First slide

Radiation

Question

Two metallic spheres S₁ and S₂ are made of the same material and have got identical surface finish. The mass of S₁ is thrice that of S₂. Both the spheres are heated to the same high temperature and placed in the same room having lower temperature but are thermally insulated from each other. The ratio of initial rate of cooling of S₁ to that of S₂ is

Moderate

A

$\frac{1}{3}$
B

$\frac{1}{\sqrt{3}}$
C

$\frac{\sqrt{3}}{1}$
D

${(1 / 3)}^{\frac{1}{3}}$

Solution

$mc (dθ / dt) = {σT}^{4} (4 {πr}^{2})$
or $(dθ / dt) \propto (r^{2} / m) . . . (1)$
Further, $m = (4 / 3) {πr}^{3} or r \propto m^{1 / 3} . . . (2)$
From eqs. (1) and (2), $(dθ / dt) \propto (1 / m^{1 / 3})$
$∴ \frac{(dθ / dt)_{1}}{(dθ / dt)_{2}} = {(\frac{m_{2}}{m_{1}})}^{1 / 3} = {(\frac{1}{3})}^{1 / 3}$

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