For a heat pump, work input W drives heat transfer Qc out of a cold reservoir into a hot reservoir. How does the source relate the heat transfer Qh delivered to the hot reservoir to Qc and W?
AQh equals Qc minus W
BQh equals W minus Qc
CQh equals Qc plus W
DQh equals Qc divided by W
Answer & Solution
Correct answer: C. Qh equals Qc plus W
1. A heat pump extracts heat transfer Qc from a cold reservoir and also uses work input W to drive the process.
2. This work input is also converted to heat transfer, so it adds to the heat delivered rather than disappearing.
3. Combining the extracted heat and the converted work gives the total heat transfer delivered to the hot reservoir: Qh = Qc + W.
4. Option A subtracts W instead of adding it, and option B reverses which term is subtracted from which, neither matching the combination described.
5. Dividing the two quantities, as in option D, does not correspond to combining two energy contributions that add together.
_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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