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Homework Help: Third law of thermodynamics

  1. Dec 7, 2007 #1
    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.
     
  2. jcsd
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