The root mean square velocity of the molecules of a gas is 1260 m s-1. The average speed of the molecules is

Question

The root mean square velocity of the molecules of a gas is 1260 m s-1. 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

upsilonav = √(8kT/mπ), upsilonrms = √(3kT/m ) ∴ ( upsilon av / upsilon rms) = (√8/π/√3) or ( upsilon av/1260) = √(8/3π ) ∴ upsilon av = 1260× √(8/3π ) = 1161 m s-1

Q. The root mean square velocity of the molecules of a gas is $1260 m s^{- 1}$ . The average speed of the molecules is

$1029 m s^{- 1}$

$1161 m s^{- 1}$

$1671 m s^{- 1}$

$917 m s^{- 1}$

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

Q. The root mean square velocity of the molecules of a gas is 1260ms−1. The average speed of the molecules is

1029ms−1

1161ms−1

1671ms−1

917ms−1