Question

A refrigerator is thermally equivalent to a box of corkboard 90mm thick and $6m^2$ 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, ${22}^{\circ }C$ below the temperature of the outside wall. The rate at which heat is taken from the interior wall while the motor is running is

• A. 400W
• B. 500W
• C. 300W
• D. 250W

Answer 1

The correct option is B

500W

Consider a time interval $\Delta t$ while the door is closed. Then the rate of heat into the box is

$\frac{Q}{\Delta t}$ = $kA\left(\frac{\Delta T}{\Delta x}\right)$ = $\left(0.05\right)\left(6\right)\left(\frac{22}{0.09}\right)$ = $73.3W$

To remove heat at this rate, while the motor runs only for a time $\left(0.15\right)\Delta t$, it must cause heat to leave at the rate,

$H$ = $\frac{73.3}{0.15}$ = $500W$