Question

The ratio of radii of spheres of metal is $1:2$. The ratio of the amounts of radiation emitted by them at same temperature will be :

• A. $1:4$
• B. $1:8$
• C. $2:1$
• D. $8:1$

Answer 1

The correct option is A $1:4$

By Stefan-Boltzmann law total power radiated from sphere is
$P=A\sigma \epsilon T^4$
where $A$ is area of the sphere, $\sigma$ is Stefan-Boltzmann's constant, $\epsilon$ is emissivity and T is temperature
At the same temperature if the ratio of radii of spheres of metal is 1:2
then
$\frac{P}{A}=constant\frac{P_1}{A_1}=\frac{P_2}{A_2}\frac{P_1}{P_2}=\frac{A_1}{A_2}=\frac{4\pi r_1^2}{4\pi r_2^2}={\left(\frac{r_1}{r_2}\right)}^2{P}_1:P_2=1:4$
option (A) is the correct answer