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A black body at a temperature $T$ radiates energy at the rate of $E \mathrm{Wm}^{-2}$. If the temperature is decreased by $T / 2$, then the energy radiated will be
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The correct answer is:
$E / 16$
According to Stefan's law, Energy radiated $E \propto T^{4}$
$$
\begin{array}{ll}
\therefore & \frac{E^{\prime}}{E}=\frac{T^{\prime}}{T}=\frac{\left(\frac{T}{2}\right)^{4}}{T^{4}}=\frac{1}{2^{4}}=\frac{1}{16} \\
\text { or } & E^{\prime}=\frac{E}{16}
\end{array}
$$
$$
\begin{array}{ll}
\therefore & \frac{E^{\prime}}{E}=\frac{T^{\prime}}{T}=\frac{\left(\frac{T}{2}\right)^{4}}{T^{4}}=\frac{1}{2^{4}}=\frac{1}{16} \\
\text { or } & E^{\prime}=\frac{E}{16}
\end{array}
$$
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