First slide

Radiation

Question

Two bulbs have filaments of lengths, Emissivities and diameters in the ratio of 2 :1. If ratio of their powers is 1 : 2 then, ratio of their temperature is

Easy

A

1 : 1
B

1 : 2
C

2 : 1
D

1 : 4

Solution

$\frac{P_{1}}{P_{2}} = \frac{σ_{1} A_{1} T_{1}^{4}}{σ_{2} A_{2} T_{2}^{4}} = \frac{σ_{1} 2 {πr}_{1} l_{1}}{σ_{2} 2 {πr}_{2} l_{2}} {(\frac{T_{1}}{T_{2}})}^{4}$
$\frac{1}{2} = \frac{2}{1} \frac{2}{1} \frac{2}{1} {(\frac{T_{1}}{T_{2}})}^{4}$
$\frac{1}{16} = {(\frac{T_{1}}{T_{2}})}^{4}$
$\frac{T_{1}}{T_{2}} = \frac{1}{2}$

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