Kinetic theory of gases · Grade 12
The kinetic theory explains gas behaviour from the motion of particles. Gas pressure comes from countless molecules bouncing off the walls, and temperature is a measure of their average kinetic energy. From a few simple assumptions we can work out how fast air molecules move: hundreds of metres per second.
Key facts
- Assumptions: many molecules in random motion; elastic collisions; negligible molecular volume; no forces except during collisions.
- Pressure is caused by molecules colliding with the walls and changing momentum.
- pV = ⅓Nm⟨c²⟩, so p = ⅓ρ⟨c²⟩ and c_rms = √(3p ÷ ρ).
- Mean kinetic energy of a molecule = (3/2)kT, proportional to absolute temperature.
- c_rms = √(3RT ÷ M) = √(3kT ÷ m).
- Internal energy of a monatomic ideal gas: U = (3/2)nRT.