40w electric bulb has 10 CM long filament of 200 micron thick tungsten wire in an evacuated glass bulb .if we assume the filament to be a perfect black body radiator. what would be it's temperature
Answers
Given info : 40W electric bulb has 10 cm long filament of 200 micron thick tungsten wire in an evacuated glass bulb .
To find : if we assume the filament to be a perfect black body radiator. what would be its temperature..
solution : area of Tungsten wire, A = πr²l
= 3.14 × (100 × 10¯⁶ m)² × (0.1 m)
= 3.14 × 10^-9 m²
power, P = 40 Watt
for perfect black body, e = 1
using formula, P = eAσT⁴ , here σ is Stefan's Boltzmann's constant.
⇒40 = 1 × 3.14 × 10^-9 × 5.6 × 10^-8 × T⁴
⇒22.747 × 10¹⁶ = T⁴
⇒T ≈ 21839 K
Therefore its temperature would be 21839 K.
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