Q. The rate of cooling at $600 \,K$, if surrounding temperature is $300\, K$ is $R$. The rate of cooling at $900\, K$ is

Kinetic Theory Report Error

A

$\frac{16}{3} R$

B

$2 R$

C

$3 R$

D

$\frac{2}{3} R$

Solution:

Rate of cooling proportional to $\left(T^{4}-T_{0}^{4}\right)$, as per Stefan's Law.
$\therefore \frac{R^{\prime}}{R}=\frac{(900)^{4}-(300)^{4}}{(600)^{4}-(300)^{4}} $
$=\frac{9^{4}-3^{4}}{6^{4}-3^{4}}=\frac{3^{4}\left(3^{4}-1\right)}{3^{4}\left(2^{4}-1\right)}$
$=\frac{80}{15}=\frac{16}{3} $
$R^{\prime}=\frac{16}{3} R$

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