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6.4 Internal Energy

GCSE Physics · AQA · Chapter 6: Molecules and Matter

A free GCSE Physics lesson for AQA (8463) from OBA School: kinetic and potential energy of particles, heating and changes of state, forces between particles, gas pressure. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define internal energy as the total kinetic and potential energy of the particles in a system
  • Explain that heating a substance raises its internal energy, which either raises its temperature or changes its state
  • Use ΔE = m c Δθ to calculate a change of internal energy when the temperature changes
  • Explain the properties of solids, liquids and gases using the forces between their particles
  • Explain in terms of particles why a gas exerts a pressure, and why heating a sealed gas raises its pressure

Key words

  • Internal energy: The total energy stored by the particles of a system: the sum of their kinetic and potential energies.
  • Kinetic energy (of particles): Energy due to the particles’ individual motion. More kinetic energy means a higher temperature.
  • Potential energy (of particles): Energy due to the particles’ positions relative to each other, linked to the forces between them.
  • Specific heat capacity (c): The energy needed to raise the temperature of 1 kg of a substance by 1 °C.
  • Forces of attraction: Forces between particles that hold them together. Strong in solids, weaker in liquids, almost zero in gases.
  • Gas pressure: The force per unit area caused by gas particles hitting a surface.

What is internal energy?

The particles in any substance are always moving, and there are forces between them. So the particles store energy in two ways:

Internal energy is the total energy stored by all the particles because of their individual motions and positions. It does not include the kinetic energy of the whole object moving, or its gravitational potential energy. A cold football kicked at high speed has lots of kinetic energy, but its internal energy is no bigger than when it sits still.

Heating changes internal energy

Heating a substance transfers energy to its particles, so its internal energy increases. This does one of two things:

  • the temperature rises; Which particle energy rises? kinetic energy – the particles move or vibrate faster; Example soup warming in a pan
  • the substance changes state (melts or boils); Which particle energy rises? potential energy – particles are pulled further apart, breaking bonds; Example ice melting at 0 °C

Cooling does the opposite: the internal energy falls. When a liquid freezes, its temperature stays constant while the potential energy of its particles decreases.

Exam tip: Temperature is linked to the average kinetic energy of the particles. Internal energy is the total of all kinetic and potential energy. A bath of warm water has far more internal energy than a cup of boiling water.

Calculating a change in internal energy

If there is no change of state, the increase in internal energy is the energy needed to raise the temperature:

ΔE = m c Δθ

ΔE = change in internal energy (thermal energy) in joules (J)

m = mass in kilograms (kg)

c = specific heat capacity in joules per kilogram per degree Celsius (J/kg °C)

Δθ = temperature change in degrees Celsius (°C)

Worked example: heating water for tea

0.50 kg of water is heated from 20 °C to 80 °C. c of water = 4200 J/kg °C.
Δθ = 80 − 20 = 60 °C
ΔE = m c Δθ = 0.50 × 4200 × 60 = 126 000 J

Answer: the internal energy increases by 126 000 J (126 kJ)

Worked example: finding a temperature rise

A 2.0 kg aluminium block gains 36 000 J of energy. c of aluminium = 900 J/kg °C.
Δθ = ΔE ÷ (m c) = 36 000 ÷ (2.0 × 900)

Answer: Δθ = 20 °C

Forces between particles explain the states

  • Solid; Forces between particles strong; hold particles in fixed positions in a 3D structure; What this means particles vibrate about fixed positions, so the solid has a fixed shape. Heated enough, the particles break free: it melts (or sublimes).
  • Liquid; Forces between particles weaker; not strong enough to keep a rigid structure; What this means particles move around each other, so liquids flow. The forces stop most particles leaving – only the most energetic escape from the surface (evaporation).
  • Gas; Forces between particles so weak they are negligible; What this means particles move fast in random directions, colliding with each other and the walls, and spread out to fill the container.

Why a gas exerts a pressure

Gas molecules move at high speed in random directions. When a molecule hits a wall, it changes direction and exerts a small force on the wall. The total force from all the impacts on each square metre is the gas pressure.

If a sealed gas is heated, its molecules gain kinetic energy and move faster on average. They hit the walls more often and with more force, so the pressure increases.

Common mistakes

  • Saying internal energy is the same as temperature. Temperature depends on the average kinetic energy; internal energy is the total kinetic + potential energy.
  • Thinking internal energy stays the same while ice melts because the temperature is constant. The potential energy of the particles is increasing, so the internal energy rises.
  • Including the movement or height of the whole object in internal energy.
  • Forgetting to work out Δθ as a difference (final − initial temperature) before using ΔE = m c Δθ.

Revision questions

Try these, then check your answers below each one.

Question 1. What is the internal energy of a substance? (Choose from: The total kinetic and potential energy of all its particles, The temperature of the substance, The kinetic energy of the whole object as it moves, The energy stored in the chemical bonds of its fuel.)

Answer: The total kinetic and potential energy of all its particles

Working: Internal energy is the total energy stored by the particles: the sum of their kinetic energies (motion) and potential energies (positions/forces between them).

Question 2. True or false? When ice melts at 0 °C, its internal energy stays the same because its temperature does not change.

Answer: False

Working: False. Energy is still being supplied. The potential energy of the particles increases as the bonds are broken, so the internal energy increases.

Question 3. 2.0 kg of water is heated so that its temperature rises by 15 °C. The specific heat capacity of water is 4200 J/kg °C. Calculate the increase in its internal energy.

Answer: 126000 J

Working: ΔE = 2.0 × 4200 × 15 = 126 000 J.

Related lessons

Continue in the full course

This lesson is section 6.4 (AGCPH0604) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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