A black body at $227^{\circ} \mathrm{C}$ radiates heat at the rate of $7 \mathrm{cal} \mathrm{cm}^{-2} \mathrm{~s}^{-1}$. At a temperature of $727^{\circ} \mathrm{C}$, the rate of heat radiated in the same units will be

Question

Aicharya · Accepted Answer

Key Idea Apply Stefan's law of radiation. $\begin{aligned} \mathrm{E} & =\sigma \mathrm{T}^4 \ \frac{\mathrm{E}_1}{\mathrm{E}_2} & =\left[\frac{\mathrm{T}_1}{\mathrm{~T}_2}ight]^4 \ \Rightarrow \quad \mathrm{E}_2 & =7\left[\frac{273+727}{273+227}ight]^4 \ & =\left(\frac{1000}{500}ight)^4 	imes 7 \ & =112 \mathrm{cal}-\mathrm{cm}^{-2} \mathrm{~s}^{-1} \end{aligned}$ .

A black body at $227^{\circ} \mathrm{C}$ radiates heat at the rate of $7 \mathrm{cal} \mathrm{cm}^{-2}…

Solution