This is an explanation of how to use the spreadsheets that come with the textbook to calculate an
equation of state properties namely pressure, volume, and temperature.
So this is a very powerful spreadsheet.
So let's go through the first tab.
The PVT tab.
So the idea is that if we can put in, we know the critical temperature, the critical pressure
and the eccentric factor then we can determine, at some temperature and pressure, values for
the volume for liquid or vapor for a two phase system.
So the first thing we need to do, we are going to do this for Toluene.
So we go to the tab that has the critical properties.
Under aromatics we find toluene.
So notice what it is listing, it's listing the critical temperature, the critical pressure
and then the eccentric factor.
And these are formatted in the same way that they appear on the other page that we started
on.
So if we select toluene and the three properties and copy and go back to the PVT tab and then
paste here.
And I've entered in the properties for toluene.
So what I'm going to do, let's look at some cases where, well, let's look at the initial
condition.
Low pressure, high pressure over 10 bar.
It says it's only one root, and that root corresponds to a low volume, low compressibility
factor, the kind of behavior we expect for a liquid.
Let's look at maybe higher temperature 350 K and maybe 0.5 MPa which is 5 bar.
So under those conditions, and notice now we have three solutions.
And those three solutions, those three solutions have different Z values and different volumes.
So the large volume of course is the vapor phase, small volume is the liquid phase, and
then the in- between point is the physically un-meaningful solution to the cubic equation.
However only one of these values is physically the correct value.
And that's the value at the lowest fugacity.
So it calculates the fugacity, notice the units are MPa.
What is going to be the stable state is the one with the lowest fugacity.
So at 350 K, 0.5 MPa, we are going to have a liquid phase for toluene.
Perhaps not too surprising at that kind of pressure if you're familiar with toluene.
So now let's lower this to 1 atm, and let's suppose we raise the temperature to the other
extreme, 600 K. Notice we are in the one root region now.
So there are no longer three solutions to the equation.
Notice 600 K is above the critical temperature 591.8 which means there can be only one solution
to the equation.
That is a fluid.
Notice the compressibility factor is close to 1 so it really is acting very similar to
an ideal gas.
If we go back to 350 K we said this was a liquid.
If we wanted to see where this toluene vaporized let's raise the temperature, 370 K. Still
the lowest fugacity is for the liquid phase so that's going to be the stable state.
We go to 400 K however, now notice if we switch things the lowest fugacity is for the vapor
phase.
So 0.097 is lower than 0.149 so we are going to be in the vapor phase.
So we should be able to adjust this, 383, just a wild guess.
Notice that these fugacities are almost the same.
The liquid one is slightly lower so if I were to raise the temperature slightly, 383.4.
9683,9680, almost identical.
So to a pretty good approximation, the boiling point of toluene at 1 bar, 0.1 MPa, is 383.4
degrees K.
The rest of the information on the spreadsheet are the intermediate values that you use to
make the calculations and to solve the cubic equation.
Another video, then, will look at the properties that it can also calculate.