For an air conditioner or refrigerator, the source defines a separate coefficient of performance, COPref. Which ratio does it use, and how is it related to COPhp for the same two reservoir temperatures?

1. An air conditioner or refrigerator is judged by how much heat transfer Qc it removes from a cold environment for a given work input, so its coefficient of performance is defined as COPref = Qc/W. 2. Since Qh = Qc + W, the heat delivered to the hot side is always larger than the heat removed from the cold side, by exactly the amount of work put in. 3. Because COPhp = Qh/W uses the larger quantity Qh in its numerator while COPref = Qc/W uses the smaller quantity Qc, an air conditioner ends up with a lower coefficient of performance than a heat pump operating between the same two temperatures. 4. Working through the algebra of Qh = Qc + W shows that COPref = COPhp - 1 for the same two reservoir temperatures. 5. Option B swaps which formula gets the plus sign, option C inverts the COPref ratio, and option D compares Qc to Qh directly and multiplies rather than subtracts, none of which matches the relationship described. _Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.5 Applications of Thermodynamics: Heat Pumps and Refrigerators_