Peoples Physics Book Version-3

19.2. Molecular Kinetic Theory of a Monatomic Ideal Gas http://www.ck12.org

19.2 Molecular Kinetic Theory of a Monatomic Ideal Gas

The empirical combined gas law is simply a generalization of observed relationships. Using kinetic theory, it is
possible to derive it from the principles of Newtonian mechanics. Previously, we thought of an ideal gas as one that
obeys the combined gas law exactly. Within the current model, however, we can give a specific definition.We treat
a monatomic ideal gas as a system of an extremely large number of very small particles in random motion that
collide elastically between themselves and the walls of their container, where there are no interaction between
particles other than collisions.

Consider some amount (natoms) of such a gas in a cubical container with side lengthL. Let’s trace the path of a
single gas atom as it collides with the walls:

FIGURE 19.1

The path of a single gas atom as it un-

dergoes collisions with the walls of its

container

Further, let’s restrict ourselves to considering the motion of the particle along thexaxis, and its collisions with
the righty−zwall, as shown in the picture. Therefore, we only considervxthe component of the velocity vector
perpendicular to they−zwall.

If the particle’s mass ism, in one collision, the particle’s momentum in thexdirection changes by

∆p= 2 mvx

Also, since it has to travel a distance 2L(back and forth, basically) in thexdirection between collisions with the
righty−zwall, the timeδtbetween collisions will be

∆t=

2 L

vx

.