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.
PRESSURE EXERTED BY A GAS . . Expression for pressure exerted by a gas Consider a monoatomic gas of N molecules each having a mass m inside a cubical container of side l as shown in the Figure . (a).
Gas molecule Container Figure . (a) Container of gas molecules Figure . (b) Collision of a molecule with the wall v x v x v x v y v y - d d d x y z x A molecule is moving with velocity towards the wall. Te molecule’s x component of velocity is reversed, whereas its y component remains unchanged.
- - - - Unit Kinetic theory of gases Not all the n molecules will move to the right, therefore on an average only half of the n molecules move to the right and the other half moves towards left side. The number of molecules that hit the right side wall in a time interval ∆ t = n Av x ∆ t ( . ) In the same interval of time ∆ t , the total momentum transferred by the molecules ∆ p = n Av x ∆ t × mv x = Av x mn ∆ t ( . ) From Newton’s second law, the change in momentum in a small interval of time gives rise to force.
The force exerted by the molecules on the wall (in magnitude)