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

\(\mathrm{E}=\sigma \mathrm{AT}^{4}\)
\(\therefore \frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}=\frac{\mathrm{A}_{2}}{\mathrm{~A}_{1}} \cdot\left(\frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}\right)^{4}\)
\(\mathrm{~A}_{2}=\frac{\mathrm{A}_{1}}{9} \quad \therefore \frac{\mathrm{A}_{2}}{\mathrm{~A}_{1}}=\frac{1}{9}\)
\(\mathrm{~T}_{1}=27+273=300 \mathrm{k}\)
\(\mathrm{T}_{2}=327+273=600 \mathrm{k}\)
\(\therefore \frac{\mathrm{T}_{2}}{\mathrm{~T}_{1}}=\frac{600}{300}=2\)
\(\therefore \frac{\mathrm{E}_{2}}{\mathrm{E}_{1}}=\frac{1}{9} \times(2)^{4}=\frac{16}{9}\)
\(\therefore \mathrm{E}_{2}=\frac{16}{9} \mathrm{E}_{1}=\frac{16}{9} \mathrm{E}\)