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Since COPhp = 1/Eff and the Carnot efficiency EffC = 1 - Tc/Th shrinks as Tc and Th get closer together, what does the source conclude about where heat pumps perform best?

AHeat pumps work equally well at any temperature gap
BHeat pumps work best with a large temperature gap
CHeat pumps work best with a small temperature gap
DHeat pumps work best only when Tc exceeds Th
Answer & Solution
Correct answer: C. Heat pumps work best with a small temperature gap
1. As Tc and Th get closer together, the ratio Tc/Th moves closer to 1, which makes the Carnot efficiency EffC = 1 - Tc/Th smaller. 2. A smaller efficiency means a larger reciprocal, so COPhp = 1/Eff grows larger as the temperature difference shrinks. 3. The source draws the practical conclusion from this: heat pumps do not work as well in very cold climates as they do in more moderate climates, where the indoor-outdoor gap is smaller. 4. This rules out option B, which claims the opposite relationship between climate and performance, and option A, which denies any dependence on temperature difference at all. 5. Tc exceeding Th would mean the supposed cold reservoir is hotter than the hot reservoir, which is not the condition the source is describing, ruling out option D. _Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators_
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