Describe molecular internal energy
Treat internal energy as a property of the system's state and identify its molecular kinetic- and potential-energy contributions.
Section 16 · Thermodynamics
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 16. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use temperature, molecular kinetic energy, pressure, volume and energy-transfer conventions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does internal energy include in the molecular model?
What you will learn
- Understand internal energy as determined by the state of a system
- Express internal energy as the sum of molecular kinetic and potential energies
- Distinguish molecular internal energy from the motion of the system as a whole
Internal energy belongs to the state of the system
The internal energy U of a system is determined by its state. For a material, it is the sum of the random kinetic energies of its molecules and the potential energies associated with interactions between those molecules.
Internal energy is a microscopic energy store. It is distinct from the kinetic energy of the whole object moving through the room and from its gravitational potential energy in an external field.
Molecular motion and arrangement both matter
Random molecular motion contributes kinetic energy; intermolecular separation and arrangement contribute potential energy. Changing the state can change these contributions even when the system is not moving as a whole.
Use the system boundary consistently. Energy transferred across that boundary can change U, while the internal energy itself describes the microscopic state inside it.
Pause and explain
A stationary gas has internal energy because its molecules move randomly and interact. Which statement is correct?
Worked example
A sealed gas sample is stationary in a container. Identify the contributions to its internal energy and one energy store that is not part of this internal energy.
Show the worked solution
- Consider molecular motion and interactions inside the gas.
- Name the two microscopic contributions.
- Distinguish energy of the sample as a whole.
Answer Internal energy is the sum of random molecular kinetic and intermolecular potential energies. The kinetic energy of the whole container moving as one object is not part of this internal energy.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
State the two molecular contributions summed to give the internal energy of a substance.
Give me a hint
Consider molecular motion and interactions between molecules.
Compare my reasoning
- Random molecular motion contributes kinetic energy.
- Molecular interactions and arrangement contribute potential energy.
- The sum of these microscopic energies is internal energy.
Internal energy is the sum of random molecular kinetic energy and intermolecular potential energy.
Look for these in your work
- Kinetic contribution stated
- Potential contribution stated
- Sum identified
A moving cart contains a warm gas in a sealed canister. Distinguish the gas's internal energy from the cart's motion.
Give me a hint
Separate microscopic motion within the gas from bulk motion of the whole system.
Compare my reasoning
- Internal energy describes random molecular kinetic and intermolecular potential energies.
- Cart motion is the centre-of-mass kinetic energy of the object as a whole.
- These are distinct energy stores.
The gas's U is microscopic; the cart's bulk kinetic energy is a separate macroscopic store.
Look for these in your work
- Microscopic scale identified
- Bulk motion identified
- Energy stores distinguished
Two samples have the same chemical substance but different states. Explain why their internal energies need not be equal.
Give me a hint
Compare molecular motion and arrangement in the two states.
Compare my reasoning
- Internal energy is determined by the system's state.
- The states can have different molecular kinetic-energy distributions or intermolecular potential energies.
- Their total microscopic energies can therefore differ.
Different states can have different molecular energy contributions, so their internal energies need not match.
Look for these in your work
- State dependence recalled
- Molecular contributions compared
- Conclusion follows
Common mistakes
- Including the centre-of-mass motion of the entire object in internal energy
- Describing internal energy as kinetic energy only
- Treating internal energy as a substance label rather than a state property
What can you explain now?
What does internal energy include in the molecular model?
Compare with the explanation
Random molecular kinetic and intermolecular potential energies
Both molecular motion and interaction energy contribute.
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Make it stick
Which microscopic energy contributions make up a system's internal energy?
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