vrms , vav and vmp are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

Question

vrms , vav and vmp are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct? (A) v rms < v av < v mp (B) v rms >v av >v mp (C) v mp < v rms < v av (D) v mp >v rms >v av

Tardigrade Admin · Accepted Answer

Root mean square speed. The root mean square speed is used to measure the velocity of particles in a gas. It is given by

v_{r m s} = \frac{3 RT}{M} = 1.732 \frac{RT}{M}

... (1)
where

M

is molar mass and

R

is gas constant,

T

is temperature.
Most probable speed

v_{p}

, is the speed most likely to be possessed by any molecule in the system.

v_{a v} = \frac{2 RT}{M} = 1.41 \frac{RT}{M}

... (2)
whereas mean speed is

v_{m p} = \frac{8 RT}{π M} = 1.6 \frac{RT}{M}

... (3)
From Eqs. (1), (2) and (3), we conclude that

V_{r m s} > V_{a v} > V_{m p}

Q. $v_{r m s}, v_{a v}$ and $v_{m p}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

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

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

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

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

Q. vrms​,vav​ and vmp​ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

vrms​<vav​<vmp​

vrms​>vav​>vmp​

vmp​<vrms​<vav​

vmp​>vrms​>vav​

Q. $v_{r m s}, v_{a v}$ and $v_{m p}$ are root mean square, average and most probable speeds of molecules of a gas obeying Maxwellian velocity distribution. Which of the following statements is correct?

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

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

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

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