+ ...
where B is called the second virial
coefficient and represents the enthalpy associated with binary
interactions in the gas. This same method is used to discuss
solution theory where enthalpic interactions are important to
understanding miscibilty.
A second approach to describing non-ideal behavior is to simply allow a
modification of the pressure (to account for enthalpic interactions)
and the volume (to account for finite excluded volume of the gas
molecules) through the van der Waals equation of state,
(P + a/V
sp2)(V
sp
- b) = RT
where the modification of pressure
follows the dependence of the second virial term, i.e. it depends on φ
2.
A third approach is to simply find a correction factor for non-ideal
behavior using the compressiblity, z,
z = PV/nRT
Typically, we use the critical point to
reduce the pressure and temperature to obtain a more universal
compressiblity function. The critical point is the point at which
the density of a liquid and a vapor become the same on increasing
temperature and pressure. Above the critical point liquid and
vapor are not distinguishable and there is no surface tension for
fluids. For CO
2 this occurs as 31ºC and 72.8 atm,
for
propane at 97ºC and 42 atm.
The reduced compressiblity is given by,
zr = PrV/nRTr,
where P
r = P/P
c and T
r = T/T
c
and P
c and T
c are the critical pressure
and temperatures.