Physics - Heat & Thermo Question with Solution | TestHub

According to the Stefan-Boltzmann law, the total power radiated by a black body is given by $P=\sigma A{T}^4$, where $A$ is the surface area and $T$ is the absolute temperature. The surface area of a sphere is $A=4\pi R^2$. For $S_1$, $P_1=\sigma (4\pi R^2)T^4$. For $S_2$, $P_2=\sigma (4\pi (2R{)}^2)T^4=\sigma (4\pi 4R^2)T^4=4\sigma (4\pi R^2)T^4$. Therefore, the ratio $\frac{P_1}{P_2}=\frac{\sigma (4\pi R^2)T^4}{4\sigma (4\pi R^2)T^4}=\frac{1}{4}$. The ratio is $1:4$.