Internal energy, temperature and thermal equilibrium
Key idea: H2 Physics lessons on temperature, ideal gases, internal energy and thermodynamic systems.
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The core idea
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Big question: What changes inside a system when it is heated?
Internal energy is the sum of random molecular kinetic energy and intermolecular potential energy. Temperature tracks mean kinetic energy, not total internal energy. When bodies are in thermal contact, energy transfers from higher to lower temperature until thermal equilibrium, where temperatures are equal and net transfer stops.
Identify the microscopic store
Internal energy U is the total random microscopic kinetic energy plus microscopic potential energy of the particles in a system. It excludes ordered kinetic energy of the whole object and gravitational potential energy of the object as a whole.
Temperature is linked to mean microscopic kinetic energy, not to the total U. A larger sample can therefore have more internal energy than a smaller sample at the same temperature; different phases can also have different U at one temperature.
Check your understanding: Two copper blocks at the same temperature have different masses. Which has greater mean kinetic energy per particle?
Neither; the means are equal. The larger block generally has greater total internal energy because it has more particles.
Describe heating as transfer, not storage
Heating is energy transferred across a system boundary because of a temperature difference. It is not a substance contained in an object. Net heating continues from higher to lower temperature until thermal equilibrium.
During warming, mean kinetic energy normally rises. During a phase change at constant temperature, mean kinetic energy stays constant while microscopic potential energy changes. Internal energy can therefore change without a temperature change.
Check your understanding: Why does supplied energy not raise temperature during ideal melting?
It increases microscopic potential energy as the structure changes; mean kinetic energy, and therefore temperature, stays constant.
Key ideas to keep
- A larger body can have more internal energy at the same temperature.
- Heating is an energy transfer, not something stored in a body.
- Thermal equilibrium means no net transfer, not no molecular exchange.
See the reasoning
Worked example
Compare temperature and internal energy without treating them as the same
Question: Two copper blocks of unequal mass begin at the same temperature. Compare their mean microscopic kinetic energy, internal energy and net heating when placed in contact.
Step 1: Use the equal temperatures
Why: Temperature concerns mean microscopic kinetic energy.
Working: Both copper blocks have the same mean microscopic kinetic energy per particle.
Step 2: Use the unequal amounts
Why: Internal energy totals microscopic energies over all particles.
Working: The larger block can have greater internal energy because it contains more particles.
Step 3: Decide the transfer
Why: Net heating is determined by temperature difference, not total internal energy.
Working: Equal temperatures mean thermal equilibrium and no net heating when the blocks touch.
Answer: Their equal thermodynamic temperatures imply equal mean microscopic kinetic energy per particle. The larger block can have greater total internal energy because it contains more particles. Since temperatures are equal, they are in thermal equilibrium and there is no net heating.
Check: Equal temperature does not require equal mass or equal total internal energy.
Use a hint if needed
Practise with support
Try this
A hot small object and a cooler large object touch. Predict the direction and stopping condition for heating without comparing their total internal energies.
Hint: Temperature, not total internal energy, fixes the direction.
Check your answer
Net heating is from the higher-temperature small object to the lower-temperature large object until their temperatures are equal. Equal internal energies are neither required nor generally produced.
Now work without the hint
Practise independently
Your turn
Explain why equal-temperature samples can have different internal energies and why energy can still transfer without being stored as 'heat'.
Check your answer
Temperature concerns mean microscopic kinetic energy, while internal energy totals microscopic kinetic and potential energies over all particles. Different masses, phases or interactions therefore change U. Heat is not a store; heating is energy crossing a boundary because of a temperature difference.
Avoid these traps
Common mistakes
Common mistake
Heat is energy stored inside a hot body.
What is wrong with this reasoning?
Show better thinking
Internal energy is the store; heating is energy transferred because of a temperature difference.
Common mistake
Equal temperature means equal internal energy.
What is wrong with this reasoning?
Show better thinking
Equal temperature means equal mean microscopic kinetic energy, not equal total internal energy.
Write for the examiner
Exam guidance
Distinguish temperature, internal energy and energy transferred by heating in every explanation.
Exam-style practice [6 marks]
Define internal energy and thermal equilibrium, and connect thermodynamic temperature to molecular motion.
Plan before you answer
- Define internal energy.
- Relate temperature to a mean quantity.
- State the equilibrium condition.
Mark your answer and compare the model
Marking points
Tick each point only if your answer states it clearly.
Model answer
U is the sum of random microscopic kinetic and potential energies. T is proportional to mean microscopic kinetic energy. Thermal equilibrium means equal temperature and no net heating between systems in thermal contact.
Come back in three days
Check what stayed with you
Recall question
Two objects have equal internal energy but different temperatures. Can they be in thermal equilibrium? Explain.
Check the answer
No. Thermal equilibrium requires equal temperature. With different temperatures, the objects exchange energy by heating when placed in thermal contact, even if their total internal energies are equal.
Syllabus and review details
This lesson covers the listed H2 Physics 9478 outcomes. Temperature and ideal-gas ideas lead into the first law of thermodynamics. Use ΔU = Q + W, where W is work done on the system; for expansion against constant external pressure, work done by the gas is pΔV and work done on the gas is −pΔV.
- GCE A-Level H2 PhysicsTopic 13(a) / Topic 13(b) / Topic 13(c) · 2027Checked against the syllabus · partial topic coverageOfficial 9478 syllabus
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027