# Showing equation of state is inaccurate based on compression factor

1. Aug 31, 2011

### TehDarkArchon

1. The problem statement, all variables and given/known data

If I was using an equation of state as so:
Vm = (RT/P) - (aRT^2)/P, where the constant a is
always positive, I would be able to determine that the compression factor is Z = Vm/Vm° = 1− a ⋅T .
This leads me to the conclusion that there is something seriously wrong with this equation of
state, and I should not use it. Why do I think so? Hint: This is a limiting case question, and
remember that Z can function as a correction factor for the perfect gas law as so: ZPVm°=RT

2. Relevant equations
Vm = (RT/P) - (aRT^2)/P
Z = Vm/Vm° = 1− a ⋅T
ZPVm°=RT
Also with something involving a limit.

3. The attempt at a solution
A compression factor makes up for the fact that a gas will act like it has more/less pressure than it actually does, which usually varies with temperature as well. I'm guessing the main problem here is that it varies directly with temperature, and no other variable, making the compression values for all gases significantly low. I'm just not sure if im going in the right direction, or how to mathematically show this...