Now, there's something that's rather interesting about what happens in

this particular system.

What we see is that if we look at two different temperatures, temperature T1 and

temperature T2, they move us up inside of that boundary for two phase equilibrium,

and we see the two isotherms on the pressure-volume diagram.

And what we see is that as a result of the increase in pressure.

And the corresponding increase in temperature as we go from T1 to T2.

What we're finding is the difference between the volume of the liquid and

the volume of the vapor are reducing.

And if we continue to go up in temperature,

we would ultimately reach a point that we would refer to as the critical point.

And that critical point Is the point at which we begin to not be

able to recognize the difference between the liquid phase and the vapor phase.

They're appearing very similar in terms of the characteristic that we're using.

The volume of the two phases, and they are coming close together.

And when they reach that critical point they are the same value.

Now let's think about what that all means with respect to forming

a path and using a system like water.

So let's start by beginning at some temperature and pressure.

In this case we're going to begin at pressure P1 and

we're going to keep the temperature constant at T2.

So if we follow Path 1, that is what we're doing is,

we're doing an iso thermal process where we're taking our vapor phase crossing

the liquid vapor phase boundary, and, going up into the all single-phase field.

So, what's happened here, is a result of the path that we've taken.

We have a continuous change of the volume of the material,

up until we reach the value of the pressure at P2.

And, once we reach that particular value, a new phase appears, and

that new phase is the liquid phase.

And when we continue up, the vapor phase has disappeared and

all we know have is the liquid phase.

So that's Path 1.

Now what we could also do is, we know that the enthalpy

Changes, as we increase the temperature.

And it also discontinuously changes at the phase boundary.

And it is discontinuously changing at that phase boundary because we have

a difference with respect to the volume of the material.

That arch, the volume of the material that's transforming into another material

as well as the entropy of the two.

So, at that particular point there is a transformation enthalpy

that's associated with going from vapor to liquid.

So that is one of our paths that we can take.

The other path is indicated by Path 2, and

what we can do is altogether avoid the transformation.

We avoid the transformation by following that path.

And as a result, what we're doing is, we are going from state one,

which is a vapor phase.

We're following that vapor phase, and eventually it becomes another phase.

And when we get to that position at the end

It is the same as it was that we followed path one.

But now, we have done that without going across the phase boundary,

and having a discontinuous change that gives us enthalpy.

Now, we do have, and we do recognize that our locations,

regardless of whether Path 1 or Path 2 is followed.

What we know is that the total integrated enthalpy has got to be the same.

Because, in fact, the enthalpy's a state function.

So, delta h is going to be the same for Path 1 as it is for Path 2.

The only difference is whether it happens as we go around the transformation or,

alternatively, if we go through the transformation.

Thank you.