Question

Two spheres of the same material have radii $1m$ and $4m$ and temperature $4000K$ and $2000K$ respectively. The energy radiated per second by the first sphere is :

• A. greater than that of the second
• B. less than that of the second
• C. equal in both cases
• D. the information is incomplete to draw any conclusion

Answer 1

The correct option is C equal in both cases

By Stefan's Law:

Power $=\sigma Ae{T}^4$

$e$ is same for both the bodies. $\sigma$ is known as Stefan's constant

$\frac{P_1}{P_2}=\frac{A_1{T}_1^4}{A_2{T}_2^4}$

$\frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}=\frac{1}{16}$

$\frac{T_1^4}{T_2^4}=\frac{16}{1}$

By the above equations we get: $P_1=P_2$