In this screencast we want to look at how to use the Peng Robinson Equation of State
(EOS) spreadsheet.
In another screencast we solve this problem where we compress a non-ideal gas in the conditions
given here.
And we calculated a number of things including the volume changes and the internal energy
and entropy.
That screencast showed the values that we obtain from the spreadsheet.
So here we want to show how we obtained those values.
But first let's look at what those values were.
For the temperature and pressure at the first state we read the volume and internal energy
and internal energy and entropy from the spreadsheet.
And likewise for the final condition at higher pressure and the same temperature.
And so the spreadsheet that we are using is from the textbook by Elliott and Lira.
Here is the link where you can download for free those spreadsheets.
And let me lead you through the steps- they are fairly straightforward- to do the calculations.
So we are going to use the critical temperature, the critical pressure, and the eccentric factor
which are listed in the spreadsheet, there is a worksheet with the critical properties.
And we are just going to copy those and paste them into the properties worksheet.
So here we are looking at the critical properties worksheet.
And I've modified the spreadsheet slightly to make things easier to see, so I've made
the numbers bigger for carbon dioxide, and I've made it so we can scroll through, and
freeze that top so we see what we are reading off, is critical temperature, critical pressure
and the eccentric factor.
So we want to select these four cells, copy them, and then move to the properties spreadsheet,
where now we happen to have nitrogen, and I'm going to paste them here.
And now we have carbon dioxide values for critical temperature, pressure and the eccentric
factor.
When we did that, if we look at the reference spreadsheet, it also copied the values into
the reference spreadsheet.
So that is the first step.
The second step is to copy the parameters for the heat capacity from the ideal gas heat
capacities worksheet, and post that also in the properties tab.
So I'm going to select the ideal gas heat capacities, again I've modified this to make
it easier to see.
So I'm going to copy, what I'm going to copy is just the four values.
And then go to the properties, and the heat capacities for those four values, the heat
capacity parameters are copied here.
And it now calculates values.
Calculating for 300 degrees and 1 MPa at present.
So it says the next step is to pick the reference pressure and temperature in the reference
state spreadsheet.
So on the reference state spreadsheet I'm going to pick 230 and 0.1 MPa.
It doesn't have to be these values so let's just use those.
And then the one other thing that's important is the 2 in this column that corresponds to
the 2 here.
And so that means it's using these conditions as the reference state.
The 2 tells us which of these three.
This value is the vapor/liquid and then if there was only one solution.
So we have to pick a number here, where there are entries in the table here.
And so the 2 works fine for this as long as we are consistent in our reference.
We are going to be able to calculate the properties.
And so now we will go back to the properties worksheet.
And we input the temperature and the pressure that we are interested in the properties worksheet
and then we are going to calculate all these values.
The volume, specific volume, internal energy, entropy, enthalpy, fugacities and departure
functions are all calculated.
So the temperature in kelvin 448.2.
The pressure, 20 bar which is 2 MPa.
We are going to read the volume off, the volume I showed you earlier.
This is U in J/mol so 19.6 kJ/mol.
And then this is entropy.
Notice also it calculates fugacity and these values on the right side, these values right
here, correspond to the departure functions.
Value of enthalpy minus an ideal gas enthalpy value, likewise for internal energy and entropy.
And then the final thing would be to calculate at the final conditions, which is the same
temperature but 275 bar which is 27.5 MPa.
And now it calculates the new, smaller volume and the internal energy changes because this
is a non-ideal gas.
And the entropy decreases because we have raised the pressure on the gas at constant
temperature.
So this spreadsheet then allows us to calculate values for a large number of compounds that
you see listed in the critical properties worksheet.
And then we can use these in calculations where state functions allow us to change functions
and properties.