Unit Overview

Ideal gases

CIE A-Level Physics· 5 min read 📊 n/a

1. Unit at a glance

This unit follows a logical arc from empirical observation to microscopic explanation: we start with experimentally derived gas laws that describe how ideal gases respond to changes in pressure, volume and temperature. These separate laws are combined into the unified ideal gas equation of state, the core macroscopic tool for ideal gas calculations.

We then move from bulk observations to a microscopic explanation of gas behaviour using the kinetic theory of gases, which connects bulk properties to the random motion of individual molecules. The unit concludes by applying this model to calculate root mean square molecular speed and define the internal energy of an ideal gas.

This unit is split into 5 connected sub-topics, ordered by increasing conceptual complexity:

Gas laws

Learn the three empirical gas laws relating pressure, volume and absolute temperature.

★★⏱ 8 min

Ideal gas equation of state

Combine the gas laws into the unified ideal gas equation and apply it to problems.

★★⏱ 10 min

Kinetic theory of gases

Explore core assumptions of kinetic theory and derive the pressure-motion relationship.

★★★⏱ 12 min

Root mean square speed

Calculate and interpret root mean square speed for ideal gas molecules.

★★★⏱ 9 min

Internal energy of ideal gas

Understand why internal energy of an ideal gas depends only on temperature.

★★★⏱ 8 min

2. Common Pitfalls

Wrong move:

Using Celsius temperature instead of absolute (Kelvin) temperature in gas calculations.

Why:

All ideal gas equations require temperature on an absolute scale; using Celsius gives systematically incorrect results.

Correct move:

Always convert temperature from °C to Kelvin by adding 273.15 before starting calculations.

Wrong move:

Confusing the molar gas constant $R$ and Boltzmann constant $k_{B}$ in the ideal gas equation.

Why:

Mixing up these constants leads to incorrect units and values, depending on whether you use moles or number of molecules.

Correct move:

Use $R$ with moles $n$ ( $P V = n R T$ ) and $k_{B}$ with number of molecules $N$ ( $P V = N k_{B} T$ ).

Wrong move:

Assuming real gases follow the ideal gas law exactly at all conditions.

Why:

The ideal gas model relies on simplifying assumptions that break down at high pressure or low temperature.

Correct move:

Use the ideal gas law as an approximation, which is most accurate for low pressures and high temperatures.

3. Quick Reference Cheatsheet

Key Concept	Formula
Ideal gas equation (moles)	$P V = n R T$
Ideal gas equation (molecules)	$P V = N k_{B} T$
Kinetic theory pressure equation	$P V = \frac{1}{3} N m < c^{2} >$
Root mean square speed	$v_{r m s} = < c^{2} >$
Average kinetic energy per molecule	$\frac{1}{2} m < c^{2} >= \frac{3}{2} k_{B} T$
Internal energy (monatomic ideal gas, n moles)	$U = \frac{3}{2} n R T$

What's Next

Begin your study of this unit with the first sub-topic on empirical gas laws, which forms the foundation for all further concepts about ideal gases. Work through each sub-topic in order, as every topic builds directly on knowledge from the previous one. Once you complete all sub-topics in this unit, you can progress to the next unit covering core thermodynamics concepts.