Question

Two hot copper spheres of radii in the ratio $2:3$ are kept in an evacuated enclosure. If each sphere is initially at a temperature $10$${}^o$C above that of the enclosure, the rates of loss of heat of the spheres will be in the ratio of

• A. 4 : 9
• B. 9 : 4
• C. 2 : 3
• D. 3 : 2

Answer 1

Answer: (A)

4 : 9

We know that radiation from the surface is given as:
$E=ϵ\sigma A{T}^4$
$E\propto r^2$
$\frac{E_1}{E_2}=\frac{r_1^2}{r_2^2}$
$\frac{E_1}{E_2}=\frac{4}{9}$