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Two spheres ' $\mathrm{S}_{1}$ ' and ' $\mathrm{S}_{2}$ ' have same radii but temperatures $\mathrm{T}_{1}$ and $\mathrm{T}_{2}$ respectively.
Their emissive power is same and emissivity is in the ratio $1: 4$. Then the ratio of $\mathrm{T}_{1}$
to $\mathrm{T}_{2}$ is
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Their emissive power is same and emissivity is in the ratio $1: 4$. Then the ratio of $\mathrm{T}_{1}$
to $\mathrm{T}_{2}$ is
Solution:
2940 Upvotes
Verified Answer
The correct answer is:
$\sqrt{2}: 1$
Emissive power $P=\sigma \mathrm{e} T^{4}$
$$
\begin{array}{l}
\therefore \sigma e_{1} T_{1}^{4}=\sigma e_{2} T_{2}^{4} \\
\frac{T_{1}^{4}}{T_{2}^{4}}=\frac{e_{2}}{e_{1}}=4 \\
\therefore \frac{T_{1}}{T_{2}}=\sqrt{2}
\end{array}
$$
$$
\begin{array}{l}
\therefore \sigma e_{1} T_{1}^{4}=\sigma e_{2} T_{2}^{4} \\
\frac{T_{1}^{4}}{T_{2}^{4}}=\frac{e_{2}}{e_{1}}=4 \\
\therefore \frac{T_{1}}{T_{2}}=\sqrt{2}
\end{array}
$$
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