The root mean square velocity of the molecules of a gas is 1260 m / s. The average speed of the molecules is

Question

The root mean square velocity of the molecules of a gas is 1260 m / s. The average speed of the molecules is (A) 1029 m s -1 (B) 1161 m s -1 (C) 1671 m s -1 (D) 917 m s -1

Tardigrade Admin · Accepted Answer

v av =√(8 k T/m π), v rms =√(3 k T/m) ∴ (v av /v rms ) =(√8 / π/√3) or (v av /1260)=√(8/3 π) ∴ v av =1260 × √(8/3 π)=1161 m s -1

Q. The root mean square velocity of the molecules of a gas is $1260 m / s$ . The average speed of the molecules is

$1029 m s^{- 1}$

$1161 m s^{- 1}$

$1671 m s^{- 1}$

$917 m s^{- 1}$

$v_{a v} = \frac{8 k T}{mπ},$
$v_{r m s} = \frac{3 k T}{m}$
$∴ \frac{v _{a v}}{v _{r m s}} = \frac{8/ π}{3}$
or $\frac{v _{a v}}{1260} = \frac{8}{3 π}$
$∴ v_{a v} = 1260 \times \frac{8}{3 π} = 1161 m s^{- 1}$

Q. The root mean square velocity of the molecules of a gas is 1260m/s. The average speed of the molecules is

1029ms−1

1161ms−1

1671ms−1

917ms−1