Question

The operating temperature of a tungsten filament in an incandescent lamp is $2000\text{K}$ and its emissivity is $0.3$. Find the surface area of the filament of a $25\text{watt}$ lamp.
Stefen's constant $\sigma =5.67\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$

• A. $0.412\times {10}^{-5}{\text{m}}^2$
• B. $0.918\times {10}^{-4}{\text{m}}^2$
• C. $0.212\times {10}^{-4}{\text{m}}^2$
• D. $0.416\times {10}^{-4}{\text{m}}^2$

Answer 1

The correct option is B $0.918\times {10}^{-4}{\text{m}}^2$

Rate of emission of energy is equal to the power of the lamp.
$\Rightarrow W=A\sigma e{T}^4$
Where $e\to$emissivity
$\Rightarrow A=\frac{W}{e\sigma T^4}$
$\Rightarrow A=\frac{25}{0.3\times 5.67\times {10}^{-8}\times (2000{)}^4}$
$\therefore A=0.918\times {10}^{-4}{\text{m}}^2$