Pressure of an ideal gas
Let us consider a θ - Φ - v - molecule colliding with a perfectly smooth wall of infinite mass (Fig.4.4). Since the collision is elastic, the magnitude of velocity v is the same before and after the collision. The angle of reflection θ is equal to the angle of incidence, and the normal component of velocity is reversed in the collision from vcosθ to - vcosθ. The force exerted by a molecule in a collision is impulsive and of short duration. The change of normal momentum ΔP of a molecule of mass m in a θ - Φ - v collision is given by

(4.15)

The number of θ - Φ - v collisions with an area dA in time dt is, from Eq.(4.8),

(4.16)

The charge is normal momentum due to all θΦv - collision in time dt is

(4.17)

The total charge in momentum in all v - collisions is found by integration as given below

(4.18)