Kinetic theory of gases
Cambridge A-Level Physics (9702) · Unit 15: Ideal gases · 7 flashcards
Kinetic theory of gases is topic 15.3 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 15 — Ideal gases , alongside The mole and Equation of state. In one line: 1. Gas consists of identical molecules in random, continuous motion. 2. Volume of molecules is negligible compared to gas volume. 3. No intermolecular forces except during collisions. 4. Collisions are perfectly elastic. 5. Duration of collision is negligible compared to time between collisions.
Marked as A2 Level: examined at A Level in Paper 4 (A Level Structured Questions) and Paper 5 (Planning, Analysis and Evaluation). It is not tested on the AS-only papers (Papers 1, 2 and 3).
The deck below contains 7 flashcards — 3 definitions, 2 key concepts and 2 calculations — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Basic assumptions of the kinetic theory of gases
1. Gas consists of identical molecules in random, continuous motion. 2. Volume of molecules is negligible compared to gas volume. 3. No intermolecular forces except during collisions. 4. Collisions are perfectly elastic. 5. Duration of collision is negligible compared to time between collisions.
What the Cambridge 9702 syllabus says
2025-2027 syllabus, in our words · A2 LevelWhat the syllabus expects you to be able to do in this topic, in plain English. For the exact wording, see the official syllabus (PDF).
- State the basic assumptions that kinetic theory makes about a gas.
- Explain how moving molecules give rise to gas pressure, and derive and use pV = ⅓Nm<c²>, where <c²> is the mean-square speed. A simple derivation is enough: treat collisions in one dimension, then extend to three using <cx²> = ⅓<c²>.
- Understand that the r.m.s. (root-mean-square) speed is cr.m.s. = √<c²>, the square root of the mean-square speed.
- Compare pV = ⅓Nm<c²> and pV = NkT and so deduce that a molecule's mean translational kinetic energy is (3/2)kT; recall this expression and use it.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in Kinetic theory of gases
- › Use specific syllabus terminology; refer to the motion, collisions, and volume of molecules when discussing kinetic theory.
- › Always square root the mean-square speed value if the question specifically asks for r.m.s. speed.
- › For kinetic theory explanations, discuss molecular collisions, changes in mean square speed, and the direct proportionality between temperature and average kinetic energy.
State the basic assumptions of the kinetic theory of gases.
1. Gas consists of identical molecules in random, continuous motion. 2. Volume of molecules is negligible compared to gas volume. 3. No intermolecular forces except during collisions. 4. Collisions are perfectly elastic. 5. Duration of collision is negligible compared to time between collisions.
Explain how molecular movement causes gas pressure.
Molecules collide with the container walls and rebound, so each collision changes the molecule's momentum. The wall exerts a force on the molecule (force = rate of change of momentum), so the molecules exert an equal and opposite force on the wall. Pressure is the total force per unit area. Faster molecules or more frequent collisions give a higher pressure.
State the relationship between pressure (p), volume (V), number of molecules (N), mass of molecule (m), and mean-square speed (⟨c²⟩).
The relationship is given by pV = (1/3)Nm⟨c²⟩, where ⟨c²⟩ represents the average of the squares of the speeds of the gas molecules.
What is the root-mean-square speed (cᵣₘₛ)?
The root-mean-square speed (cᵣₘₛ) is the square root of the mean (average) of the squares of the speeds of the molecules in a gas. It is calculated as cᵣₘₛ = √⟨c²⟩.
How is the average translational kinetic energy of a molecule related to absolute temperature (T)?
The average translational kinetic energy of a molecule is directly proportional to the absolute temperature. It is given by (1/2)m⟨c²⟩ = (3/2)kT, where k is the Boltzmann constant.
How can you derive the relationship between root-mean-square speed and temperature?
Starting with pV = (1/3)Nm⟨c²⟩ and pV = NkT, equate to obtain (1/3)Nm⟨c²⟩ = NkT. Simplify to ⟨c²⟩ = 3kT/m. Therefore, cᵣₘₛ = √(3kT/m).
How does increasing the temperature of a gas affect the root-mean-square speed of its molecules?
Increasing the temperature of a gas increases the root-mean-square speed of its molecules. Since cᵣₘₛ = √(3kT/m), a higher temperature (T) results in a higher cᵣₘₛ, indicating faster-moving molecules.
Review the material
Read full revision notes on Kinetic theory of gases — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 15 — Ideal gases
Kinetic theory of gases sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Kinetic theory of gases deck
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