Question 834: Thermodynamics & KTG

Question

A black body at temperature $$127^{\circ} \mathrm{C}$$ radiates heat at the rate of $$5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}$$. At a temperature $$927^{\circ} \mathrm{C}$$, its rate of emission in units of $$\mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$$ will be

Accepted Answer

From Stefan $$-$$ Boltzmann's Law
$$\begin{aligned}
& E=\sigma T^4 \
& \Rightarrow E \propto T^4
\end{aligned}$$
$$\begin{aligned}
	herefore \quad \frac{\mathrm{E}_1}{\mathrm{E}_2} & =\left(\frac{\mathrm{T}_1}{\mathrm{~T}_2}ight)^4=\left(\frac{400}{1200}ight)^4 \
\frac{\mathrm{E}_1}{\mathrm{E}_2} & =\frac{1}{81} \
\mathrm{E}_2 & =81 	imes \mathrm{E}_1 \
& =81 	imes 5 \
& =405 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}
\end{aligned}$$

Answer

405

Answer

35

Answer

45

Answer

350

Thermodynamics & KTG

A black body at temperature $127^{\circ} \mathrm{C} radiates heat at the rate of 5 \mathrm{~cal} / \mathrm{cm}^2 \mathrm{~s}. At a temperature 927^{\circ} \mathrm{C}, its rate of emission in units of \mathrm{cal} / \mathrm{cm}^2 \mathrm{~s}$ will be

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