The pumps coefficient of performance is 3.8, and the heat pumpdelivers 7.54 MT o

Question

The pumps coefficient of performance is 3.8, and the heat pumpdelivers 7.54 MT of thermal energy to the building each hour. Ifthe ehat pump is a carnot engine working in reverse, at what ratemust work be done to run the heat pump? The answer should be 440 W, but I need help on the method togetting this.. The pumps coefficient of performance is 3.8, and the heat pumpdelivers 7.54 MT of thermal energy to the building each hour. Ifthe ehat pump is a carnot engine working in reverse, at what ratemust work be done to run the heat pump? The answer should be 440 W, but I need help on the method togetting this..

Explanation / Answer

We have coefficient of performance K =QC/(QH-QC) Here K = 3.8 QH = 7.54MJ 3.8 = QC/(7.54MJ-QC) 28.652MJ - 3.8QC = QC Then QC = 5.969MJ Then work done W = QH-QC                               =7.54MJ - 5.969MJ                               = 1.571MJ So rate of work done is (1.571*106J)/(3600s) =436.38W ˜ 440W                               =7.54MJ - 5.969MJ                               = 1.571MJ So rate of work done is (1.571*106J)/(3600s) =436.38W ˜ 440W

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