An inventor has built an engine X and claims that its
efficiency εx is greater than the efficiency ε of an ideal engine
operating between the same two temperatures. Suppose you couple
engine X to an ideal refrigerator (Fig. 2a) and adjust the cycle of
engine X so that the work per cycle it provides equals the work per
cycle required by the ideal refrigerator. Treat this combination as a
single unit and show that if the inventor’s claim were true (if εx>ε)
, the combined unit would act as a perfect refrigerator (Fig.
2b), transferring energy as heat from the low-temperature reservoir to
the high-temperature reservoir without the need for work.
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