Question

The tungsten filament of an electric lamp has a length of $0.5\text{m}$ and a diameter $6\times {10}^{-5}\text{m}$. The power rating of the lamp is $60\text{W}$. Assuming the radiation from the filament is equivalent to 80% of a perfect black body radiator at the same temperature, estimate the steady state temperature of the filament (Stefan's constant $=5.7\times {10}^{-8}{\text{W m}}^{-2}{\text{K}}^{-4}$)

• A. $1972\text{K}$
• B. $2200\text{K}$
• C. $1933\text{K}$
• D. $1790\text{K}$

Answer 1

The correct option is C $1933\text{K}$

From Stefan-Boltzmann law,
$P=e\sigma A{T}^4$
Surface area of cylindrical filament,
$A=2\pi rh$
Under steady state condition,
Power radiated from filament $\left(P\right)$ = Power received
$\Rightarrow 0.8\times 5.7\times {10}^{-8}\times 2\pi \times 3\times {10}^{-5}\times 0.5\times T^4=60$
$\Rightarrow T={\left[\frac{60}{0.8\times 5.7\times {10}^{-8}\times 2\pi \times 3\times 0.5\times {10}^{-5}}\right]}^{1/4}$
$\Rightarrow T=1933\text{K}$
Hence, option (c) is the correct answer.