# Third law of thermodynamics

1. Dec 7, 2007

### plmokn2

1. The problem statement, all variables and given/known data
BY consideration of the pressure coefficient dp/dt|V determine whether a real system can be governed by the van der Waals equation, the ideal gas equation.

2. Relevant equations
pV=nRT ideal gas
(p+a/V^2)(V-b)=nRT Van der Walls
dp/dT|V=dS/dV|T

3. The attempt at a solution
Using a Maxwell relation we can rewrite the pressure coefficient as dS/dV|T, which must equal 0 as T->0 from the third law. So then we need to check the behaviour of the two equations of state:

Van der Walls I get the pressure coefficient=nR/(V-b)=1/T (p+a/V^2) which goes to infinity as T goes to zero.

Similarly I get for an ideal gas the coefficient =nR/V=p/T which I don't think goes to zero either.

So it looks like neither works. I was expecting the ideal gas to fail since it doesn't take into account intermolecular forces and non-zero molecular volume, but I'm a bit surprised the van der Waal equation doesn't work, so if someone could check my working I'd appreciate it.
Thanks

ps.dp/dT|V means partial dp by dT at constant V.