Determine the heat capacity at a constant volume for a Van der Waals gas

[Like Tony Stark]

Homework Statement

Find an expression for $c_v$ for a Van der Waals gas

Relevant Equations

1)$S=NS_0+NRLn((U/N+aN/V)^c(V/N-b))$ (fundamental equation)
2)$U/N+aN/V=TRC$
Where $S$ is entropy, $N$ number of moles, $S_0$ a constant, $R$ the ideal gas constant, $V$ the volume of the gas, $U$ internal energy and $a$ and $b$ the Van der Waals coefficients

Hi, what I've done so far is solving equation 2) for $U$, and replacing what I get in equation 1).
Then, $c_V$ is equal to the partial derivative of $S$ with respect to T times T, so I've done that. The derivative is $CNR/T$, so $c_V=CNR$ but those aren't the correct units for $c_V$.

 

[Chestermiller]

What is C supposed to be? Your 2nd equation is key. $$Nc_v=\left(\frac{\partial U}{\partial T}\right)_V$$