The Mechanics of Molecular Collisions

Let us first consider the mechanics of collisions between an average molecule of species 1 and an average molecule of species 2. The molecule of species 1 has velocity and the molecule of species 2 has velocity M2. 

The momentum of these two average molecules is and mi2M2 where and m2 are the masses of the respective molecules. The total momentum of the pair of molecules is m Mi + m2M2. This total momentum of the pair of molecules is conserved on collision. That is, if m i and u 2 represent the velocities after collision, then the law of conservation of momentum requires that 

The momemtum transferred from species 1 to species 2 is the left-hand member of Eq. 2.1.1 

Momentum transferred from a molecule of 1 to a molecule of 2 through collision 

Our next task is to calculate the average velocity after collision u. This calculation requires us to make some statement about the type of collision undergone by the two molecules. In an inelastic collision two bodies collide and stick together. Momentum is conserved in this collision but the kinetic energy of the bodies is not usually conserved. In an elastic collision the two bodies collide and then move apart again. Momentum must be conserved in this type of collision also but the important difference between an inelastic 13 

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