It is desired to slip an aluminum ring over a steel bar. At 10 the inside diameter of the ring is 4.550 and the diameter of the rod is 4.580 . In order for the ring to slip over the bar, the ring is heated. Once the aluminum ring is slipped over the bar, the ring and bar are allowed to equilibrate at a temperature of 10 . The ring is now stuck on the bar
a) If the temperatures of both the ring and the bar are changed together, should the system be heated or cooled to remove the ring?
b) Find the temperature at which the ring can be removed.