A level Physics · Edexcel 9PH0 · Topic 9B

Ideal gases and kinetic theory

Key points

Absolute zero is the temperature at which molecules have minimum internal energy; temperatures in gas laws must be in kelvin.
Ideal gas equation: $pV = NkT$ , where $N$ is the number of molecules and $k = 1.38 \times 10^{-23}$ J K $^{-1}$ (or $pV = nRT$ with moles).
Boyle's law: for a fixed mass at constant temperature, $pV$ is constant. Pressure is also proportional to $T$ at constant volume.
Kinetic theory: molecules collide elastically with the walls; each collision changes momentum, and the force per unit area gives pressure. $pV = \frac{1}{3}Nm\langle c^2\rangle$ .
Mean molecular kinetic energy: $\frac{1}{2}m\langle c^2\rangle = \frac{3}{2}kT$ , so it is proportional to absolute temperature. r.m.s. speed $= \sqrt{\langle c^2\rangle}$ .
Assumptions: negligible molecule volume, no forces except during collisions, random motion, collisions take negligible time.
Core practical: investigate how the pressure of a fixed mass of gas varies with volume at constant temperature (Boyle's law).

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A gas is a huge number of molecules moving randomly and colliding with each other and the walls. The ideal gas equation summarises how pressure, volume and temperature are related, and kinetic theory explains why.

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