Prove the internal pressure pT = (?U / ?V)T = T (?p / ?T)V – p and calculate the internal pressure f

Prove the internal pressure πT = (∂U / ∂V)T = T (∂p / ∂T)V – p and calculate the internal pressure for a gas that obeys the equation of state p(V-nb) = nRT, where b and R are constants. Use Maxwell relations! Hint: Write the expression of πT in terms of dp, dT, T, p.