Q146 / 150 · MHT CET 2021 (21 Sep Shift 1) · Physics

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

  • Correct answer
    A
    $\frac{16 \mathrm{E}}{9}$
  • B
    $\frac{8 \mathrm{E}}{9}$
  • C
    $\frac{4 \mathrm{E}}{9}$
  • D
    $\frac{E}{9}$

Solution

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

Hence, the correct answer is option: 'A'.

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