Question

A 100 W bulb has tungsten filament of total length 1.0 m and radius $4\times {10}^{-5}$ m. The emissivity of the filament is 0.8 and $\sigma =6.0\times {10}^{-8}W{m}^{-2}{K}^4$. Calculate the temperature of the filament when the bulb is operating at correct wattage.

Answer 1

$\frac{Q}{t}=eA\sigma T^4$

$\Rightarrow T^4=\frac{Q}{teA\sigma }$

$\Rightarrow T^4$

= $\frac{100}{0.8\times 2\times 3.14\times 4\times {10}^{-5}\times 1\times 6\times {10}^{-8}}$

= T = 1697.0 = 1700 K.