1. (a) Prove that no 2-temperature refrigerator operating between reservoirs at hotter and colder temperatures Th and Tc has a greater coefficient of performance than a Carnot refrigerator. Use diagrams of the type introduced in the chapter.

(b) Find the minimum amount of electrical energy needed to create 0.50 kg of ice from water at 0 °C in a household freezer that rejects heat to a room at 20 °C.

2. Show that a heat pump with a coefficient of performance COPh greater than a heat pump that operates on a Carnot cycle would violate Clausius' statement of the second law.