#### 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^{−2}K^{4}. 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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Solution 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 Concept: Stefan's Law.