Kinetic Theory

Topic-by-topic explanations

1. Introduction

Kinetic theory connects gas behaviour to molecular motion using statistical averages and simplifying assumptions.

2. Molecular nature of matter

Matter consists of atoms or molecules. In the ideal-gas model, molecular volume is negligible, intermolecular forces are negligible except during collisions, and collisions are elastic.

3. Behaviour of gases

The ideal gas law pV=nRT describes macroscopic behaviour. Boyle's, Charles's and pressure laws follow when other variables are held fixed.

4. Kinetic theory of an ideal gas

Gas pressure comes from molecular momentum transfer to container walls. Kinetic theory gives pV=(1/3)Nm⟨c²⟩ and rms speed c_rms=√(3RT/M).

5. Law of equipartition of energy

Equipartition assigns ½k_BT to each active quadratic degree of freedom per molecule. A monatomic ideal gas has three translational degrees of freedom.

6. Specific heat capacity

For f active degrees of freedom, U=(f/2)nRT and C_v=fR/2. For a monatomic ideal gas, C_v=3R/2 and C_p=5R/2.

7. Mean free path

Mean free path is the average distance travelled between molecular collisions. It increases as number density or pressure decreases if other conditions remain comparable.

Formula sheet

Use SI units, state assumptions, show your working and check units before finalising an answer.

Worked example

Common errors and revision checklist

Use Kelvin; distinguish rms speed from average speed; only count degrees of freedom active in the relevant temperature range.

• Write the governing law before substituting values.
• Show units and signs/directions.
• Check whether assumptions are satisfied.