On a hot day, you are in a sealed, insulated room. The room contains a refrigera

Question

On a hot day, you are in a sealed, insulated room. The room contains a refrigerator, operated by an electric motor. The motor does work at the rate of 249 W when it is running. Assume the motor is ideal (no friction or electrical resistance) and that the refrigerator operates on a reversible cycle. In an effort to cool the room, you turn on the refrigerator and open its door. Let the temperature in the room be 317 K when this process starts, and the temperature in the cold compartment of the refrigerator be 259 K. At what net rate is heat added to (+) or subtracted from (-) the room and all of its contents?
W

Explanation / Answer

efficiency of a reversible engine=1-(Tl/Th)
where Tl and Th are temperatures of the low temp zone(sink) and high temperature source

efficiency=1-259/317=.183
hence heat gain by the room/time=249*.183=45.567
if we consider refrigerator and room as a single whole system using first law of thermodynamics
heat change=0 since room is insulated
work done(power)=249 W
hence there should be an increase in the internal energy of the room.

work done +heat=internal energy

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