Question

A cubical box of volume $216c{m}^3$ is made up of 0.1 cm thick wood. The inside is heated electrically by a 100 W heater. It is found that the temperature difference between the inside and the outside surface is $5^{\circ }C$ in steady state. Assuming that the entire electrical energy spent appears as heat, find the thermal conductivity of the material of the box.

Answer 1

V = $216c{m}^3$ , a = 6 cm

Surface area = $6a^2=6\times 36\times {10}^{-4}{m}^2$

l = 0.1 cm

$\frac{Q}{t}=100W$

$\frac{Q}{t}=\frac{kA(T_1-T_2)}{l}$

$\Rightarrow 100=\frac{k\times 6\times 36\times {10}^{-4}\times 5}{0.1\times {10}^{-2}}$

$\Rightarrow 100=k\times 6\times 36\times {10}^{-1}\times 5$

$\Rightarrow k=\frac{100}{6\times 36\times 5\times {10}^{-1}}$

=$\frac{100\times 10}{6\times 36\times 5}$

= 0.9259 W / m${}^{\circ }C$