First slide

Radiation

Question

A black body is heated from27° to 127°C. The ratio of their energies of radiation emitted will be

Easy

A

81 : 256
B

27 : 64
C

9 : 16
D

3 : 4

Solution

From Stefan's law, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature of the body.
That is $E = {σT}^{4}$
where $σ$ is Stefan's constant.
Given,
initial temperature $T_{1}$ = 273 + 27 = 300K
final temperature $T_{2}$ = 127 + 273 = 400 K
Hence, we have
$\frac{E_{1}}{E_{2}} = \frac{{T^{4}}_{1}}{{T^{4}}_{2}} = \frac{{(300)}^{4}}{{(400)}^{4}} = \frac{81}{256}$
Therefore, $E_{1} : E_{2}$ = 81 : 256

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