For a van der Waals gas, show that [ C_{P}-C_{V}=frac{T R^{2} V^{3}}{R T V^{3}-2 a(V-b)^{2}} ]

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For a van der Waals gas, show that

\[ C_{P}-C_{V}=\frac{T R^{2} V^{3}}{R T V^{3}-2 a(V-b)^{2}} \]

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