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If a black body emits $0.5 \mathrm{~J}$ of energy per second when it is at $27^{\circ} \mathrm{C}$, then the amount of energy emitted by it when it is at $627^{\circ} \mathrm{C}$ will be
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Verified Answer
The correct answer is:
$40.5 \mathrm{~J}$
Given, $\begin{aligned} T_{1} &=27^{\circ} \mathrm{C}=(273+27) \mathrm{K}=300 \mathrm{~K} \\ T_{2} &=627^{\circ} \mathrm{C} \\ &=(627+273) \mathrm{K} \\ &=900 \mathrm{~K} \end{aligned}$
Energy emitted per second
$$
\begin{aligned}
&E_{1}=0.5 \mathrm{~J} \\
&E_{2}=?
\end{aligned}
$$
According to Stefan's Boltzmann law,
Energy radiated per unit area per second is given by
$$
\begin{aligned}
E &=\sigma T^{4} \\
\Rightarrow \quad \frac{E_{2}}{E_{1}} &=\left(\frac{T_{2}}{T_{1}}\right)^{4} \\
&=\left(\frac{900}{300}\right)^{4}=81 \\
\Rightarrow \quad E_{2} &=81 E_{1}=81 \times 0.5 \\
&=405 \mathrm{~J}
\end{aligned}
$$
Energy emitted per second
$$
\begin{aligned}
&E_{1}=0.5 \mathrm{~J} \\
&E_{2}=?
\end{aligned}
$$
According to Stefan's Boltzmann law,
Energy radiated per unit area per second is given by
$$
\begin{aligned}
E &=\sigma T^{4} \\
\Rightarrow \quad \frac{E_{2}}{E_{1}} &=\left(\frac{T_{2}}{T_{1}}\right)^{4} \\
&=\left(\frac{900}{300}\right)^{4}=81 \\
\Rightarrow \quad E_{2} &=81 E_{1}=81 \times 0.5 \\
&=405 \mathrm{~J}
\end{aligned}
$$
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