if we're looking at metallic materials, we would like to have our

inert reference material to be a metallic material itself.

So, let's say we're interested in studying the behavior of aluminum.

Aluminum is going to melt at 660 degrees, and therefore,

we want to choose a reference material that is not going to have

any reactions during that temperature range.

And so what we might use is a material like platinum.

Platinum is a very high melting temperature, it's metallic and so

it's going to have very similar thermal characteristic

as the material that we're actually studying.

So we also want them to have about the same mass.

So we want essentially the same sort of thermal mass.

Now what we're going to do is to alter the temperature of our furnace and

we're doing this at a rate which is very, very, very slow so

that we can establish a state of equilibrium.

And so the slope of the line that I have drawn up there is the cooling rate and

we can measure the temperature of the sample, we can measure the temperature

of our inert reference and we can measure the temperature of the furnace.

One of the things that's generally of interest to us is to measure

the difference in temperature between the sample and the inert reference.

And we'll see why that becomes very important.

So what we're now looking at is our drop in temperature.

And eventually what's going to happen is we're going to reach a point where,

in the case of a pure material, we're going to go from

a single-phase liquid to a single-phase solid.

And as a result of that,

we're going to see what we're looking at here which is a horizontal rest line.

Effectively we see that there is an abrupt change in the slope

of this cooling curve and it's occurring at the temperature of the transformation.

Now what's happening here is, if we go back and we look at our expression for

free energy and how it relates to the internal energy, or

the enthalpy, of our transformation, or our heat, and

the entropy of the process and the entropy change that's occurring.

Is that if we're looking at the melting temperature, we're looking at the change

in the entropy of the liquid phase and the associated solid phase.

Now, at equilibrium those two are equal to one another in terms of the free energies.

So the free energy of the liquid is equal to the free energy of the solid.