Summary Kinetic Theory of Gases

KINETIC THEORY OF GASES
(KTG)
(SHORT NOTES)
 Postulates of KTG:
1. Molecules size negligible
2. Molecules assumed to be hard sphere and all collisions elastic
3. No interaction among molecules =>
total energy = kinetic energy + potential energy =kinetic energy
(as molecules are not in rest therefore potential energy =zero so total
energy= kinetic energy
4. Collision time is negligible
5. Effect of gravity on molecule is neglected
6. Real gases obeys ideal gas law: PV=nRT, at very high temperature and very
low pressure only

 Boyel’s law : temperature constant (isothermal), so pressure inversely proportional to
volume
 Charle’s law: pressure constant (isobaric), so volume directly proportional to
temperature
 Gay lussac law: constant volume (isochoric), so pressure directly proportional to
temperature
 Dalton’s law: pressure exerted by a mixture of non interacting gases is equal to the sum
of their partial pressure hence for a mixture of n gases the total pressure of gas is :
P= P1+P2+P3+….+Pn


N
 PV = nRT or PV = RT (N: no. of gas molecules, Na: Avogadro’s constant) or
Na
m
PV = RT (m: mass of gas, Mwt: molecular weight of gas) or
Mwt
PV = NKT(N: no. of gas molecules, K: Boltzman’s constant or
ρRT
P= (ρ: density)
Mwt

1 2 1mN 2
 Average pressure exerted by gas: P = ρ(Vrms ) = (Vrms)
3 3V
(Vrms: root mean square velocity, m:g given mass, N: no. of molecules)

 Maxwell’s Distribution of Velocity:
2 RT
1. Vmp = √ (Vmp: most probable velocity in m/s, T: temperature in Kelvin, M:
M
molecular weight in KG)
8 RT
2. Vav = √ ( take units same as above, Vav: average velocity)
πm