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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.

  • 6 key terms
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Student handouts

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Warm-up

Answer each one, then check.

  1. 1

    What is kinetic energy?

    Show answerHide answer

    Energy stored in moving objects

  2. 2

    What is the equation for a change in thermal energy?

    Show answerHide answer

    \(\Delta E = mc\Delta\theta\)

  3. 3

    What is temperature a measure of?

    Show answerHide answer

    How hot something is

  4. 4

    What is a system?

    Show answerHide answer

    An object or group of objects

  5. 5

    What is potential energy?

    Show answerHide answer

    Stored energy due to position or bonds

Learning Objectives

  1. 1Define internal energy.
  2. 2Explain how heating changes the energy stored within a system.
  3. 3Use \(\Delta E = mc\Delta\theta\) to calculate the energy for a temperature change.
  4. 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.

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.

Show the solutionHide the solution
  1. 1 Temperature change \(60 - 20 = 40\) °C
  2. 2 Substitute \(\Delta E = 0.50 \times 4200 \times 40\)
  3. 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. 1 Same temperature The particles have the same average kinetic energy
  2. 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.

  • Temperature

    Related to the average kinetic energy of the particles.

  • Internal energy

    The total, including potential energy.

  • Heating

    Increases internal energy by raising temperature or changing state.

  • 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...?

  1. 1Define internal energy.
  2. 2Say heating increases internal energy.
  3. 3Link kinetic energy to temperature.
  4. 4Link potential energy to change of state.
  5. 5Use \(\Delta E = mc\Delta\theta\).
  6. 6Compare two objects.
  7. 7Explain cooling.
  8. 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.

Questions and answers

10 questions set on this lesson, with the mark schemes and model answers open.

1. Exam question State 2 marks Easier

What is meant by the internal energy of a system?

Mark scheme — 2 marks available

  • Total of kinetic energy — 1 mark
  • and potential energy of all the particles — 1 mark

Model answer

The total kinetic energy and potential energy of all the particles that make up the system.

2. Exam question Explain 3 marks Easier

A beaker of water is heated. Explain what happens to the energy stored within the water and to its temperature.

Mark scheme — 3 marks available

  • Internal energy increases — 1 mark
  • Particles gain kinetic energy — 1 mark
  • Temperature rises — 1 mark

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.

3. Exam question Calculate 3 marks Easier

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.

Mark scheme — 3 marks available

  • Temperature change 40 °C — 1 mark
  • Correct substitution — 1 mark
  • 84 000 J — 1 mark

Model answer

\(0.50 \times 4200 \times 40 = 84\,000\) J

4. Exam question Explain 2 marks Easier

1.0 kg of water and 2.0 kg of water are both at 50 °C. Which has more internal energy? Explain your answer.

Mark scheme — 2 marks available

  • 2.0 kg of water — 1 mark
  • More particles so more total energy — 1 mark

Model answer

2.0 kg, because it has twice as many particles at the same average kinetic energy, so its total energy is greater.

5. Exam question Explain 4 marks Easier

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.

Mark scheme — 4 marks available

  • Internal energy increases — 1 mark
  • Potential energy of particles increases — 1 mark
  • Kinetic energy does not increase — 1 mark
  • Temperature stays constant — 1 mark

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.

6. Multiple choice 1 mark Easier

Internal energy is the total of...

  1. A kinetic energy only
  2. B the temperature
  3. C the mass
  4. D kinetic and potential energy of the particles Correct

Why: It includes both.

7. Multiple choice 1 mark Core

Heating a substance...

  1. A increases its internal energy Correct
  2. B decreases it
  3. C does not change it
  4. D removes particles

Why: Energy is transferred to the particles.

8. Multiple choice 1 mark Core

Temperature is related to the particles'...

  1. A potential energy
  2. B average kinetic energy Correct
  3. C colour
  4. D number

Why: Faster particles mean a higher temperature.

9. Multiple choice 1 mark Core

During melting the temperature...

  1. A rises quickly
  2. B falls
  3. C stays constant Correct
  4. D doubles

Why: The energy goes into potential energy.

10. Multiple choice 1 mark Stretch

Which has more internal energy: 1 kg or 2 kg of water at the same temperature?

  1. A 1 kg
  2. B They are equal
  3. C Cannot tell
  4. D 2 kg Correct

Why: There are more particles.