Kinetic Theory of Gases

Thermodynamics, the subject of the previous unit, is fundamentally a macroscopic science: it describes a gas only through bulk, measurable parameters such as its pressure, temperature, and volume, without asking what the gas is actually doing at the level of its individual particles. Kinetic theory takes the complementary, microscopic view -- treating a thermodynamic system as a vast collection of moving molecules -- and asks how those same macroscopic quantities, pressure and temperature, actually arise from that underlying molecular motion. In this sense kinetic theory forms a genuine bridge between Newtonian mechanics, which governs how each individual molecule moves, and thermodynamics, which describes only the resulting bulk behaviour. Kinetic theory explains the observable, macroscopic behaviour of a gas -- its pressure, its temperature, and the historical gas laws -- by applying Newton's laws of motion to an idealised molecular picture of what is really happening inside the gas. None of the model's assumptions is strictly, perfectly true of any real gas, yet a model built on them can still be applied successfully to every gas. The whole theory rests on a set of ten postulates.

1. A gas consists of an extremely large number of identical molecules, each behaving essentially as a rigid, elastic point particle.
2. The actual volume occupied by the molecules themselves is negligible compared with the volume of the container that holds the gas, so the molecules are effectively treated as point masses.
3. The molecules are in continuous, completely random motion, moving with a wide range of different speeds and in every possible direction, with no preferred direction of motion.
4. The average distance between two molecules is very much larger than the size of a single molecule, so a molecule spends far more time moving freely than it does in physical contact with another molecule.
5. Molecules exert no force of attraction or repulsion on one another except during the brief instant of an actual collision.
6. These collisions -- both molecule-molecule and molecule-wall -- are perfectly elastic, so that there is no loss of kinetic energy during any collision.
7. Between two successive collisions, a molecule travels in a straight line with uniform velocity.
8. Since the molecules exert force on each other only during a collision, they possess no potential energy at any other instant, and the total energy of the system is purely kinetic.
9. The collisions themselves are effectively instantaneous -- the time a molecule actually spends in the act of colliding is negligible compared with the much longer time it spends travelling freely between one collision and the next.
10. Even though the molecules move in a completely random, chaotic manner, each individual molecule still obeys Newton's laws of motion at every instant.

Together, these ten postulates convert a gas -- which looks featureless and static to the naked eye -- into a well-defined mechanical system of billions of tiny, independently moving particles, to which the ordinary tools of Newtonian mechanics (momentum, force, energy) can be directly applied. Every macroscopic gas law derived in the rest of this unit, from the expression for pressure to the ideal gas equation, ultimately traces back to just these ten assumptions.