Question

A 100 W bulb has tungsten filament of total length 1.0 m and radius 4 × 10⁻⁵ m. The emissivity of the filament is 0.8 and σ = 6.0 × 10⁻⁸ W m⁻²K⁴. Calculate the temperature of the filament when the bulb is operating at correct wattage.

Answer 1

Given:
Power of the bulb, P = 100 W
Length of the filament, l = 1.0 m
Radius of the filament, r = 4 × 10⁻⁵ m

According to Stefan's law,

$\frac{\mathrm{Energy}\mathrm{radiated}}{\mathrm{Time}}=e\mathit{·}A\sigma T^4$

Here, e is the emissivity of the tungsten and σ is Stefan's constant.

$\therefore P=e\mathit{·}\mathit{\left(}\pi r^{\mathit{2}}\mathit{\right)}\sigma T^4$
$$\begin{gathered} \Rightarrow 100=\left(0.8\right)\times 3.14\times {\left(4\times {10}^{-5}\right)}^2\times 6\times {10}^{-8}\times T^4 \\ \Rightarrow T=1700\mathrm{K}\left(\mathrm{approximately}\right) \end{gathered}$$