A Carnot engine works between two heat reservoirs as a refrigerator. It does 50 J of work to remove 100 J from the cold reservoir and gives off 150 J to the hot reservoir during each cycle. Its coefficient of performance COP = Qc /W = (100 J) / (50 J) = 2.

(a) What is the efficiency of the Carnot engine when it works as a heat engine between the same two reservoirs?

(b) Show that no other engine working as a refrigerator between the same two reservoirs can have a COP greater than 2.