KEY CONCEPTS Kinetic Theory Of Gases 1. Assumption of kinetic theory of gases (1) (2) (3) (4) (5) (6)
A gas consist of particles called molecules which move randomly in all directions. These molecules obey Newton’s law of motion. Size of molecule negligible in comparison to average separation between the molecules. The forces on molecule are negligible except at the time of collision. All collision between molecules or between molecules and wall are pefectly elastic. Time of collision is very small. For large number of molecules the density and distribution of molecules with different velocities are independent of position, direction and time.
2. Pressure of an ideal gas
P=
1 1 ρ v 2 = ρ v 2 rms 3 3
Here
v
= mean square speed
vrms = root mean square speed ρ = density of gas P=
2 1 2 ( ρv ) 3 2 rms
P=
2 E 3
E=
3 P 2
3 PV 2 3. R.M.S. velocity – depends on tempearture only for any gas. So total K.E.
Vrms =
P=
K=
v12 + v 22 + v32 +..........+ v 2n n
1 2 ρv rms 3
vrms =
3P ρ
=
3RT M
4. Most Probable velocity – velocity which maximum number of molecules may have
vmp =
2 RT M
5. Average velocity
vavg =
v1 + v 2 + ......... + vn . =0 n
2