Question

At what temperature will the filament of $100W$ lamp operate, if it is supposed to be perfectly black body of area $1.0c{m}^2$ ?

• A. $3449K$
• B. $2049K$
• C. $3000K$
• D. $3010K$

Answer 1

Answer: (B)

$\sigma =5.67\times 10^{-5}\text{erg}c{m}^{-2}{s}^{-1}{K}^{-4}$
Power of lamp $=100W=100J{s}^{-1}$
$\therefore$ Rate of emission of energy,
$E=100\times 10^{7}erg{s}^{-1}\left(\because 1J=10^{7}erg\right)$
Area, $A=1c{m}^2$, temperature, $T=$ ?
According to Stefan-Boltzmann law, we get
$E=\sigma T^4\times A$
$\therefore T{T}^4=\frac{E}{\sigma A}=\frac{100\times 10^7}{5.67\times 10^{-5}\times 1}=\frac{100\times 10^{12}}{5.67}$
$\Rightarrow T={\left(\frac{100}{5.67}\right)}^{1/4}\times 10^3=2.049\times 10^3$
$=2049K$