Gas Molecule Collisions


In proving PV = (1/3)Nmc*2 from kinetic model, where P is the pressure, V is the total volume of container, N is total mole of gas, m is mass and c is the speed, we say that momentum just before impact of a gas particle at the container wall is mu, and momentum just after is -mu, thus change in momentum is 2mu. It is assumed that all collisions between gas molecules and wall are completely elestic.

It seems that in this case, the energy is conserved but momentum is not. Is this correct? If it is really the case, then it is completely different from the cases we learnt about collisions in the part of Mechanics, where we only learnt about collisions with momentum conserved while energy can be increases, decreased or the same. So what makes gas particles collide differently from the objects we studied in Mechanics? Is there any other 'special' particles collide like gas particles?


The elastic collisions between gas molecules and the walls of their container are exactly the same as the collisions we dealt with in mechanics. The total momentum is conserved. You were looking only at the change in momentum of the molecule. The wall of the container also suffered a change in momentum, equal to and opposite that of the molecule. The reason the container does not get a velocity as a result of the collision with the molecule is that over on the other side of the container another molecule was being hit by a nearby molecule at the same time. The chances of it happening this way are about 100%. Remember how many molecules there are in a mole.

With each collision if we divide the change in momentum of the molecule by the duration of the collision (remember impulse) we get the force felt by the container. The sum of these collision impulses over all the molecules hitting the container walls is the total force on the container. Divided by the area of the container surface it is the pressure. If the collisions are the result of a sudden release of energy, as in an explosion, the force on the inside of the container may exceed its strength and blow it apart. If momentum were not conserved we would not see this phenomena.