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A black body, at a temperature of $227^{\circ} \mathrm{C}$, radiates heat at a rate of $20 \mathrm{cal} \mathrm{m}^{-2} \mathrm{~s}^{-1}$. When its temperature is raised to $727^{\circ} \mathrm{C}$, the heat radiated by it in cal $\mathrm{m}^{-2} \mathrm{~s}^{-1}$ will be closest to
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The correct answer is:
640 .
The temperature of the black body is
$$
T_1=227^{\circ} \mathrm{C}=500 \mathrm{~K} \text {. }
$$
$\therefore \quad$ Using Stefan's law, the rate of heat radiation per unit area per unit time is
$$
E_1=\sigma T^4 \Rightarrow 20=\sigma(500)^4 \Rightarrow \sigma=\frac{20}{(500)^4} .
$$
Now the temperature of the blackbody is raised to
$$
T_2=727^{\circ} \mathrm{C}=1000 \mathrm{~K}
$$
$\therefore \quad$ Rate of heat radiation per unit area
$$
\begin{aligned}
E_2 & =\sigma T_2^4=\frac{20}{(500)^4} \times(1000)^4 \\
& =20 \times 2^4=320 \mathrm{cal} \mathrm{m}^{-2} \mathrm{~s}^{-1} .
\end{aligned}
$$
$$
T_1=227^{\circ} \mathrm{C}=500 \mathrm{~K} \text {. }
$$
$\therefore \quad$ Using Stefan's law, the rate of heat radiation per unit area per unit time is
$$
E_1=\sigma T^4 \Rightarrow 20=\sigma(500)^4 \Rightarrow \sigma=\frac{20}{(500)^4} .
$$
Now the temperature of the blackbody is raised to
$$
T_2=727^{\circ} \mathrm{C}=1000 \mathrm{~K}
$$
$\therefore \quad$ Rate of heat radiation per unit area
$$
\begin{aligned}
E_2 & =\sigma T_2^4=\frac{20}{(500)^4} \times(1000)^4 \\
& =20 \times 2^4=320 \mathrm{cal} \mathrm{m}^{-2} \mathrm{~s}^{-1} .
\end{aligned}
$$
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