The root mean square velocity, vrms , the average velocity vav and the most probable velocity,vmp of the molecules of the gas are in the order:

Question

The root mean square velocity, vrms , the average velocity vav and the most probable velocity,vmp of the molecules of the gas are in the order: (A) vmp > vav > vrms (B) vrms > vav > vmp (C) vav > vmp > vrms (D) vmp > vrms > vav

Tardigrade Admin · Accepted Answer

v rms =√(3 kT / m ), v av =√(8 kT / m π) and v mp =√(2 kT / m ) ⇒ v rms: v av: v mp =1: 0.92: 0.816 ∴ v rms > v av > v mp .

Q. The root mean square velocity, $v_{r m s}$ , the average velocity $v_{a v}$ and the most probable velocity, $v_{m p}$ of the molecules of the gas are in the order:

$v_{m p} > v_{a v} > v_{r m s}$

$v_{r m s} > v_{a v} > v_{m p}$

$v_{a v} > v_{m p} > v_{r m s}$

$v_{m p} > v_{r m s} > v_{a v}$

$v_{r m s} = \frac{3 k T}{m}, v_{a v} = \frac{8 k T}{mπ}$ and $v_{m p} = \frac{2 k T}{m}$
$\Rightarrow v_{r m s} : v_{a v} : v_{m p} = 1 : 0.92 : 0.816$
$∴ v_{r m s} > v_{a v} > v_{m p} .$

Q. The root mean square velocity, vrms​ , the average velocity vav​ and the most probable velocity,vmp​ of the molecules of the gas are in the order:

vmp​>vav​>vrms​

vrms​>vav​>vmp​

vav​>vmp​>vrms​

vmp​>vrms​>vav​