Spheres A and B are initially at 800 K, and they are simultaneously quenched in large constant temperature baths, each having a temperature of 320 K. The following parameters are associated with each of the spheres and their cooling processes.
(a) Show in a qualitative manner, on T - t coordinates, the temperatures at the center and at the surface for each sphere as a function of time. Briefly explain the reasoning by which you determine the relative positions of the curves.
(b) Calculate the time required for the surface of each sphere to reach 415 K.
(c) Determine the energy that has been gained by each of the baths during the process of the spheres cooling to 415 K.