Physics - Heat & Thermo Question with Solution | TestHub

The total radiant power (P) of a black body is given by Stefan-Boltzmann Law: $P=\sigma A{T}^4$, where A is the surface area and T is the absolute temperature. For a sphere, $A=4\pi R^2$. So, $P=\sigma (4\pi R^2)T^4$. The ratio of powers will be:$$\frac{P_A}{P_B}=\frac{\sigma (4\pi R_A^2)T_A^4}{\sigma (4\pi R_B^2)T_B^4}={\left(\frac{R_A}{R_B}\right)}^2{\left(\frac{T_A}{T_B}\right)}^4$$ Given$\frac{R_A}{R_B}=\frac{1}{2}$ and $\frac{T_A}{T_B}=\frac{2}{1}$.$$\frac{P_A}{P_B}={\left(\frac{1}{2}\right)}^2{\left(\frac{2}{1}\right)}^4=\frac{1}{4}\times 16=4$$ The ratio of total radiant power of body A to body B is 4:1, so the answer is 4.