First slide

Radiation

Question

A black body is heated from $27^{0} C to 127^{0} C$ . The ratio of their energies of radiation emitted will be

Moderate

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 $T_{1} = 273 + 27 = 300 K$
final temperature $T_{2} = 127 + 273 = 400 K$
Hence, we have
$\frac{E_{1}}{E_{2}} = \frac{{T_{1}}^{4}}{{T_{2}}^{4}} = \frac{{(300)}^{4}}{{(400)}^{4}} = \frac{81}{256}$
Therefore, $E_{1} : E_{2} = 81 : 256$

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