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Find (∂V/∂T) of a Van der Waals Gas using variables?

  1. Sep 10, 2012 #1
    Find (∂V/∂T) of a Van der Waals Gas using variables?
    Evaluating a Derivative of the van der Waals Equation using the Cyclic Rule


    For the van der Waals equation of state:
    V-b(P+ a/v^2)=RT

    the derivative (∂V/∂T)p is difficult to obtain directly because finding an equation for V in terms of P or T requires solving the cubic equation:
    PV^3 - (bP +RT)V^2 + a(V-b)=0

    a and b are two parameters that take into account the size of the molecule and the strength of the attractive interaction.

    Because P is linear in the van der Waals equation, it should be easier to find the partial derivatives:
    (∂P/∂T)v and (∂V/∂P)T = 1/(∂P/∂V)T

    needed to utilize the cyclic rule.

    Using the cyclic rule, find
    (∂V/∂T)P

    Express your answer in terms of the parameters, constants, and variables in the van der Waals equation (P,V,R,T,a,and b).

    What exactly is (∂V/∂T) at a constant P in terms of P,V, R, T, a, and b? Thanks!
     
  2. jcsd
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