Let the ends of a copper rod 100 cm long be maintained at 0°c. suppose that the center of the rod is heated to 100°c by an external heat source and that this situation is maintained until a steady state has been reached. a)- find the steady-state temperature distribution. b)- at time t=0 (after the steady state has been reached), let the heat source be removed. at the same instant, let the end x = 0 be placed in thermal contact with a reservoir at 20°c, while the other end remains at 0°c. find the temperature as a function of position and time. c)-plot the temperature u versus x for t = 5, 20, 200, and 500 sec. also plot u versus t for x = 25, 50, and 75 cm. d)-what limiting value does the temperature at the center of the rod approach after a long time? e)-how much time must elapse before the center of the rod cools to within 1°c of its limiting value?