Question

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

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

Answer 1

Answer: (B)

$\sigma=5.67 \times 10^{-5} \text{erg} cm ^{-2} s ^{-1} K ^{-4}$
Power of lamp $=100\, W =100\, Js ^{-1}$
$\therefore$ Rate of emission of energy,
$E=100 \times 10^{7} \,erg\, s ^{-1} \left(\because 1 J =10^{7} \,erg \right)$
Area, $A=1 \,cm ^{2}$, 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} $
$=2049\, K$