An isolated system contains an incompressible substance with heat capacity C = kT, where k is a constant. The system is initially divided in two parts, with 1/3 of the mass at T1 and 2/3 of the mass at T2. The divider is removed and the system eventually attains equilibrium.
a) Derive an expression for TF , the final temperature attained, in terms of T1 and T2.
b) Derive an expression for the entropy produced written in terms of TF ; T1; T2; m; k.