Question

Assume a sample of an ideal gas in a vessel. The velocities of molecules in the sample are between $2m/s$ to $5m/s$. If the velocity of molecules $(v)$ and the number of molecules $(n)$ are related as $n=7v-v^2-10$, then the most probable velocity (in $m/s$ ) in the sample is
(Here $v$ is measured in $m/s$ ).

Answer 1

Answer: 3.50

$n=7v-v^2-10$
For most probable velocity, $\frac{dn}{dv}=0$
( $\because n$ is maximum at this velocity.)
$7-2v=0$
$\Rightarrow v=\frac{7}{2}=3.5m/s$