Gas

Card # 43 Mean velocity of gas molecules It is defined as the arithmetic mean of the velocities of the gas molecules. If V1 ,V2 , V3,V4 ......VN are the velocities of N gas molecules then Mean velocity of gas molecules V =

V=

V1 + V2 + .... + Vn N

8kT πm

Root mean square velocity of gas molecules

V2 =

V12 + V2 2 + .... + Vn 2 N

Vrms = V 2 =

V12 + V2 2 + .... + Vn 2 N

It is defined as the square root of the mean of the square of the velocities of the gas molecules

1 mV 2

2

=

Vrms = V 2 =

Vrms ==

3 kT 2

3kT 3nkT = m m

3RT m

Most probable velocity of gas molecules The velocity which is possible by maximum number of molecules in a gas sample is called most probable velocity

Vmp ==

2kT m

It is clear Vmp : V : Vrms ==

2kT 8kT 3kT : : πm m m

Mean free path It is the average distance a molecule travels between collisions. Between two collisions molecule moves in a straight line path. The greater the gas density and larger the molecule the shorter the mean free path would be. Expression for mean free path ( λ ) is

λ=

1 Here n= number of molecules per unit volume in the gas 4π 2r 2 n

r = radius of molecule