What is internal energy in the context of thermodynamics?

Internal energy is the total energy contained within a system due to the kinetic and potential energies of its molecules. In thermodynamics, it is a crucial concept as it helps in understanding how energy is stored and transferred within a system. It is a state function, meaning it depends only on the current state of the system, not on how the system reached that state.

How is internal energy related to temperature and heat?

Internal energy is directly related to temperature, as an increase in temperature generally increases the kinetic energy of the molecules, thereby increasing the internal energy. Heat is a form of energy transfer that can change the internal energy of a system. When heat is added to a system, it can increase the internal energy by raising the temperature or causing a phase change.

What is the difference between internal energy and enthalpy?

Internal energy is the total energy contained within a system, while enthalpy is a measure of the total heat content of a system. Enthalpy is defined as the internal energy plus the product of pressure and volume of the system (H = U + PV). It is particularly useful in processes occurring at constant pressure, such as many chemical reactions.

How can internal energy be changed in a thermodynamic process?

Internal energy can be changed by transferring heat to or from the system, performing work on or by the system, or through a combination of both. According to the first law of thermodynamics, the change in internal energy is equal to the heat added to the system minus the work done by the system (ΔU = Q - W).

Why is internal energy considered a state function in thermodynamics?

Internal energy is considered a state function because its value depends only on the current state of the system, characterized by properties such as temperature, pressure, and volume, rather than the path taken to reach that state. This means that the change in internal energy between two states is the same regardless of the process used to transition between those states.

Why is "Saying $U$ depends on $p$ or $V$ for ideal gas" a common mistake in Internal energy?

Why it happens: Common misconception. How to avoid it: For ideal gas, U depends ONLY on T. Changing p or V at constant T doesn't change U. Source: 9702 Examiner Reports 2022-2024

ThermodynamicsCambridge International A Levels Physics (9702)

Internal energy

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Internal Energy Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Total energy of particles. For ideal gas depends only on $T$ .

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

16.1.1 — Define internal energy.
16.1.2 — Compute $U$ for ideal gas.

Internal energy

Sum of KE + PE of particles.

Definition. Total of all KE (random thermal motion) and PE (intermolecular interactions) of particles.

Ideal gas. Intermolecular PE = 0 (negligible forces). $U$ is all KE. $U = \tfrac{3}{2}NkT = \tfrac{3}{2}nRT \quad (\text{monatomic})$

Key result. For ideal gas, $U$ depends ONLY on $T$ . NOT on $V$ or $p$ separately.

Real gases. Have intermolecular PE; $U$ depends on $V$ also.

Cambridge tip. State 'depends only on $T$ for ideal gas'.

$U$ = KE + PE total.
Ideal gas: $\frac{3}{2}NkT$ .
Function of $T$ only.

See the full worked example for internal energy →

How it’s examined

Internal energy on Paper 4. Most-tested: definition + ideal gas value (5-7 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.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

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Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Internal energy, ready to print or save as PDF.

Step-by-step worked examples — Internal energy

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

1Internal energy of ideal gas (5 marks)
Extended• internal energy
Question
Find internal energy of 1.0 mol of monatomic ideal gas at 300 K. $R = 8.31$ . (5 marks)
Step-by-step solution
1. Step 1
  $U = \frac{3}{2}nRT$ .
  $U = \tfrac{3}{2} \times 1.0 \times 8.31 \times 300 \approx 3740 \text{ J}$
Answer
$U \approx 3740$ J.

Key Formulae — Internal energy

The formulae you need to memorise for internal energy 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 internal energy
$U = \tfrac{3}{2} N k T = \tfrac{3}{2} n R T$
When to use
For MONATOMIC ideal gas only. Diatomic and polyatomic have more degrees of freedom.

Key Definitions and Keywords — Internal energy

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

Internal energy
Examiner keyword
Total kinetic plus potential energy of all particles in a system.

Common Mistakes and Misconceptions — Internal energy

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

✕Saying $U$ depends on $p$ or $V$ for ideal gas
9702 Examiner Reports 2022-2024
Why it happens
Common misconception.
How to avoid it
For ideal gas, $U$ depends ONLY on $T$ . Changing $p$ or $V$ at constant $T$ doesn't change $U$ .

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Internal energy — frequently asked questions

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

ThermodynamicsCambridge International A Levels Physics (9702)

Internal energy

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

PreviousNext

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Study Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Internal energy, ready to print or save offline.

Internal Energy Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Total energy of particles. For ideal gas depends only on $T$ .

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

16.1.1 — Define internal energy.
16.1.2 — Compute $U$ for ideal gas.

Internal energy

Sum of KE + PE of particles.

Definition. Total of all KE (random thermal motion) and PE (intermolecular interactions) of particles.

Ideal gas. Intermolecular PE = 0 (negligible forces). $U$ is all KE. $U = \tfrac{3}{2}NkT = \tfrac{3}{2}nRT \quad (\text{monatomic})$

Key result. For ideal gas, $U$ depends ONLY on $T$ . NOT on $V$ or $p$ separately.

Real gases. Have intermolecular PE; $U$ depends on $V$ also.

Cambridge tip. State 'depends only on $T$ for ideal gas'.

$U$ = KE + PE total.
Ideal gas: $\frac{3}{2}NkT$ .
Function of $T$ only.

See the full worked example for internal energy →

How it’s examined

Internal energy on Paper 4. Most-tested: definition + ideal gas value (5-7 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.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Internal energy, ready to print or save as PDF.

Step-by-step worked examples — Internal energy

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

1Internal energy of ideal gas (5 marks)
Extended• internal energy
Question
Find internal energy of 1.0 mol of monatomic ideal gas at 300 K. $R = 8.31$ . (5 marks)
Step-by-step solution
1. Step 1
  $U = \frac{3}{2}nRT$ .
  $U = \tfrac{3}{2} \times 1.0 \times 8.31 \times 300 \approx 3740 \text{ J}$
Answer
$U \approx 3740$ J.

Key Formulae — Internal energy

The formulae you need to memorise for internal energy 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 internal energy
$U = \tfrac{3}{2} N k T = \tfrac{3}{2} n R T$
When to use
For MONATOMIC ideal gas only. Diatomic and polyatomic have more degrees of freedom.

Key Definitions and Keywords — Internal energy

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

Internal energy
Examiner keyword
Total kinetic plus potential energy of all particles in a system.

Common Mistakes and Misconceptions — Internal energy

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

✕Saying $U$ depends on $p$ or $V$ for ideal gas
9702 Examiner Reports 2022-2024
Why it happens
Common misconception.
How to avoid it
For ideal gas, $U$ depends ONLY on $T$ . Changing $p$ or $V$ at constant $T$ doesn't change $U$ .

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Internal energy — frequently asked questions

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

Internal energy

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Internal energy of ideal gas (5 marks)

Ideal gas internal energy

Internal energy

✕Saying UUU depends on ppp or VVV for ideal gas

Practice questions

Past paper style quiz

Assess your understanding

Internal energy — frequently asked questions

Internal energy

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Internal energy of ideal gas (5 marks)

Ideal gas internal energy

Internal energy

✕Saying UUU depends on ppp or VVV for ideal gas

Practice questions

Past paper style quiz

Assess your understanding

Internal energy — frequently asked questions

✕Saying $U$ depends on $p$ or $V$ for ideal gas

✕Saying $U$ depends on $p$ or $V$ for ideal gas