Answer to Question #264959 in Electric Circuits for Moonlight

Question

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

Answer 1

Solution;

Given;

P=1kW=100W

r=0.1mm=1×10^-4m

L=50cm=0.5m

Now;

Power radiated from filament=Power revieved.

$P=Ae\sigma T^4$

Here;

A=2πrL

e is emissivity ,for black body is 1

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

$T^4=\frac{1000}{2π×1×10^{-4}×0.5×1×5.7×10^{-8}}$

$T^4=5.584×10^{13}$

$T=2733.66K$