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respectively. If they are coated with a material of same emissivity, rate of radiation of ${ }^{\prime} \mathrm{S}_{1}{ }^{\prime}$ is $\mathrm{E}$ then rate of radiation of $\mathrm{S}_{2}{ }^{\prime}$ is (spheres are of the same material)
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$\frac{E}{9} .$
$\begin{array}{l}
\mathrm{E}=\sigma \times 4 \pi \mathrm{R}^{2} \times \mathrm{T}^{4} \\
\mathrm{E}^{\prime}=\sigma \times 4 \pi(3 \mathrm{R})^{2} \times\left(\frac{\mathrm{T}}{3}\right)^{4} \\
\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\frac{(3)^{2}}{(3)^{4}}=9 \\
\therefore \mathrm{E}^{\prime}=9 \mathrm{E} .
\end{array}$
\mathrm{E}=\sigma \times 4 \pi \mathrm{R}^{2} \times \mathrm{T}^{4} \\
\mathrm{E}^{\prime}=\sigma \times 4 \pi(3 \mathrm{R})^{2} \times\left(\frac{\mathrm{T}}{3}\right)^{4} \\
\therefore \frac{\mathrm{E}^{\prime}}{\mathrm{E}}=\frac{(3)^{2}}{(3)^{4}}=9 \\
\therefore \mathrm{E}^{\prime}=9 \mathrm{E} .
\end{array}$
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