Before we start we need to do some basic reviewing of the Gibbs function,

which is the function in which we can control

the energy of the system through the pressure and the temperature.

First of all, the Gibbs function, like the energy function,

like the entropy, is a state function.

So that means we're only interested in the beginning of the process and

the final state of the process.

At equilibrium, if we have more than one phase involved,

what is required is that the Gibbs free energy of the two phases that

are participating in the equilibrium, have got to be equal to one another.

And for spontaneous process,

that is one which will flow in the direction that we normally visualize time,

we would expect to see that the Gibbs free energy for that process is less than zero.

And so what we'll do, is we're going to apply these concepts to consider a very

simple problem, where we're looking at the solidification of a pure substance.

And here what I mean by a pure substance, it is a material that melts at

a single temperature when the pressure of the system is fixed.

So we can begin to understand how these basic thermodynamics, that we've

just described in the previous lesson, how they can actually be vary useful in

determining a characteristic of a material that we already know something about.

And that is, we're going to be looking at the solidification of a pure substance,

that is, a material that has a single melting temperature at a fixed pressure.

Now one of the things we know, is that with respect to the free energy function,

is that at a state of equilibrium,

the two phases that are at equilibrium must be at the same temperature.

And that defines for

us then what we refer to as the melting temperature of the pure substance.

Now we also have to consider the behavior of the liquid phase and

the behavior of the solid phase.

And what you see here, is not arbitrarily drawn, but I've indicated the red phase

as having a more negative slope than does the blue phase.

And that all makes sense from the point of view of the equation when we

fix the pressure of the system and therefore the dP term becomes 0.

So what we're now going to look at is the variation in the free energy as

the function of temperature.

And it follows the negative at the entropy.

So we know that the entropy of the liquid phase is going to be greater than

the entropy of the solid.

And hence, because of the way the equation in written,

what we're seeing is a decrease in that free energy that's associated

with the liquid behavior and the solid behavior of the material.

To continue this on just a little bit more and define a few more concepts,

we're now going to be looking at constant pressure.

And we're going to be looking at the expression for the Gibbs free energy.

And we're going to be plotting the free energy of the phases that are involved and

the temperature.

Here's our liquid phase, and we correspondingly look at the blue phase for

the solid.

And we see they cross, and

where they cross then defines the melting temperature of the material.