Consider a system consisting of two objects A and B, when A and B have initial temperature T_A and T_B, and heat capacities C_VA and C_VB independent of temperature. This system is put to work so that it can provide work W, until both reaches a final temperature T_F, where T_A>T_F>T_B.
(a) Find the maximum mechanical work that can be extracted from this system.
(b) Obtain the equilibrium temperature reached after all the work in (a) was extracted.