Q. A body at $300^{\circ} C$ radiates $10\, J\, cm ^{-2}\, s ^{-1}$. If Sun radiates $10^{5}\, J\, cm ^{-2}\, s ^{-1}$, then its temperature is :

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A

$3000^{\circ} C$

B

$5457^{\circ} C$

C

$300 \times 10^{4}{}^{\circ}C$

D

$5730^{\circ} C$

Solution:

We use $E \propto T^{4}$
$\Rightarrow \frac{10}{10^{5}}=\frac{(300+273)^{4}}{T^{4}}$
$\Rightarrow T =5730\, K$
$\Rightarrow T =5457^{\circ} C$

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