Question #264959

Calculate the steady state temperature of a tungsten bulb rated 1Kw,it's filament length is 50cm and radius 0.1mm, assumed it to be a black body


1
Expert's answer
2021-11-16T10:00:32-0500

Solution;

Given;

P=1kW=100W

r=0.1mm=1×10-4m

L=50cm=0.5m

Now;

Power radiated from filament=Power revieved.

P=AeσT4P=Ae\sigma T^4

Here;

A=2πrL

e is emissivity ,for black body is 1

σ\sigma is Stefan Boltzmann's constant;5.7×10-8W/m2K4

T4=10002π×1×104×0.5×1×5.7×108T^4=\frac{1000}{2π×1×10^{-4}×0.5×1×5.7×10^{-8}}

T4=5.584×1013T^4=5.584×10^{13}

T=2733.66KT=2733.66K









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