Since a heat engine's efficiency is Eff = W/Qh, and a heat pump's coefficient of performance is COPhp = Qh/W, how are Eff and COPhp related, and what does this imply about the size of COPhp?
ACOPhp equals 1/Eff, so COPhp is always greater than 1
BCOPhp equals Eff, so COPhp is always less than 1
CCOPhp equals Eff squared, so COPhp can be any positive value
DCOPhp and Eff are unrelated quantities entirely
Answer & Solution
Correct answer: A. COPhp equals 1/Eff, so COPhp is always greater than 1
1. COPhp is defined as Qh/W, which is exactly the reciprocal of Eff = W/Qh.
2. This relationship is stated directly: COPhp = 1/Eff.
3. Since the efficiency of any real heat engine is always less than 1, taking its reciprocal always gives a number greater than 1.
4. This means COPhp is always greater than 1, the opposite of option B's claim that it stays below 1.
5. The relationship is a simple reciprocal, not a square, and the two quantities are directly tied together rather than unrelated, ruling out options C and 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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