(a) Why must all reversible engines (operating between the same reservoirs) have

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(a) Why must all reversible engines (operating between the same reservoirs) have the same efficiency? Try an argument by contradiction: imagine that two reversible engines exist with e1 > e2. Reverse one of them (into a heat pump) and use the work output from the engine to run the heat pump. What happens? (If it seems fine at first, switch the two.)

(b) Most heat pumps incorporate an auxiliary electric heater. For relatively mild outdoor temperatures, the electric heater is not used. However, if the outdoor temperature gets very low, the auxiliary heater is used to supplement the heat pump. Why?

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