Let vrms, vmp and vavg represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, (vrms)2: (vmp)2: (vavg)2 is

Question

Let vrms, vmp and vavg represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, (vrms)2: (vmp)2: (vavg)2 is (A) 8: 3π: 2π (B) 8: 2π: 3π (C) 3π: 2π: 8  (D)  3: 2: 8

Tardigrade Admin · Accepted Answer

∵ : : vrms = √(3RT/M) , vmp = √(2RT/M) and vavg = √(8RT/ π M) ∴ : :: (vrms)2: (vmp)2: (vavg)2 = (3RT/M): (2RT/M): (8RT/π M) = 3 π: 2 π: 8

Q. Let $v_{r m s}, v_{m p}$ and $v_{a vg}$ represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, $(v_{r m s})^{2} : (v_{m p})^{2} : (v_{a vg})^{2}$ is

$8 : 3 π : 2 π$

$8 : 2 π : 3 π$

$3 π : 2 π : 8$

$3 : 2 : 8$

$∵ v_{r m s} = \frac{3 RT}{M}, v_{m p} = \frac{2 RT}{M}$ and $v_{a vg} = \frac{8 RT}{π M}$
$∴ (v_{r m s})^{2} : (v_{m p})^{2} : (v_{a vg})^{2} = \frac{3 RT}{M} : \frac{2 RT}{M} : \frac{8 RT}{π M}$
= $3 π : 2 π : 8$

Q. Let vrms​,vmp​ and vavg​ represent the root mean square, the most probable and the average velocities respectively, in case of a gaseous system in equilibrium at certain temperature. Then, (vrms​)2:(vmp​)2:(vavg​)2 is

8:3π:2π

8:2π:3π

3π:2π:8

3:2:8