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Answer to Question #5548 in Molecular Physics | Thermodynamics for cncrowell

Question #5548
A refrigerator operates with Carnot efficiency
between temperatures −4.8C and 36.1C.
What is its coefficient of performance?
Expert's answer
The coefficient of performance or COP at the Carnot efficiency is defined to be:
data:image/png;base64,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
where QH is the heat supplied to the hot reservoir
W is the work consumed by the heat pump

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