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Homework Statement
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I'm stuck on part c of the attached problem:
Homework Equations
$$C_P  C_V = \left[P + \left( \frac {∂U}{∂V} \right)_T \right]\left( \frac {∂V}{∂T} \right)_P$$
$$P + \left( \frac {∂U}{∂V} \right)_T = T \left( \frac {∂P}{∂T} \right)_V$$
$$\left(P + \frac {a}{V^2} \right)(V  b) = RT$$
The Attempt at a Solution
I need to use the bottom two equations to find to find ##P + \left( \frac {∂U}{∂V} \right)_T ## and ##\left( \frac {∂V}{∂T} \right)_P## and plug these expressions in the top equation for C_{P}  C_{V}.
I've found $$\left (\frac {∂P}{∂T} \right)_V = \frac {R}{V  b}$$
$$∴ P + \left( \frac {∂U}{∂V} \right)_T = \frac {RT}{V  B}$$
But I'm having trouble finding ##\left (\frac {∂V}{∂T} \right)_P## because I can't seem to make V the subject of the Van der Waals gas expression.
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