Two spheres $\mathrm{S}_1$ and $\mathrm{S}_2$ have same radii but temperatures $T_1$ and $T_2$ respectively.…
Two spheres $\mathrm{S}_1$ and $\mathrm{S}_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio $T_1: T_2$ is
$2: 1$
$\sqrt{2}: 1$
$1: \sqrt{2}$
$1: 2$
Solution
Given: $\frac{\mathrm{Q}_1}{\mathrm{~A}_1 \mathrm{t}}=\frac{\mathrm{Q}_2}{\mathrm{~A}_2 \mathrm{t}}$
But $A_1=A_2$ as radii are same
$\begin{array}{ll}
\therefore & \mathrm{Q}_1=\mathrm{Q}_2 \\
\therefore & \mathrm{e}_1 \sigma \mathrm{AT}_1^4=\mathrm{e}_2 \sigma \mathrm{AT}_2^4 \\
\therefore & \frac{\mathrm{~T}_1^4}{\mathrm{~T}_2^4}=\frac{\mathrm{e}_2}{\mathrm{e}_1}=\frac{4}{1} \\
\therefore & \frac{\mathrm{~T}_1}{\mathrm{~T}_2}=\left(\frac{4}{1}\right)^{\frac{1}{4}}=\frac{\sqrt{2}}{1}
\end{array}$