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

Answer: 1

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