A black rectangular surface of area 'A' emits energy 'E' per second at $27^{\circ} \mathrm{C}$. If length and breadth are reduced to $\frac{1}{3}$ rd of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomesA) $\frac{4 \mathrm{E}}{9}$B) $\frac{7 E}{9}$C) $\frac{10 \mathrm{E}}{9}$D) $\frac{16 \mathrm{E}}{9}$

Home » A black rectangular surface of area ‘A’ emits energy ‘E’ per second at . If length and breadth are reduced to rd of initial value and temperature is raised to then energy emitted per second becomesA) B) C) D)

A black rectangular surface of area ‘A’ emits energy ‘E’ per second at $27^{\circ} \mathrm{C}$ . If length and breadth are reduced to $\frac{1}{3}$ rd of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomes
A) $\frac{4 \mathrm{E}}{9}$
B) $\frac{7 E}{9}$
C) $\frac{10 \mathrm{E}}{9}$
D) $\frac{16 \mathrm{E}}{9}$

Physics

A black rectangular surface of area ‘A’ emits energy ‘E’ per second at $27^{\circ} \mathrm{C}$ . If length and breadth are reduced to $\frac{1}{3}$ rd of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomes
A) $\frac{4 \mathrm{E}}{9}$
B) $\frac{7 E}{9}$
C) $\frac{10 \mathrm{E}}{9}$
D) $\frac{16 \mathrm{E}}{9}$

Answer is (D)
$\mathrm{E}=\mathrm{e} \sigma \cdot \mathrm{A}\left(\mathrm{T}^{4}-\mathrm{T}_{0}^{4}\right) \text { and } \mathrm{A}=\ell \mathrm{b}$
When $\ell$ and $b$ changes to $\frac{\ell}{3}$ is and $\frac{b}{3}$
$\begin{array}{l} A \rightarrow \frac{A}{9} \\ \frac{E^{\prime}}{E}=\frac{A^{\prime}}{A} \frac{(327+373)^{4}}{(27+273)^{4}} \\ \therefore \frac{E^{\prime}}{E}=\frac{1}{9}\left(\frac{600}{300}\right)^{4} \\ \therefore E^{\prime}=\frac{1}{9} \times(2)^{4} \times E \\ E^{\prime}=\frac{16 E}{9} \end{array}$

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