F = ∆ ∆ p t = nmAv x ( . ) Pressure, P = force divided by the area of the wall P = F A = nmv x ( . ) Since all the molecules are moving completely in random manner, they do not have same speed. So we can replace the term v x by the average v x in equation ( .
) The x-component of momentum of the molecule after collision = −m v x The change in momentum of the molecule in x direction =Final momentum – initial momentum = − mv x − mv x = − mv x According to law of conservation of linear momentum, the change in momentum of the wall = mv x In x direction, the total momentum of the system before collision is equal to momentum of the molecule ( mv x ) since the momentum of the wall is zero. According to the law of conservation of momentum the total momentum of system after the collision must be equal to total momentum of system before collision. The momentum of the molecule (in x direction) after the collision is − mv x and the momentum of the wall after the collision is mv x . So total momentum of the system after the collision is ( mv x − mv x ) = mv x which is same as the total momentum of the system before collision.
Note The number of molecules hitting the right side wall in a small interval of time ∆ t is calculated as follows. The molecules within the distance of v x ∆ t from the right side wall and moving towards the right will hit the wall in the time interval ∆ t. This is shown in the Figure . .
The number of molecules that will hit the right side wall in a time interval ∆ t is equal to the product of volume ( Av x ∆ t ) and number density of the molecules ( n ). Here A is area of the wall and n is