A black rectangular surface of area ' $a$ ' emits energy ' $E$ ' per second at $27^{\circ} \mathrm{C}$. If…

A black rectangular surface of area ' $a$ ' emits energy ' $E$ ' per second at $27^{\circ} \mathrm{C}$. If length and breadth is reduced to $\left(\frac{1}{3}\right)^{\text {rd }}$ of initial value and temperature is raised to $327^{\circ} \mathrm{C}$ then energy emitted per second becomes
  1. $\frac{16 \mathrm{E}}{9}$
  2. $\frac{8 \mathrm{E}}{9}$
  3. $\frac{4 \mathrm{E}}{9}$
  4. $\frac{E}{9}$

Solution

$\mathrm{E}=\mathrm{e} \sigma \mathrm{AT}^4 \text { and } \mathrm{A}=\ell \mathrm{b}$ $\frac{E^{\prime}}{E}=\frac{A^{\prime}(327+273)^4}{A(27+273)^4}$ $\frac{E^{\prime}}{E}=\frac{1}{9}\left(\frac{600}{300}\right)^4$ $\begin{aligned} & \therefore \mathrm{E}^{\prime}=\frac{1}{9} \times(2)^4 \times \mathrm{E} \\ & \Rightarrow \mathrm{E}^{\prime}=\frac{16 \mathrm{E}}{9} \end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 1)

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