1. Tardigrade
  2. Question
  3. Physics
  4. Assume a sample of an ideal gas in a vessel. The velocities of molecules in the sample are between 2 m / s to 5 m / s. If the velocity of molecules (v) and the number of molecules (n) are related as n=7 v-v2-10, then the most probable velocity (in m / s ) in the sample is (Here v is measured in m / s ).

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

Kinetic Theory

Solution:

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