A Carnot air conditioner takes energy from the thermal energyof a room at 70 deg

Question

A Carnot air conditioner takes energy from the thermal energyof a room at 70 degrees F and transfers it as heat to the outdoors,which is at 96 degrees F. For each joule of electric energyrequired to operate the air conditioner, how mnay joules areremoved from the room? A Carnot air conditioner takes energy from the thermal energyof a room at 70 degrees F and transfers it as heat to the outdoors,which is at 96 degrees F. For each joule of electric energyrequired to operate the air conditioner, how mnay joules areremoved from the room?

Explanation / Answer

Hello, A Carnot cycle operating as a reverse heat pump (i.e. air conditioner) has aCoefficient of Performance (COP) this is similar to an efficiencybut since it's value can be greater than 1 so it has thealternative name Coefficient of Performance. The COP can be definedas the ratio of the heat extracted from a low temperature source tothe work done to accomplish that extraction. For this application the COP can be calculated as COP = 1 / ((Th / TL) - 1) where Th is the higher temperature and TL is the lowertemperature. Then you can use this relation COP = QL / W

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