What is the equation of state for an ideal gas?

The equation of state for an ideal gas is expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature in Kelvin. This equation relates the physical properties of an ideal gas and is fundamental in understanding gas behavior in Physics, particularly at the Cambridge International A Levels.

How does the ideal gas equation relate to real gases?

The ideal gas equation assumes that gas particles do not interact and occupy no volume, which is not true for real gases. However, at high temperatures and low pressures, real gases approximate ideal behavior. Deviations occur under conditions of high pressure and low temperature, where intermolecular forces and molecular volume become significant. Understanding these deviations is crucial for Cambridge International A Levels Physics students.

Why is the ideal gas constant (R) important in the equation of state?

The ideal gas constant (R) is crucial because it provides the proportionality factor that relates the energy scale to the temperature scale in the ideal gas equation. It ensures that the units of pressure, volume, and temperature are consistent, allowing the equation to accurately describe the behavior of ideal gases. In Cambridge International A Levels Physics, mastering the use of R is essential for solving problems involving gases.

What assumptions are made in the ideal gas equation?

The ideal gas equation assumes that gas particles are point masses with no volume, there are no intermolecular forces between particles, and that all collisions between particles are perfectly elastic. These assumptions simplify the behavior of gases, making it easier to study their properties in Physics, especially at the Cambridge International A Levels.

How can the ideal gas equation be applied in practical scenarios?

The ideal gas equation can be applied to calculate the unknown properties of a gas when the other properties are known, such as determining the volume of a gas at a given temperature and pressure. It is also used in stoichiometry to relate the volumes of gases involved in chemical reactions. For Cambridge International A Levels students, applying this equation in practical scenarios helps in understanding real-world applications of gas laws.

Why is "Using °C in $pV = nRT$" a common mistake in Equation of state?

Why it happens: Habit. How to avoid it: ALWAYS Kelvin in gas law. T(K) = T(°C) + 273. Source: 9702 Examiner Reports 2022-2024

Cambridge International A Levels Physics (9702)

Equation of state

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Short Notes - Equation of state

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Detailed Study Notes

Detailed notes on Ideal Gases for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Equation of State Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Ideal gas law $pV = nRT$ . Boyle, Charles, pressure laws.

At a glance

$pV = nRT = NkT$ .
$R = 8.31$ , $k = 1.38 \times 10^{-23}$ .
Use Kelvin for $T$ .
Boyle: $pV$ = const at constant $T$ .
1 mol at STP: 22.4 L.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

15.2.1 — Use ideal gas equation.
15.2.2 — Apply Boyle's and Charles's laws.

Ideal gas law

$pV = nRT$ .

Ideal gas equation. $pV = nRT$ .

Alternative. $pV = NkT$ where $N = nN_A$ and $k = R/N_A$ is Boltzmann constant.

Special cases.

Boyle's law. $T$ constant: $pV$ = constant.
Charles's law. $p$ constant: $V \propto T$ .
Pressure law. $V$ constant: $p \propto T$ .

STP. 0°C (273 K), 1 atm ( $1.013 \times 10^5$ Pa). 1 mol occupies 22.4 L.

Cambridge tip. $T$ ALWAYS in Kelvin.

For a fixed amount of ideal gas, pressure and volume are inversely related at constant temperature (Boyle's law); higher T raises the isotherm.

$pV = nRT$ .
Three special cases.
STP: 22.4 L per mol.

See the full worked example for equation of state →

Quick recap

$pV = nRT = NkT$ .
Kelvin for $T$ .
Boyle, Charles, pressure laws.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

Ideal gas law.
$R$ and $k$ values.
STP values.

How it’s examined

Ideal gas on every Paper 4. Most-tested: $pV = nRT$ (5-6 marks), Boyle's law (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Take this whole topic with you

Step-by-step worked examples — Equation of state

Step-by-step solutions to past-paper-style questions on equation of state, written exactly the way a tutor would explain them at the board.

1 $pV = nRT$ (6 marks)
Extended• Adapted from 9702/42 May/Jun 2024• ideal gas
Question
Find the volume occupied by 1.0 mol of ideal gas at $0°$ C and 1.0 atm. $R = 8.31$ J/(mol·K), $p = 1.013 \times 10^5$ Pa. (6 marks)
Step-by-step solution
1. Step 1
  $pV = nRT$ .
  $V = \dfrac{nRT}{p} = \dfrac{1.0 \times 8.31 \times 273}{1.013 \times 10^5}$
2. Step 2
  Evaluate.
  $V \approx 0.0224 \text{ m}^3 = 22.4 \text{ L}$
Answer
$V = 22.4$ L (1 mol at STP).
2Boyle's law (5 marks)
Extended• Boyle
Question
Gas at 200 kPa, 0.50 L is compressed to 0.25 L at constant temperature. Find new pressure. (5 marks)
Step-by-step solution
1. Step 1
  At constant $T$ , $pV$ = const.
  $p_1 V_1 = p_2 V_2 \Rightarrow p_2 = \dfrac{200 \times 0.50}{0.25} = 400 \text{ kPa}$
Answer
$p_2 = 400$ kPa.

Key Formulae — Equation of state

The formulae you need to memorise for equation of state on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Ideal gas law
$pV = nRT = NkT$
$R$
gas constant 8.31 J/(mol·K)
$k$
Boltzmann constant $1.38 \times 10^{-23}$ J/K
$N$
number of particles
When to use
Ideal gas at moderate conditions. $R = N_A k$ .

Key Definitions and Keywords — Equation of state

Definitions to memorise and the exact keywords mark schemes credit for equation of state answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Ideal gas
Examiner keyword
Gas obeying $pV = nRT$ exactly. Real gases approximate at low pressure and high temperature.
Boyle's law
Examiner keyword
At constant $T$ , $pV$ = constant for fixed mass of gas.
Charles's law
Examiner keyword
At constant $p$ , $V \propto T$ .

Common Mistakes and Misconceptions — Equation of state

The traps other students keep falling into on equation of state questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Using °C in $pV = nRT$
9702 Examiner Reports 2022-2024
Why it happens
Habit.
How to avoid it
ALWAYS Kelvin in gas law. $T(K) = T(°C) + 273$ .

Equation of state — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Equation of state

Short Notes - Equation of state

Detailed Study Notes

At a glance

What you’ll learn

Quick recap

Memorise this

How it’s examined

Take this whole topic with you

1pV=nRTpV = nRTpV=nRT (6 marks)

2Boyle's law (5 marks)

Ideal gas law

Ideal gas

Boyle's law

Charles's law

✕Using °C in pV=nRTpV = nRTpV=nRT

Equation of state — frequently asked questions

1 $pV = nRT$ (6 marks)

✕Using °C in $pV = nRT$