Compare the rate of loss of heat from a metal sphere at \(627^{\circ} \mathrm{C}\) with the rate of loss of heat from the same sphere at \(327^{\circ} \mathrm{C}\), if the temperature of the surrounding is \(27^{\circ} \mathrm{C}\). (nearly)

The heat loss is given as \(\mathrm{R}=\mathrm{e} \sigma \mathrm{A}\left(\mathrm{T}^4-\mathrm{T}_0^4\right)\)
Let surrounding temperature be denoted as \(\mathrm{T}\) Heat loss from the metal sphere at a temperature \(\mathrm{T}_1\)
\(\mathrm{R}_1=\operatorname{e} \sigma \mathrm{A}\left(\mathrm{T}_1^4-\mathrm{T}_0^4\right)\)
Heat loss from the metal sphere at a temperature \(\mathrm{T}_2\)
\(R_2=e \sigma A\left(T_2^4-T^4\right)\)
\(\begin{aligned}\therefore \quad \frac{\mathrm{R}_1}{\mathrm{R}_2} & =\frac{\mathrm{T}_1^4-\mathrm{T}^4}{\mathrm{~T}_2^4-\mathrm{T}^4}=\frac{900^4-300^4}{600^4-300^4} \\\frac{\mathrm{R}_1}{\mathrm{R}_2} & =5.3\end{aligned}\)