Question

In an ideal gas at temperature $T$ , the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^{q}$ . A good estimate for $q$ is

Answer 1

Pressure exerted by molecules of a gas on the walls $p=\frac{1}{3}nmc^{2}$
$\therefore p \propto c^{2}$
But $c \propto \sqrt{T}$ and $c^{2} \propto T$
$\therefore \, P \propto T$
$\because \, \, \, $ Force $=P\times A$
$\therefore \, F \propto T^{1}$
$q=1$