Consider the following equation:

$${C}_{p}-{C}_{v}=-T{\left(\frac{dp}{dV}\right)}_{T,n}{\left[{\left(\frac{dv}{dT}\right)}_{P,n}\right]}^{2}$$

If the equation of state for a non ideal gas is taken to be:

$$P\left(V-nb\right)=nRT$$

Simplify the right hand side of the equation to find the difference between the constant pressure specific heat and constant volume specific heat for a non ideal gas.

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