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.

Now, what we know is, that when we are below

the equilibrium melting temperature, what we know is that,

the free energy of the solid phase is less than the free energy of the liquid phase.

And when you look at this behavior that I've plotted here,

that's exactly what you're saying.

And what we can do is, we can talk about taking a liquid from a temperature

above the equilibrium melting temperature, and what that says is,

the free energy of the liquid phase is less than that of the solid.

And what I'm going to do, is I'm going to super cool that.

And what I mean by super cooling is, I'm going to be very careful about changing

the temperature and maintaining the liquid phase.

And let's say that I'm able to do that at the tip of the arrow.

And once that material then transforms from the liquid phase to a solid phase,

there is a corresponding decrease in the free energy.

That tells me that this process is spontaneous.

That is, liquid's going to go to solid but solid is not going to go back to liquid.

And that's going to give us the delta G or the change in free energy,

between the system in which we have liquid, then ultimately,

the system that we have solid.

So, we can look at this delta G as being like a driving force.

Or, alternatively, what we can do, is we can define a driving force in terms of

something we refer to as the undercooling.

And what we mean by the undercooling is, that is the temperature that we

are cooling to below the equilibrium melting temperature, so

we talk about then positive undercooling.

Now let's say that I am able to carry the process on again.

This time what I'm able to do, is I follow along that arrow,

I supercool to a much lower temperature.

And now when I look at the behavior that explains or illustrates the differences

between the free energy of the liquid and the solid, I see a change delta G sub V,

that's in terms of the change in free energy per unit volume.

And what I see is a larger difference in the second case,

which tells me that as I go to more undercooling,

I'm going to see a larger driving force.

And again, that can be done by looking at the associated under cooling terms.

So, we can look at these things equivalently.

I hope this illustrates the concepts that we've been

developing associated with the change in free energy.

In using a very simple system like a pure substance and

the melting of that pure substance.

In the next lesson,

we're going to be introducing some very basic concepts in the area of kinetics.

Kinetics are important because rather than thermodynamics, which focuses on

equilibrium, with respect to kinetics we're going to be involved in time.

Thank you.

2.11B Basic Thermodynamics Part 2

Material Behavior

与讲师见面