NARRATOR: I'm gonna provide a brief introduction
to the virial equation state so just look at the equation,
pressure times volume over RT,
if that's an ideal gas, this number is equal to one
where the volume that I'm using in this equation,
this is a molar volume so, liters per mole for example.
And of course, remember this is absolute temperature,
for example Kelvin,
and then pressure and the ideal gas constant.
That's ideal gas, virial equation then
has additional terms where
this term B is the second virial coefficient.
And of course, C is third virial coefficient and so forth.
So B, C and D are functions of temperature.
Now there's a theoretical basis for the virial coefficient.
But we're not gonna worry about that now.
And certainly this is not gonna be good for all molecules,
particularly not good for polar compounds.
And now an approximation
start carrying out the large number terms.
An approximation would be PV over RT is equal to just
the first term namely the second virial coefficient.
Keep in mind, this PV over RT
is the compressibility factor Z,
and then we can make an additional approximation
by substituting, so one over V is equal to P over RT,
for an ideal gas.
Well, this is not an ideal gas.
We're assuming it obeys a virial coefficient,
but again we can make an approximation.
And this means that we're given pressure and temperature
we can calculate volume with this equation.
Now, what we do to apply to the virial coefficient
is we estimate B by using some correlations so,
so B is related to critical temperature,
critical pressure times another constant.
Now this is the acentric factor
and that's something
we can look up for a given pure component.
The other terms, so B1 is, again this is results from
correlations to reduce temperature over 4.2 so,
to be, as we mentioned is a function of temperature
to reduce temperature is the temperature of the system
divided by the critical temperature.
And then B zero is again a function
of the reduced temperature raised to the 1.6 power.
So if we look up critical pressure,
temperature and acentric factor,
we can calculate the second virial coefficient
and an estimate for virial coefficient.
And then use the virial equation
with the second variable coefficient to
get a better estimate for example volume
than we would get from just the ideal gas law.