Question

Two spheres of same material and radii 5m and 2m are at temperature 200K and 2500K respectively.The ratio of energies radiated by them per second is

Answer 1

Gives

$r_1=5m\\r_2=2m\\T_1=200K\\T_2=2500K$

We know that stefan's law

$E=\sigma AT^4$

$\frac{E_1}{E_2}=\frac{A_1T_1^4}{A_2T_2^4}$

$\frac{E_1}{E_2}=\frac{r_1^2T_1^4}{r_2T_2^4}$

$\frac{r_1}{r_2}=\frac{5}{2}$

$\frac{E_1}{E_2}=\frac{25}{4}\times(\frac{200}{2500})^4=\frac{4}{15625}$