First slide

Radiation

Question

The tungsten filament of an electric lamp has a surface area A and a power rating P. If the emissivity of the filament is e and $σ$ is Stefan's constant, the steady temperature of the filament will be

Easy

A

$P / (Aeσ)$
B

$[P / (Aeσ)]^{2}$
C

$[P / (Aeσ)]^{1 / 2}$
D

$[P / (Aeσ)]^{1 / 4}$

Solution

We know that the energy radiated per second per unit area at temp. T is given by $= {σeT}^{4}$
The power radiated from the filament of area A is given by $P = ({σeT}^{4}) \times A$
$∴ T = {(\frac{P}{Aeσ})}^{1 / 4}$

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