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Equation 12 15 shows that the greater the temperature difference between

Equation 12.15 shows that the greater the temperature difference between the reservoirs of a heat engine, the greater the engine’s Carnot efficiency. Suppose you had the choice of raising the temperature of the high-temperature reservoir by a certain number of kelvins or lowering the temperature of the low-temperature reservoir by the same number of kelvins.

(a) To produce the largest increase in efficiency, you should choose (1) to raise the high-temperature reservoir, (2) to lower the low-temperature reservoir, (3) both 1 and 2 produce the same change in efficiency, so it does not matter which you choose. Explain.

(b) Prove your answer to part (a) mathematically.

(a) To produce the largest increase in efficiency, you should choose (1) to raise the high-temperature reservoir, (2) to lower the low-temperature reservoir, (3) both 1 and 2 produce the same change in efficiency, so it does not matter which you choose. Explain.

(b) Prove your answer to part (a) mathematically.

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