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Adiabatic Expansion problem

  1. Jan 30, 2010 #1
    1. The problem statement, all variables and given/known data
    One mole of Ar initially at 325K undergoes an adiabatic expansion against a pressure Pexternal=0 from a Volume of 10.5L to 95.0L. Calculate the final Temperature using Ideal Gas and Van der Waals equations of state. Assume Cv,m=(3/2)R.

    2. Relevant equations
    P=(RT/Vm-b) - (n2a/v2

    3. The attempt at a solution
    I assumed Cp,m=20.8 J/mol K and Cv,m=12.47 J/mol K due to the ratios.
    Also since it's adiabatic q=0
    Initial Volume = 10.5 L
    Final Volume = 95.0 L

    Using my professors notes for an example of a similar problem I found the equation:

    Tf = Ti*(Vm,i / Vm,f) gamma

    Gamma - Cp,m/Cv,m . So gamma = 1.4

    My math was Tf=325 K * (10.5L/95L)0.4

    My concern is I'm not sure if I won't get full credit since I didnt really use the van der waals equation of state or even the ideal gas law to my knowledge.

    Can anyone provide some help?
  2. jcsd
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