Thermodynamics

This guide covers Topic 16, Thermodynamics, in full — subtopics 16.1 Internal energy and 16.2 The first law of thermodynamics — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is A Level content and completes the core thermal physics strand begun in Temperature and Ideal Gases.

Before studying this

This resource assumes specific heat capacity from Temperature, and the kinetic theory model from Ideal Gases.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — A Level, Topic 16

16.1 Internal energy — understanding that internal energy is determined by the state of the system, and that it can be considered to be the sum of the random distribution of kinetic and potential energies associated with the molecules of a system.

16.2 The first law of thermodynamics — recalling and using W = pΔV for the work done when the volume of a gas changes at constant pressure, and understanding the difference between the work done by the gas and the work done on the gas; recalling and using the first law of thermodynamics, expressed in terms of the increase in internal energy, the heating of the system, and the work done on the system, ΔU = q + W.

Internal energy

The internal energy of a system is the sum, over all the molecules in the system, of their random distribution of kinetic energies (due to their random thermal motion) and their potential energies (due to the intermolecular forces between them). Internal energy is determined entirely by the state of the system — its temperature, volume and phase — not by how that state was reached.

Increasing the temperature of a system increases the average kinetic energy of its molecules, and therefore increases its internal energy. Changing the phase of a system (e.g. melting or boiling) changes the potential energy component of internal energy, without necessarily changing its temperature — this is consistent with the flat regions of a cooling curve covered in Temperature.

Work done by/on a gas

When a gas changes volume at constant pressure, the magnitude of the work done is:

W = pΔV

Here W = pΔV gives the work done by the gas on its surroundings during an expansion (ΔV positive). This is not automatically the same W that appears in the first law equation ΔU = q + W below, where W is defined as the work done on the system — so when substituting pΔV into the first law, an expanding gas (which does work on its surroundings) contributes a negative W, and a compressed gas (surroundings doing work on it) contributes a positive W.

The first law of thermodynamics

The first law of thermodynamics is a statement of conservation of energy applied to a thermodynamic system:

ΔU = q + W

where ΔU is the increase in internal energy of the system, q is the thermal energy supplied to the system (heating), and W is the work done on the system. Each term can be positive or negative depending on the direction of energy transfer: heating the system or doing work on it increases its internal energy; the system heating its surroundings or doing work on its surroundings decreases its internal energy.

Worked example. A gas absorbs 500 J of thermal energy and does 200 J of work by expanding against a constant external pressure. Since the gas does work on its surroundings, the work done on the gas is W = −200 J. The change in internal energy:

ΔU = q + W = 500 + (−200) = 300 J

The gas’s internal energy increases by 300 J.

Internal energy is a state function — it depends only on the current state of the system (its temperature, for an ideal gas), never on the process or path used to reach that state. Two different routes between the same start and end states give the same ΔU, even if q and W individually differ along each route.

Four named processes

Process	Condition	Consequence
Isothermal	Constant temperature	ΔU = 0, so q = −W
Adiabatic	No heat transfer	q = 0, so ΔU = W
Isobaric	Constant pressure	pΔV is the work done by the gas, so work done on it is W = −pΔV (negative for an expansion) and ΔU = q − pΔV
Isovolumetric	Constant volume	W = 0, so ΔU = q

The isothermal row follows from ΔU depending only on temperature for an ideal gas: at constant temperature, ΔU must be zero regardless of what q and W do individually. The isovolumetric row follows because no work is done on or by a gas unless its volume changes.

Common mistakes

• Mixing up the sign convention for W — W in ΔU = q + W is the work done on the system; if the system does work on its surroundings (e.g. expands), W must be entered as negative.
• Treating internal energy as only kinetic energy — it includes both the kinetic energy of random molecular motion and the potential energy from intermolecular forces.
• Assuming internal energy depends on the process used to reach a state — it is a state function, determined only by the current state of the system.
• Forgetting W = pΔV only applies at constant pressure — a different approach is needed if pressure changes during the process.

Quick revision checklist

• Internal energy = sum of random kinetic + potential energies of molecules
• pΔV is the magnitude of the work done at constant pressure; in ΔU = q + W an expansion enters as W = −pΔV and a compression as W = +p|ΔV|
• ΔU = q + W, and correctly signing q and W for the direction of energy transfer
• Internal energy depends only on the state of the system, not the path taken

Related resources

• Ideal Gases — the previous A Level topic
• Oscillations — the next A Level topic
• Temperature — specific heat capacity and latent heat, used alongside the first law
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.