A refrigerator is thermally equivalent to a box of cork board 90 mm thick and `6m^2` in iner 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

Explanation

Consider a time interval `Deltat` during which the door is closed. As approximation, take the heat conduction to be steady ober `Deltat`.
Then the rate of heat into the box is
`(DeltaQ)/(Deltat)=kA((DeltaT)/(Deltax))=(0.05)(5.6)((22.2)/(0.090))=69.1W`
To remove this heat, the motor must, since it runs only for a time (0.15) `Deltat`, cause heat to leave at the rate `69.1//0.15=460W`.