If the absolute temperature of a black- body is double what would… - Vidyadip

Question

If the absolute temperature of a black- body is double what would be its effect on emitted energy?

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Answer

From Stefan's law the rate of emitted radiation energy
$\begin{aligned}& E=\sigma T^4 \\& E^1=\sigma(2 T)^4 \\\therefore \quad & \frac{E^1}{E}=\frac{\sigma(2 T)^4}{\sigma(T)^4}=\frac{16}{1} \\\Rightarrow \quad & E^1=16 E\end{aligned}$
i.e. the rate of emitted radiation energy would remain 16th times of the inittal rate.

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