Question

A light bulb is constructed from $2cm$ of tungsten wire of diameter $50\mu m$ and is enclosed in an evacuated glass bulb. What temperature does the filament reach when it is operated at a power of $1$ watt. (Assume the emissivity of the tungsten surface is $0.35$ Stefan's constant $=5.67\times {10}^{-4}c{m}^{-2}{K}^{-4}$.

• A. $2000K$
• B. $4000K$
• C. $2500K$
• D. $1200K$

Answer 1

The correct option is A $2000K$

Given : $l=2cm=0.02m$ $d=50\mu m=50\times {10}^{-6}m$ $P=1W$
Also, $\sigma =5.67\times {10}^{-8}{m}^{-2}{K}^{-4}$ $\sigma =0.35$
Surface area of the wire $A=\pi dl=\pi (50\times {10}^{-6})\left(0.02\right)=3.14\times {10}^{-6}{m}^2$
Using Stefan's law, $P=\sigma Ae{T}^4$
$\therefore$ $1=5.67\times {10}^{-8}\times 3.14\times {10}^{-6}\times 0.35T^4$
$⟹T=2000K$