I'm going to describe an interactive simulation that calculates the fugacity, in this case
for water from the Peng-Robinson Equation of State. And the location of this interactive
simulation, so that you can use it on your own, is given here on the Wolfram Demonstration
Project Website. What the simulation does is plot the log of pressure versus log of
volume. And then at a given point, as indicated by this dot, it reads off the pressure, the
fugacity, the fugacity coefficient and of course the fucagity coefficient is just the
fugacity over the pressure for the pure material, and it also reads off the temperature. The
point can be moved by changing the pressure, changing the volume. You'll notice here that
the fugacity is close to, but not the same as, the pressure when we're in this two phase
region at this particular pressure. Let's look at various conditions to get a better
physical feel for how the fugacity changes. So here's the interactive simulation. What
this simulation does is calculate the fugacity at different conditions. So you can see at
relatively low pressure, fugacity and pressure are almost the same. We're in the two phase
region, the fugacity coefficient, .97, that's the same as saying fugacity and pressure,
very similar. If we change the volume, all I'm doing, at constant pressure, is changing
the relative amounts of liquid and vapor. And since the liquid and vapor in equilibrium
in this two phase region have the same fugacity we don't change the fugacity. And so I can
move it within this region, no change. If I increase the pressure, now the fugacity
coefficient and fugacity are different. The fugacity is lower than the pressure. We are
at a higher temperature. Still in the two phase region we don't change the fugacity.
Now if I increase the volume enough to go into the one phase region, notice what happens.
I'm at higher temperature for this pressure and the fugacity coefficient went up, the
fugacity is closer to the pressure. And then of course if I lower the pressure I can go
back into that region. But let's go look at high pressure back in the two phase region.
Now if I decrease the volume enough, now I'm in the compressed liquid regime and notice
the dramatic difference between fugacity and pressure. So the temperature is lower, right,
if I, let's go back into the two phase region. And I'm at 568 K. And as I decrease the volume
I move into the compressed liquid. Now I'm in much lower temperatures. And now the fugacity
coefficient is very small, fugacity is very small, because what we are really comparing,
and perhaps it would be easier to see, let's look at a slightly higher pressure. So we
have here a pretty large difference between the fugacity and the pressure. At this temperature,
if I were to decrease the pressure, eventually I get close to the phase envelope and now
fugacity is much closer to the pressure. You can use this interactive simulation to give
you a better feeling for how fugacity changes. Keep in mind when we change the pressure in
the two phase region, we change the temperature. Outside the two phase region, if we change
either the pressure or the volume we are going to change the temperature.