Spectrum of a black body at two temperature 27,^oC and 327,^oC is shown in figure. Let A

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10-2.Transmission of Heat

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The spectrum of a black body at two temperature $27\,^oC$ and $327\,^oC$ is shown in the figure. Let $A_1$ and $A_2$ be the areas under the two curves respectively. The value of $\frac {A_2}{A_1}$ is

A

$1\,\,:\,\,16$

B

$4\,\,:\,\,1$

C

$2\,\,:\,\,1$

D

$16\,\,:\,\,1$

Solution

Area under given curve represents emissive power and emissive power $\propto T^{4} \Rightarrow A \propto T^{4}$

$\Rightarrow \frac{A_{2}}{A_{1}}=\frac{T_{2}^{4}}{T_{1}^{4}}=\frac{(273+327)^{4}}{(273+27)^{4}}=\left(\frac{600}{300}\right)^{4}=\frac{16}{1}$

Standard 11

Physics

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