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Question
A 100 W bulb has tungsten filament of total length 1.0 m and radius 4 × 10−5 m. The emissivity of the filament is 0.8 and σ = 6.0 × 10−8 W m−2K4. Calculate the temperature of the filament when the bulb is operating at correct wattage.
Solution
Given:
Power of the bulb, P = 100 W
Length of the filament, l = 1.0 m
Radius of the filament, r = 4 × 10−5 m
According to Stefan's law,
`("Energy radiated"/ "time") = e.AsigmaT^4`
Here, e is the emissivity of the tungsten and σ is Stefan's constant.
∴ `P = e.(pir^2)sigmaT^4 `
`⇒ 100 =(0.8)xx 3.14xx(4xx10^-5)xx6xx10^-8xxT^4`
`⇒ T = 1700K ("approximately")`
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