Page 248 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 20

Kinetic Theory

of Matter

KINETIC THEORYOFGASES

The kinetic theory of gases holds that a gas is composed of very small particles, called molecules, which are in
constant random motion. The molecules are far apart relative to their dimensions and do not interact with one
another except in collisions.
The pressure a gas exerts is due to the impacts of its molecules; there are so many molecules in even a small
gas sample that the individual blows appear as a continuous force. Boyle’s law is readily understood in terms
of the kinetic theory of gases. Expanding a gas sample means that its molecules must travel farther between
successive impacts on the container walls and that the impacts are spread over a larger area. Hence an increase
in volume means a decrease in pressure, and vice versa.

MOLECULAR ENERGY
According to the kinetic theory of gases, the average kinetic energy of the molecules of a gas is proportional to
the absolute temperature of the gas. This relationship is usually expressed in the form
3
KE av = kT
2
where k = Boltzmann’s constant = 1.38 × 10 −23 J/K. Actual molecular energies vary considerably on either
side of KE av .
At absolute zero, 0 K, gas molecules would be at rest, which is why this is such a significant temperature. At
any given temperature, all gases have the same average molecular energy. Therefore, in a gas whose molecules
are heavy, the molecules move more slowly on the average than do those in a gas at the same temperature whose
molecules are light.
Charles’s law follows directly from the above interpretation of temperature. Compressing a gas causes its
temperature to rise because molecules rebound from the inward-moving walls of the container with increased
energy, just as a tennis ball rebounds with greater energy when it is struck by a moving racket. Similarly,
expanding a gas causes its temperature to fall because molecules rebound from the outward-moving walls with
decreased energy.

233