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Physics · Particle model of matter
Internal energy
Explain that internal energy is the total kinetic and potential energy of the particles, and describe how heating changes it, using \(\Delta E = mc\Delta\theta\) for temperature changes.
Warm-up
Answer each one, then check.
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1
What is kinetic energy?
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Energy stored in moving objects
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2
What is the equation for a change in thermal energy?
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\(\Delta E = mc\Delta\theta\)
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3
What is temperature a measure of?
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How hot something is
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4
What is a system?
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An object or group of objects
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5
What is potential energy?
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Stored energy due to position or bonds
Learning Objectives
- 1Define internal energy.
- 2Explain how heating changes the energy stored within a system.
- 3Use \(\Delta E = mc\Delta\theta\) to calculate the energy for a temperature change.
- 4Distinguish temperature from internal energy.
INTERNAL ENERGY
Internal energy is the total kinetic energy and potential energy of all the particles that make up a system.
Heating increases the energy of the particles. This either raises the temperature of the system or produces a change of state.
Where the Energy Goes
Kinetic energy relates to temperature.
Temperature or Change of State?
Temperature rises
- The kinetic energy of the particles increases.
- The average speed of the particles increases.
- Calculate with \(\Delta E = mc\Delta\theta\).
State changes
- The potential energy of the particles increases.
- The particles move further apart or become free.
- The temperature stays the same.
Energy for a Temperature Rise
Calculate the energy needed to raise the temperature of 0.50 kg of water from 20 °C to 60 °C. c = 4200 J/kg °C.
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- 1 Temperature change \(60 - 20 = 40\) °C
- 2 Substitute \(\Delta E = 0.50 \times 4200 \times 40\)
- 3 Answer \(\Delta E = 84\,000\) J
Answer84 000 J (84 kJ)
Comparing Internal Energy
Which has more internal energy: 1.0 kg of water at 50 °C or 2.0 kg of water at 50 °C?
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- 1 Same temperature The particles have the same average kinetic energy
- 2 Different mass 2.0 kg has twice as many particles, so twice as much total energy
Answer2.0 kg of water has more internal energy.
Key Ideas
Learn the links.
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Temperature
Related to the average kinetic energy of the particles.
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Internal energy
The total, including potential energy.
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Heating
Increases internal energy by raising temperature or changing state.
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Cooling
Decreases internal energy.
More Energy
Explain what happens to the internal energy and the temperature of a beaker of water as it is heated (a) from 20 °C to 60 °C (b) while ice at 0 °C is melting.
1. Say what changes in the particles.
2. Say what happens to temperature.
A good answer shows: (a) Internal energy increases, mainly kinetic energy, so the temperature rises. (b) Internal energy increases as potential energy rises, but the temperature stays at 0 °C.
Can I...?
- 1Define internal energy.
- 2Say heating increases internal energy.
- 3Link kinetic energy to temperature.
- 4Link potential energy to change of state.
- 5Use \(\Delta E = mc\Delta\theta\).
- 6Compare two objects.
- 7Explain cooling.
- 8Use correct units.
Summary & Exam Focus
- Internal energy = total kinetic + potential energy of the particles.
- Heating raises temperature or changes state.
- Temperature relates to kinetic energy.
- \(\Delta E = mc\Delta\theta\).
Exam focus
What is meant by the internal energy of a system? (2 marks) (2 marks)
The total kinetic and potential energy of all the particles.
Key terms
The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.
- Internal energy
- The total kinetic and potential energy of all the particles in a system.
- Kinetic energy
- Energy of movement.
- Potential energy
- Energy stored because of forces between particles.
- Specific heat capacity
- Energy needed to raise 1 kg by 1 °C.
- Temperature
- A measure of the average kinetic energy of particles.
- System
- An object or group of objects.
Practice questions
Have a go at each one before you open its answer.
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Question 1 State 2 marks
What is meant by the internal energy of a system?
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Model answer
The total kinetic energy and potential energy of all the particles that make up the system.
Mark scheme
- Total of kinetic energy — 1 mark
- and potential energy of all the particles — 1 mark
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Question 2 Explain 3 marks
A beaker of water is heated. Explain what happens to the energy stored within the water and to its temperature.
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Model answer
Heating increases the energy of the particles, so the internal energy increases. The kinetic energy of the particles increases, so the temperature rises.
Mark scheme
- Internal energy increases — 1 mark
- Particles gain kinetic energy — 1 mark
- Temperature rises — 1 mark
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Question 3 Calculate 3 marks
Calculate the energy needed to raise the temperature of 0.50 kg of water from 20 °C to 60 °C. Specific heat capacity of water = 4200 J/kg °C.
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Model answer
\(0.50 \times 4200 \times 40 = 84\,000\) J
Mark scheme
- Temperature change 40 °C — 1 mark
- Correct substitution — 1 mark
- 84 000 J — 1 mark
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Question 4 Explain 2 marks
1.0 kg of water and 2.0 kg of water are both at 50 °C. Which has more internal energy? Explain your answer.
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Model answer
2.0 kg, because it has twice as many particles at the same average kinetic energy, so its total energy is greater.
Mark scheme
- 2.0 kg of water — 1 mark
- More particles so more total energy — 1 mark
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Question 5 Explain 4 marks
Ice at 0 °C is heated and melts to water at 0 °C. Explain what happens to the internal energy and to the temperature during melting.
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Model answer
The internal energy increases because energy is supplied. The energy increases the potential energy of the particles as bonds are weakened, but does not increase their average kinetic energy, so the temperature stays the same.
Mark scheme
- Internal energy increases — 1 mark
- Potential energy of particles increases — 1 mark
- Kinetic energy does not increase — 1 mark
- Temperature stays constant — 1 mark
Quick check
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Internal energy is the total of...
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D: kinetic and potential energy of the particles
It includes both.
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Heating a substance...
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A: increases its internal energy
Energy is transferred to the particles.
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Temperature is related to the particles'...
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B: average kinetic energy
Faster particles mean a higher temperature.
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During melting the temperature...
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C: stays constant
The energy goes into potential energy.
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Which has more internal energy: 1 kg or 2 kg of water at the same temperature?
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D: 2 kg
There are more particles.
Downloads
Free to keep, print and annotate.
- Internal energy.pptx Built from the lesson script on 30 September 2026. View
- Internal energy - Completed Notes.docx The full notes for the lesson, to revise from. Built from the lesson script on 30 September 2026. View
- Internal energy - Exam Questions.docx Built from the lesson script on 30 September 2026. View
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