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  4. A black rectangular surface of area A emits energy E per second at 27 ° C . If length and breadth are reduced to 1/3rd of initial value and temperature is raised to 327 ° C , then energy emitted per second becomes

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Q. A black rectangular surface of area $A$ emits energy $E$ per second at $27 \,{}^\circ C$ . If length and breadth are reduced to $1/3^{rd}$ of initial value and temperature is raised to $327 \,{}^\circ C$ , then energy emitted per second becomes

NTA AbhyasNTA Abhyas 2020Thermal Properties of Matter

Solution:

$E=e\sigma .A\left(T^{4} - T_{0}^{4}\right) \, and \, A=lb \, $
When $l$ and b changes to $\frac{l}{3}$ and $\frac{b}{3}$
$A \rightarrow \frac{A}{9}$
$\frac{E^{′}}{E}=\frac{A^{′}}{A}\frac{\left(327 + 273\right)^{4}}{\left(27 + 273\right)^{4}}$
$\therefore \, \, \frac{E^{′}}{E}=\frac{1}{9}\left(\frac{600}{300}\right)^{4}$
$\therefore \, \, E^{′}=\frac{1}{9}\times \left(2\right)^{4}\times E$
$E^{′}=\frac{16 E}{9}$