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An Inventor Has Built An Engine X And Claims That Its Efficiency X Is Greater Th

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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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