Kinetic Theroy Of Gases

Card # 42 Kinetic theory of Gases: Kinetic theory of gases is a theory which explains the physical properties of gases such as pressure, temperature, elasticity, diffusion, expansion etc. This theory was developed by Clausius and Maxwell. This theory explains the physical properties of gases in terms of the motion of its molecules. Assumptions 1. Every gas is composed of minute particles called molecules. 2. The volume of the molecules is negligible when compared with the size of the container. 3. The molecules are treated as they are hard sphere. 4. During random motion the molecules make perfectly elastic collisions with each other and with the walls of the container. 5. The molecules do not exert any force of repulsion or attraction on each other expect during collisions. 6. Between two collisions the molecules move in a straight line at constant speed. 7. Molecules obey Newton’s law of motion. Pressure exerted by a Gas According to Kinetic theory of gases the molecules of a gas are in a state of continuous random motion. During their random motion, they collide with the walls of the container and in each collision they impart a certain momentum to the wall. Pressure of a gas depends on this momentum. Pressure of gas P = P= (1/3) ρ V

mNV 2 3V

2

d e n s ity =

M ass (ρ=M/V) V o lu m e

M = m N or Mass of gas = mass of one molecule x number of molecules 2

P= (2/3) (ρ V )/2 P=

2 2 x mean kinetic energy per unit volume E = 3 3

V 2 = mean square velocity o the molecules V12 + V2 2 + .... + Vn 2 2 V = N The average or mean K.E. of a Gas molecule is given by

1 mV 2

2

=

3 kT 2

Here k = Boltzmann’s constant = 1.38 x 10 −23 Jk −1