A refrigerator is thermally equivalent to a box of cork board 90 mm thick and 6 m2 in inner surface area, the thermal conductivity of cork being 0.05 W/mK. The motor of the refrigerator runs 15% of the time while the door is closed. The inside wall of the door, when it is closed, is kept, on an average, 22°C below the temperature of the outside wall. The rate at which heat is taken from the interior wall while the motor is running is
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a
400 W
b
500 W
c
300 W
d
250 W
answer is B.
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Detailed Solution
Consider a time interval Δt while the door is closed. Then the rate of heat into the box isQ∆t=kA∆T∆x=(0.05)(6)220.09=73.3W To remove heat at this rate, while the motor runs only for a time (0.15) Δt, it must cause heat to leave at the rate,H=73.30.15=500W