$($ I need step by step solution only with proper explanation and solving of each and every step $)$ One mole of an ideal van der Waals fluid is contained in a cylinder fitted with a piston. The initial

temperature of the gas is $T_1,$ and the initial volume is $v_1.$ A reversible heat source with a constant

heat capacity $C$ and with an initial temperature $T_0$ is available. The gas is to be compressed to

a volume of $v_f$ and brought into thermal equilibrium with the reversible heat source. What is the

maximum work that can be delivered to the reversible work source, and what is the final temperature?