Classic Kinetic Theory of Gases

In the classical kinetic theory of gases, a gas molecule is assumed to be moving at a constant velocity in a straight line except at the instant of time when it collides with another molecule or the wall of the container. Its path is then a broken line in space, as in Figure 3.4.6.

Figure 3.4.6

The position in three dimensional space at time t can be represented by three functions

x = f(t), y = g(t), z = h(t).

All three functions, f, g, and h are continuous for all values of t. At the time t of a collision, at least one and usually all three derivatives dx/dt, dy/dt, dz/dt will be undefined because the speed or direction of the molecule changes abruptly. At any other time t, when no collision is taking place, all three derivatives dx/dt, dy/dt, dz/dt will exist.

Figure 3.4.7: Points where f is continuous but nondifferentiable