynamics
determines stability, to change phase requires
dynamic action. In the liquid phase
and gas phase, this can occur through local
thermodynamic fluctuations. Of course, in the solid
phase, say a metal, we can lock in non-equilibrium phases
through heat treating, that's a commonly
used methodology in the sugar example
that I gave in the earlier videos is another
example of something that is dynamically stable but not
thermodynamically stable. That's it for this video. Thanks and have a great day.