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A very small hole in an electric furnace is used for heating metals. The hole nearly acts as a black body. The area of the hole is $200 \mathrm{~mm}^2$. To keep a metal at $727^{\circ} \mathrm{C}$, heat energy flowing through this hole per sec, in joules is $\left(\sigma=5.67 \times 10^{-8} \mathrm{Wm}^{-2} \mathrm{~K}^{-4}\right)$
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Verified Answer
The correct answer is:
$11.34$
By Stefan's law
If the absolute temperature of a black body is $T$, then the energy $E$ emitted per second per unit surface area of the body
$$
\begin{aligned}
& E \propto T^4 \\
& E=\sigma \cdot A T^4
\end{aligned}
$$
Given,
$$
\begin{aligned}
\sigma & =5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4 \\
T & =727+273=1000 \mathrm{~K} \\
A & =200 \times 10^{-6} \mathrm{~m} \\
E & =5.67 \times 10^{-8} \times\left(200 \times 10^{-6}\right) \times(1000)^4 \\
& =5.67 \times 2 \times 10^{-12} \times 10^{12} \\
& =11.34 \mathrm{~J} / \mathrm{s}
\end{aligned}
$$
If the absolute temperature of a black body is $T$, then the energy $E$ emitted per second per unit surface area of the body
$$
\begin{aligned}
& E \propto T^4 \\
& E=\sigma \cdot A T^4
\end{aligned}
$$
Given,
$$
\begin{aligned}
\sigma & =5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^2 \mathrm{~K}^4 \\
T & =727+273=1000 \mathrm{~K} \\
A & =200 \times 10^{-6} \mathrm{~m} \\
E & =5.67 \times 10^{-8} \times\left(200 \times 10^{-6}\right) \times(1000)^4 \\
& =5.67 \times 2 \times 10^{-12} \times 10^{12} \\
& =11.34 \mathrm{~J} / \mathrm{s}
\end{aligned}
$$
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