This is an explanation of using the properties tab on the Peng Robinson Equation of State
(EOS) spreadsheet.
So, single component system, as we mentioned, and let's continue to look at toluene.
So again we can go to the tab for critical properties, copy the three parameters that
we use.
And now we are going to put these in the properties tab.
That's only part of what we need to do in order to apply this to calculate enthalpy
and entropy, Gibb's free energy.
We need to put the heat capacity constants.
So, likewise if we go to the tab IG heat capacities, ideal gas heat capacities, and ABC and D parameters.
That expands the heat capacity as a polynomial in temperature.
So if I copy these and, again going back to the properties tab, paste them here.
And so notice I had to go and change the width of the columns to be able to see the numbers
because I made the fonts bigger, I expanded the scale.
And you would have to go into review in office 2007 and un-protect first the spreadsheet
because the spreadsheet is set up so that only certain cells allow you to change things,
the rest, if you changed you would change the calculations and it's trying to avoid
you doing that.
So we now have critical properties and heat capacity and we need both of those when we
are talking about calculating the enthalpies and entropies.
And if we look at where we were before, a tenth of a and 350.
Look at the fugacity.
This says, again, we are at liquid phase, like we saw before.
And then that z value being lower here than here.
The volume lower, we know it's liquid phase.
The lower fugacity is the stable values.
And now it gives the enthalpies relative to differences from ideal gases.
But let's look at, going to 390.
So this should put us in the vapor phase.
Here again we have the fugacities.
And the fugacity now is lower for the vapor phase so it gives us the difference between
the ideal gas values and the values at the conditions we are at for H, U and S. And of
course also for fugacity.
So you've noticed when we've done these calculations we don't have absolute values for H, U and
S here.
And we always work in relative values, but if we pick a reference state.
So there is a tab for reference state.
And right now the reference state chosen is three, which it says is in the one root region.
So that is physically not reasonable.
It says you much chose a row with a calculable number not one with the number symbol and
NUM.
So if we change this to 2, and we have to un-protect the sheet to do that again.
And now we go back to our properties.
Now we have values for H, U and S. So in this three phase region it calculates values, of
course ones that are physically meaningful are the ones with the lowest fugacities.
So the conditions we picked are vapor phase, here's the enthalpy, H, U and S.
We should be able to go back to 383.4 where the fugacities are almost identical for the
vapor and the liquid.
And so now we have enthalpies, 47,000 for the vapor, 13,800 for the liquid, so we can
calculate the heat of vaporization.
It's not this middle value, right, but it's instead the difference between the vapor value
and the liquid value.
Likewise we have the entropy of vapor, much higher than entropy of the liquid.
And so we can then use the spreadsheet to get values for real gases.
So these take account of the fact that fugacities, entropies, internal energies, and enthalpies,
all depend on pressure as well as on temperature.