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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

    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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