First slide

Radiation

Question

The spectrum of a black body at two temperatures 27°C and 327°C is shown in the figure. Let $A_{1} and A_{2}$ be the areas under the two curves respectively. Find the value of $\frac{A_{2}}{A_{1}}$ .

Moderate

A

16 : 1
B

8 : 1
C

9 : 4
D

16 : 9

Solution

Area under given curve represents emissive power and emissive power $\propto T^{4} \Rightarrow A \propto T^{4}$
$\Rightarrow \frac{A_{2}}{A_{1}} = \frac{{T^{4}}_{2}}{{T^{4}}_{1}} = \frac{{(273 + 327)}^{4}}{(273 + 27) 4} = {(\frac{600}{300})}^{4} = \frac{16}{1}$

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