Answer to Question #229472 in Molecular Physics | Thermodynamics for Sridhar

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

$E=\sigma AT^4$

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

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

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

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