And moreover, if I choose my initial volume to be so large that my gas is
very, very dilute. Then it ought to behave as an ideal gas,
and I can use the properties of ideal gases to establish what the entropy ought
to be at that very large volume. Or alternatively very low density, so as
the density goes to 0. So in that case delta s, which is going
to be the entropy at the new volume compared to the entropy at almost
infinite volume. Is this integral from ideal volume to V2,
and I can plot that, effectively. So, here, I have what is the molar
entropy of an ideal gas? And given my gas, if it's behaving
ideally, I can do that from the partition function.
Remember what I'll need for that, I'll need to know its mass.
I'll need to know its moments of inertia, I'll need to know its vibrational
frequencies. But with those in hand, I can compute, in
a spreadsheet, what the entropy must be. And so for ethane for instance at 400
Kelvin, I would get 246.45 joules per mole Kelvin, at one bar.
And then, using data that I would measure for, ethylene at 400 Kelvin.
I could determine, as this integral goes along, what's happening to the entropy.
And so it's going down, down, down, down, down as the density is increasing.
And certainly, by the way, from concept standpoint, that should seem sensible.
The entropy should be being reduced as I am decreasing the volume, increasing the
density. There's clearly less disorder as I give
my gas less volume to occupy. So, for real gases, where we don't have
an analytical equation of state the way we do for the ideal gas.
we really have to do these measurements. We would have to look at, how does the
pressure vary with temperature? Over a range of different volumes.
And I didn't mean to make you go so, I'll go back there for a second.
and in this case we would also you could also do that with different densities as
opposed to different volumes, that's what's plotted here.