Two bodies, with heat capacities C1 and C2 (assumed independent of temperature) and initial temperatures T1 and T2 respectively, are placed in thermal contact. Show that their final temperature Tf is given by Tf=(C1T1+C2T2)/(C1+C2). If C1 is much larger than C2, show that Tf≈T1+C2(T2−T1)/C1.