The tungsten filament of an electric lamp has a length of `0.5m` and a diameter `6xx10^(-5)m`. The power rating of the lamp is `60 W`. Assuming the radiation from the filament is equivalent to `80 %` that of a perfect black body radiator at the same temperature, estimate the steady temperature of the filament.(Stefan constant `=5.7xx10^(-8)Wm^(-2)K^(-4)`)

Explanation

When the temperature is steady,
power radiated from filament `=` power received `=60W`
`:. 0.8xx5.7xx10^(-8)xx2pixx3xx10^(-5)xx0.5xxT^(4)=60`
since surface area of cylindrical wire is `2pirh` with the usual notation.
`:. T=((60)/(0.4xx5.7xx10^(-8)xx2pixx3xx10^(-5)))^(1//4)=1933K`