Question

A cubical box of volume 216 cm³ 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°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

Volume of the cube, V = a³ = 216 cm³
Edge of the cube, a = 6 cm
Surface area of the cube = 6a²
= 6 (6 × 10⁻²)²
= 216 × 10⁻⁴ m²
Thickness, l = 0.1 cm = 0.1 × 10^–2 m
Temperature difference, Δ T = 5°C
The inner surface of the cube is heated by a 100 W heater.
∴ Power, P = 100 W
Power = Energy per unit time
∴ Rate of flow of heat inside the cube, R = 100 J/s
Rate of flow of heat is given by
$$\begin{gathered} \frac{\mathrm{\Delta Q}}{\mathrm{\Delta }t}=\frac{\Delta \mathrm{T}}{{\displaystyle \frac{l}{\mathrm{kA}}}} \\ 100=\frac{\mathrm{k}\times 216\times {10}^{-4}\times 5}{0.1\times {10}^{-2}} \\ \mathrm{k}=0.9259\mathrm{W}/\mathrm{m}°\mathrm{C} \end{gathered}$$