Question

The rectangular surface of area $8cm\times 4cm$ of a black body at a temperature of ${127}^{\circ }C$ emits energy at the rate of $E$ per second. If the length and breadth of the surface are each reduced to half of the initial value and the temperature is raised to ${327}^{\circ }C$, the rate of emission of energy will become

• A. $\frac{3}{8}E$
• B. $\frac{81}{16}E$
• C. $\frac{9}{16}E$
• D. $\frac{81}{64}E$

Answer 1

The correct option is D $\frac{81}{64}E$

Stefan's law states, $power\propto area\times temperatur{e}^4$

Let final power be E'.

Then, $\frac{E^{\prime }}{E}=\frac{4\times 2}{8\times 4}(\frac{600}{400}{)}^4=\frac{81}{64}$

$\Rightarrow E^{\prime }=\frac{81}{64}E$