(A Level) Ideal gases and kinetic theory

Learning objectives

Use the mole as the SI unit of amount of substance, and convert between amount in moles, number of particles and mass using the Avogadro constant NA.

Describe an ideal gas as one for which pV is proportional to thermodynamic temperature, and use pV = nRT and pV = NkT, with the Boltzmann constant k = R/NA.

State the simplifying assumptions of the kinetic model of a gas: random motion, elastic collisions, negligible molecular volume, no forces between molecules except in collisions, and collision times much shorter than the time between collisions.

Explain gas pressure as the rate of change of momentum of molecules striking the walls, and derive pV = ⅓Nm⟨c²⟩ by analysing one molecule in a box and using ⟨c²⟩ = 3⟨cₓ²⟩.

Calculate the root-mean-square speed of gas molecules, and equate pV = ⅓Nm⟨c²⟩ with pV = NkT to show that each molecule has a mean kinetic energy of translation of (3/2)kT, which depends only on temperature.