Question

Two spheres made of same material have radii in the ratio 2 : 1. If both the spheres are at same temperature, then what is the ratio of heat radiation energy emitted per second by them?

• A. 1 : 4
• B. 4 : 1
• C. 3 : 4
• D. 4 : 3

Answer 1

The correct option is B 4 : 1

Radiation emitted per second depends on the temperature of the body.
Stefan's law states that the rate of emission of radiant energy by unit area of perfectly black body is directly proportional to the fourth power of its absolute temperature.
$E\propto A{T}^4$
or $E\propto r^2$
($\because A=\pi r^2$ and T is same for both the spheres)
where r is radius of sphere.
$\frac{E_1}{E_2}=\frac{r_1^2}{r_2^2}$
$={\left(\frac{2}{1}\right)}^2=\frac{4}{1}$
$=4:1$
Note : A black body at absolute temperature T surrounded by another black body at absolute temperature $T_0$ not only loses an amount of energy $\sigma T^4$, thus the amount of heat lost by the former per unit time is given by
$E=\sigma (T^4-T_0^4)$
This law is stefan Boltzmann's law.