Equation of state
Cambridge A-Level Physics (9702) · Unit 15: Ideal gases · 7 flashcards
Equation of state is topic 15.2 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 15 — Ideal gases , alongside The mole and Kinetic theory of gases. In one line: An ideal gas is defined by the relationship pV ∝ T, where p is pressure, V is volume, and T is the thermodynamic temperature (in Kelvin). This proportionality indicates that for a fixed amount of gas, the ratio of pV to T remains constant.
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 — 4 definitions, 2 key concepts and 1 calculation — covering the precise wording mark schemes reward. Use the 4 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.
Some cards in this deck are on other syllabus topics: 15.3 Kinetic theory of gases. Each card is labelled with its topic.
What defines an ideal gas in terms of pressure, volume, and temperature
An ideal gas is defined by the relationship pV ∝ T, where p is pressure, V is volume, and T is the thermodynamic temperature (in Kelvin). This proportionality indicates that for a fixed amount of gas, the ratio of pV to T remains constant.
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).
- Understand that an ideal gas is one that obeys pV ∝ T, with T the thermodynamic temperature.
- Recall and use the ideal gas equation in two forms: pV = nRT, with n the number of moles (amount of substance), and pV = NkT, with N the number of molecules.
- Recall the relation k = R/NA for the Boltzmann constant k.
Also in this deck: 15.3 Kinetic theory of gases
- 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 these topics
- › 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.
Topic 15.2 · Equation of state
What defines an ideal gas in terms of pressure, volume, and temperature?
An ideal gas is defined by the relationship pV ∝ T, where p is pressure, V is volume, and T is the thermodynamic temperature (in Kelvin). This proportionality indicates that for a fixed amount of gas, the ratio of pV to T remains constant.
Topic 15.2 · Equation of state
State the ideal gas equation using the amount of substance (number of moles).
The ideal gas equation, using the amount of substance (n), is pV = nRT, where p is pressure, V is volume, n is the number of moles, R is the ideal gas constant (8.31 J/mol·K), and T is the thermodynamic temperature.
Topic 15.2 · Equation of state
State the ideal gas equation using the number of molecules.
The ideal gas equation, using the number of molecules (N), is pV = NkT, where p is pressure, V is volume, N is the number of molecules, k is the Boltzmann constant, and T is the thermodynamic temperature.
Topic 15.2 · Equation of state
Define the Boltzmann constant (k) in terms of the ideal gas constant (R) and Avogadro's constant (Nᴀ).
The Boltzmann constant (k) is defined as the ideal gas constant (R) divided by Avogadro's constant (Nᴀ): k = R / Nᴀ. This constant relates the average kinetic energy of particles in a gas to the gas's temperature.
Topic 15.2 · Equation of state
If you double the number of moles of an ideal gas in a closed container at constant volume, what happens to the pressure if the temperature remains constant?
If the number of moles (n) is doubled in a closed container at constant volume (V) and constant temperature (T), the pressure (p) will also double, according to the ideal gas law pV = nRT. Since V, R, and T are constant, p is directly proportional to n.
Topic 15.3 · Kinetic theory of gases
How does an increase in temperature affect the average kinetic energy of the molecules in an ideal gas?
An increase in temperature leads to an increase in the average kinetic energy of the molecules in an ideal gas. This is because temperature is directly proportional to the average kinetic energy of the gas molecules. This relationship is embodied in the kinetic theory of gases.
Topic 15.2 · Equation of state
A container holds 2 moles of an ideal gas at 300K. If the volume is 0.02 m³, what is the pressure of the gas?
Using pV = nRT, we can calculate the pressure: p = nRT/V = (2 mol * 8.31 J/mol·K * 300 K) / 0.02 m³ = 249300 Pa (or 249.3 kPa).
Review the material
Read full revision notes on Equation of state — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 15 — Ideal gases
Equation of state 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 Equation of state deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
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