KINETIC THEORY OF GASES

“With thermodynamics one can calculate almost everything crudely; with kinetic theory, one can calculate fewer things, but more accurately.” - Eugene Wigner . . Postulates of kinetic theory of gases Kinetic theory is based on certain assumptions which makes the mathematical treatment simple. None of these assumptions are strictly true yet the model based on these assumptions can be applied to all gases.

. All the molecules of a gas are identical, elastic spheres. . The molecules of different gases are different.

. The number of molecules in a gas is very large and the average separation between them is larger than size of the gas molecules. . The molecules of a gas are in a state of continuous random motion.

. The molecules collide with one another and also with the walls of the container. Unit Kinetic theory of gases . The molecules of the gas are in random motion.

They collide with each other and also with the walls of the container. As the collisions are elastic in nature, there is no loss of kinetic energy, but a change in momentum occurs. The molecules of the gas exert pressure on the walls of the container due to collision on it. During each collision, the molecules impart certain momentum to the wall.

Due to transfer of momentum, the walls experience a continuous force. The force experienced per unit area of the walls of the container determines the pressure exerted by the gas. It is essential to determine the total momentum transferred by the molecules in a short interval of time. A molecule of mass m moving with a velocity v  having components ( v x , v y , v z ) hits the right side wall.

Since we have assumed that the collision is elastic, the particle rebounds with same speed and its x-component is reversed. This is shown in the Figure . (b). The components of velocity of the molecule after collision are (— v x , v y , v z ).

The x-component of momentum of the molecule before collision = mv x . These collisions are perfectly elastic so that there is no loss of kinetic energy during collisions. . Between two successive collisions, a molecule moves with uniform velocity.

. The molecules do not exert any force of attraction or repulsion on each other except during collision. The molecules do not possess any potential energy and the energy is wholly kinetic. .

The collisions are instantaneous. The time spent by a molecule in each collision is very small compared to the time elapsed between two consecutive collisions. . These molecules obey Newton’s laws of motion even though they move randomly.