Write a general expression by combining the first and second law of thermodynamics

Question

(A) Write the general expression for dU by combining the first and second law for a mole of substance. Then divide by dV and impose a constant temperature to obtain an expression for

(∂U/∂V)T

(B) Using the appropriate Maxwell equation, show that (∂U/∂V)_T = T (∂P/∂T)_V – P

(C) What is the expression of (∂U/∂V)_T for an ideal gas?
(D) What is the expression of (∂U/∂V)_T for a van der Waals?

Summary

The question belongs to Chemical Engineering and it is about calculating the Q, W, ΔU, ΔH, ΔG, ΔA, ΔS for 1 mole of an ideal gas expanding isothermally and reversibly from 10bar to 1bar at 20°C.

Note: The solution is in handwritten format.