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PARTICLE MODEL OF MATTER · CHAPTER 5 OF 10

​Particles and states of matter

Why can a whole jug of water have more internal energy than a small glass at the same temperature? And why can ice absorb energy while melting without getting warmer? In this chapter, you’ll explore how energy is stored by particles and discover why internal energy and temperature are different quantities.

By the end, you’ll be able to…

  • Define internal energy in terms of particle kinetic and potential energy.
  • Explain how temperature relates to average particle kinetic energy.
  • Explain why two samples at the same temperature can have different internal energies.
  • Describe how heating and cooling change a substance’s internal energy.
  • Explain why internal energy can change during a change of state while temperature stays constant.

What is internal energy?

A system is the object or substance we choose to study, such as the water in a glass.

Its internal energy is the total kinetic energy and potential energy of all its particles.

Kinetic energy is associated with movement. Particles in liquids and gases move from place to place. Particles in solids also have kinetic energy because they vibrate about fixed positions.

Potential energy is associated with the particles’ positions and the interactions between them. Changing their arrangement or separation can change this energy.

Internal energy is measured in joules (J).

Kinetic energy

A particle vibrating in a solid One pink particle moves a small distance to either side of its fixed position. A stationary marker underneath shows the fixed position. The particle stays the same size. Fixed position

Vibrating about a fixed position

Particles have kinetic energy because they move. In a solid, they vibrate about fixed positions.

One enlarged particle is shown. Its movement is exaggerated; its size stays unchanged.

Potential energy

The same two attracting particles before and after separation The upper view shows particles A and B close together. A downward arrow indicates energy transferred to separate them. The lower view shows the same particles farther apart, with greater particle potential energy. Before · Close together A B Energy transferred to separate them A B After · Farther apart

Greater particle potential energy

Separating attracting particles requires energy. Their potential energy increases.

A and B identify the same two particles in both views. This is a simplified model of separation, not a diagram of melting ice.

Internal energy = total particle kinetic energy + total particle potential energy

What does temperature tell us?

In the GCSE particle model, temperature is related to the average kinetic energy of the particles.

Temperature is commonly measured in degrees Celsius (°C), whereas internal energy is measured in joules (J).

At a higher temperature, the particles have greater average kinetic energy. In a solid, they vibrate more vigorously about their fixed positions.

The word “average” matters: particles do not all have exactly the same kinetic energy.

Heating transfers energy into a system. If this raises its temperature, the particles’ average kinetic energy increases.

Predict before you reveal

A solid is warmed without melting. What happens to its particles: do they grow larger, stop vibrating or vibrate more vigorously?

Look inside a warming solid

Make your prediction, then tick the box to reveal the warmer solid.

20°C 40°C

The particles already vibrate at 20°C.

At 40°C, the particles vibrate more vigorously. Their average kinetic energy is greater. They remain the same size and still vibrate about fixed positions.

Enlarged model: vibration is exaggerated. Each animation runs briefly, then stops. Untick and tick again to replay the warmer model.

Same temperature, same internal energy?

Temperature tells us about average particle kinetic energy. Internal energy includes the total kinetic and potential energy of all the particles.

Imagine a small glass and a large jug containing water at 20°C. Their particles have the same average kinetic energy, but the jug contains more water particles.

For the same substance in the same state at the same temperature, a larger sample has greater total internal energy.

A temperature reading alone therefore cannot tell us how much internal energy a sample has.

Which water sample has greater internal energy?

Both samples contain liquid water at 20°C. Choose your prediction.

Sample A · 100g

20°C

Sample B · 200g

20°C

Enlarged models: each dot represents the same large number of water molecules. Sample B contains twice as many molecules.

Which sample has greater internal energy?

Try again. Both samples have the same temperature, but Sample A contains fewer water particles.

Correct. Sample B contains more water particles. At the same temperature and in the same state, this larger sample has greater total internal energy.

Equal temperatures mean equal average particle kinetic energies here. They do not mean equal total internal energies.

Does heating always raise the temperature?

Heating transfers energy from a hotter object or region to a cooler one. Energy is transferred; heating does not mean that a substance called “heat” enters the object.

When energy transferred into a substance raises its temperature, its particles gain average kinetic energy.

However, energy transfer can also produce a change of state.

During melting or boiling of a pure substance at constant pressure, its internal energy increases while its temperature stays constant.

During melting, the transferred energy changes the particles’ arrangement and interactions, increasing their potential energy. During boiling, energy is needed to separate particles against attractive forces. In both cases, their average kinetic energy stays constant while the pure substance changes state at constant pressure.

For water, melting and boiling do not break the water molecules apart. The molecules remain water molecules.

Follow the energy

Imagine heating pure ice from −10°C until it has completely melted. Before revealing each stage below, predict whether the temperature will rise or stay constant.

Energy enters. What changes?

Predict what happens to the temperature and particles, then select each stage to explore.

−10°C · Solid ice −10°C −5°C 0°C Warming to its melting point 0°C Constant throughout melting

What you see

Ice stays solid as it warms. During melting, the cube becomes smaller as liquid water forms around it.
The ice is solid. Energy enters. The ice remains solid. Energy enters. Ice becomes liquid water.

Enlarged particle model

Gentle vibration about fixed positions. More vigorous vibration about fixed positions. A closer, irregular arrangement. Particles can move past one another.

Temperature: The ice starts at −10°C.

Particle movement: Its particles already vibrate about fixed positions.

Energy: The ice has internal energy: the total kinetic and potential energy of its particles.

Temperature: Rises from −10°C to 0°C.

Particle movement: The particles vibrate more vigorously. Their size stays unchanged and they remain in the solid arrangement.

Energy: Average particle kinetic energy increases. The ice’s internal energy increases.

Temperature: Stays at 0°C throughout melting.

Particle arrangement: Particles leave their fixed positions and become able to move past one another. The same water molecules remain.

Energy: Particle potential energy increases, while average kinetic energy stays constant. Internal energy increases.

Water is unusual: its particles become more closely packed when ice melts. Potential energy depends on their interactions and arrangement, not just their average separation.

Once all the ice has melted, further heating can raise the liquid water’s temperature.

Pure water at normal atmospheric pressure. Particle arrangements are simplified two-dimensional models, not molecular structures. Movement is exaggerated and animation speeds are illustrative. Animations stop after a few seconds; choose another stage and return to replay.

What happens when a substance cools?

When energy is transferred out of a substance and its temperature falls, its particles’ average kinetic energy decreases.

During freezing of a pure substance at constant pressure, energy is transferred out while the temperature stays constant. Particle potential energy decreases as the solid arrangement forms.

During condensation, particle potential energy also decreases as energy is transferred to the surroundings.

The particles continue to vibrate in the solid. Freezing does not mean that particle movement stops.

INTERACTIVE QUICK CHECK

Check your understanding

Choose one answer for each question. You can change your answers.
1 What is the internal energy of a system?
Not quite. This is related to temperature. Internal energy includes the total kinetic and potential energy of all the particles.
Correct. Internal energy includes both contributions from all the particles in the system.
Not quite. Internal energy is measured in joules. Temperature is a different quantity, commonly measured in degrees Celsius.
2 Two samples contain liquid water at 25°C. Sample A has a mass of 100g; Sample B has a mass of 300g. Which statement is correct?
Not quite. Equal temperatures do not mean equal internal energies. Sample B contains more water particles.
Not quite. Both temperatures are 25°C. A larger mass does not automatically mean a higher temperature.
Correct. For the same substance in the same state at the same temperature, the larger sample has greater total internal energy.
3 Pure water boils at 100°C at constant normal atmospheric pressure. What happens to the particles as energy is transferred to change liquid water into water vapour?
Correct. Energy is needed to separate the water molecules against attractive forces, increasing their potential energy. Their average kinetic energy stays constant because the temperature remains at 100°C during boiling.
Not quite. At constant normal atmospheric pressure, the temperature stays at 100°C while pure water boils. The transferred energy increases particle potential energy rather than average kinetic energy.
Not quite. Boiling is a physical change. The water molecules remain water molecules; energy is needed to separate them, not to break them apart.
INTERACTIVE CHALLENGE

A student says, “The ice stayed at 0°C while it melted, so its internal energy did not change.” Explain why the student is wrong.

Consider both kinetic energy and potential energy. Assume pure ice melts at constant normal atmospheric pressure.

Internal energy includes the total kinetic and potential energy of all the particles.

The constant temperature means that the particles’ average kinetic energy stays constant during melting.

However, energy is transferred into the ice and increases the particles’ potential energy as the solid arrangement changes. Its internal energy therefore increases, even though its temperature does not.

CHAPTER 5

Chapter summary

  • Internal energy is the total kinetic and potential energy of all the particles in a system. It is measured in joules (J).
  • Particle kinetic energy is associated with movement, including vibration in solids. Particle potential energy is associated with positions and interactions.
  • Temperature is related to average particle kinetic energy, rather than total internal energy.
  • For the same substance in the same state at the same temperature, a larger sample has greater internal energy.
  • Heating transfers energy into a system. This can raise its temperature or produce a change of state.
  • During melting or boiling of a pure substance at constant pressure, potential energy and internal energy increase while temperature stays constant.
  • During freezing at constant pressure, particle potential energy decreases. Particles continue to vibrate in the solid.