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

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##.

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