[UPSC CSE 2002] Black Body Radiation (Q480, 30M)

A bulb filament is constructed from a tungsten wire of length 2\text{ cm} and diameter 50\text{ }\mu\text{m}. It is enclosed in a vacuum bulb. What temperature does it reach when it is operated at a power of 1 watt? Given:

(i) Emissivity of tungsten \varepsilon = 0.4

(ii) Stefan's constant \sigma = 5.67 \times 10^{-8}\text{ watt/m}^2\text{ K}^4.