Relate temperature rise to internal energy
Connect a temperature increase to an increase in internal energy while distinguishing what temperature does and does not measure.
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 happens to an object's internal energy when its temperature rises?
What you will learn
- Relate a rise in temperature to an increase in internal energy
- Use molecular kinetic-energy reasoning
- Recognise that internal energy can also change through molecular potential energy
A temperature rise signals increased internal energy
When an object's temperature rises, its internal energy increases. At the molecular level, the average random kinetic energy is greater at the higher temperature.
Temperature is not the total internal energy: the amount and type of material also matter. Equal temperature does not imply equal U, and a temperature change alone does not specify the numerical energy change without more information.
Internal energy may change without a temperature rise
Energy can also change molecular potential energy, for example during a change of state. That makes it possible for internal energy to increase while temperature stays constant during a phase transition.
For this syllabus outcome, the core relationship is that a rise in temperature of an object corresponds to an increase in its internal energy. Use the system's state and process together when interpreting an energy change.
Pause and explain
Two objects are at the same temperature but have different masses. Must their internal energies be equal?
Worked example
A sealed metal block is warmed without changing its mass or state. Describe the change in its internal energy.
Show the worked solution
- Identify that its temperature rises.
- Apply the syllabus relationship.
- State the direction of the internal-energy change.
Answer Its internal energy increases; the average random kinetic energy of its particles also increases.
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Test this topic →From guided practice to a new situation
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.
A metal sample warms from 290 K to 330 K without changing state. State what happens to its internal energy and explain the molecular link.
Give me a hint
Apply the temperature-rise relationship and consider random molecular motion.
Compare my reasoning
- The temperature rises by 40 K.
- The object's internal energy increases.
- Its average random molecular kinetic energy is greater at the higher temperature.
Internal energy increases as the sample warms, with greater average random molecular kinetic energy.
Look for these in your work
- Temperature increase identified
- Direction of U change correct
- Molecular explanation given
A student says two bodies at 300 K have equal internal energy. Give one reason this conclusion is not justified.
Give me a hint
Distinguish temperature from total energy and consider amount of material.
Compare my reasoning
- Temperature relates to molecular energy per particle on average.
- Total internal energy depends on how many particles and the material's state.
- Equal temperature alone does not establish equal total U.
They may contain different amounts or materials, so equal temperature does not guarantee equal internal energy.
Look for these in your work
- Temperature distinguished from total U
- Amount/material noted
- Conclusion qualified
A pure substance melts while energy is supplied at constant temperature. Explain how internal energy can still change.
Give me a hint
During a phase change, energy changes molecular arrangement rather than raising temperature.
Compare my reasoning
- The temperature can stay constant during melting.
- Energy changes the molecular potential-energy contribution.
- Internal energy can therefore increase without a temperature rise.
Internal energy increases as molecular potential energy changes, even though the temperature remains constant.
Look for these in your work
- Constant temperature recognised
- Potential-energy store identified
- Internal-energy change explained
Common mistakes
- Claiming temperature equals total internal energy
- Claiming internal energy cannot change at constant temperature
- Using a temperature change alone to calculate energy without material data
What can you explain now?
What happens to an object's internal energy when its temperature rises?
Compare with the explanation
It increases
A temperature rise is associated with increased internal energy.
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Make it stick
Why does a temperature rise imply an internal-energy increase, but equal temperatures do not prove equal total internal energies?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.