Chapter 12 — Kinetic Theory

Kinetic theory explains the behaviour of gases by considering them as collections of rapidly moving atoms or molecules in incessant random motion, with elastic collisions determining pressure, temperature, and other macroscopic properties based on molecular parameters.

Kinetic theory is a powerful framework developed by Maxwell and Boltzmann that connects macroscopic gas properties to microscopic molecular behaviour. The theory shows that pressure arises from elastic molecular collisions with container walls (P = ⅓nmv²), and temperature is a direct measure of average molecular kinetic energy (½m⟨v²⟩ = (3/2)kBT). Through the ideal gas equation PV = kBNT and Avogadro's law, kinetic theory explains gas laws, predicts molecular speeds (root mean square speed vrms = √(3kBT/m)), and derives specific heat capacities using the law of equipartition of energy. The theory also yields molecular-scale insights: interatomic distances in gases are ~10 times larger than in solids/liquids, but mean free paths are ~100 times larger than interatomic distances, explaining why gases diffuse slowly despite high molecular speeds.

1. 01Kinetic theory derives pressure from elastic molecular collisions: P = ⅓nmv², linking it directly to molecular mass m, number density n, and mean squared speed v²
2. 02Temperature is the average translational kinetic energy per molecule: ½m⟨v²⟩ = (3/2)kBT; independent of gas type or pressure, it depends only on absolute temperature T
3. 03Ideal gas equation PV = µRT (or PV = kBNT) emerges from kinetic theory; real gases obey it at low pressures and high temperatures when molecular interactions become negligible
4. 04Law of equipartition of energy: each translational and rotational degree of freedom contributes ½kBT; each vibrational mode contributes kBT (both kinetic and potential energy)
5. 05Root mean square speed vrms = √(3kBT/m); at same temperature, lighter molecules move faster; this governs diffusion rates and explains isotope separation
6. 06Mean free path l = 1/(√2πnd²) is ~100 times larger than interatomic distance, allowing gases to flow and diffuse despite frequent collisions; smaller at higher pressures and temperatures