Question

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

• A. $\frac{4E}{9}$
• B. $\frac{7E}{9}$
• C. $\frac{10E}{9}$
• D. $\frac{16E}{9}$

Answer 1

Answer: (D)

$E=e\sigma .A\left(T^4-T_0^4\right)andA=lb$
When $l$ and b changes to $\frac{l}{3}$ and $\frac{b}{3}$
$A\to \frac{A}{9}$
$\frac{E^{\prime }}{E}=\frac{A^{\prime }}{A}\frac{{\left(327+273\right)}^4}{{\left(27+273\right)}^4}$
$\therefore \frac{E^{\prime }}{E}=\frac{1}{9}{\left(\frac{600}{300}\right)}^4$
$\therefore E^{\prime }=\frac{1}{9}\times {\left(2\right)}^4\times E$
$E^{\prime }=\frac{16E}{9}$