Internal Energy and Particle Motion

This lesson covers internal energy and its relationship to particle motion as required by the AQA GCSE Physics specification (4.3.2). Understanding internal energy is essential for explaining how heating a substance affects its temperature and state. Internal energy is a key concept that links the particle model to thermal energy transfers.

---

What Is Internal Energy?

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

Internal energy = total kinetic energy + total potential energy of all particles

• Kinetic energy of particles: the energy associated with the movement (vibration, rotation, translation) of particles. The faster the particles move, the greater their kinetic energy.
• Potential energy of particles: the energy associated with the forces of attraction (bonds) between particles. This depends on the distances between particles and the strength of the forces holding them together.

Exam Tip: Internal energy is NOT the same as temperature. Temperature is related to the AVERAGE kinetic energy of particles. Internal energy is the TOTAL of all kinetic and potential energies of ALL particles. A large, cold object can have more internal energy than a small, hot object because it contains more particles.

---

How Heating Affects Internal Energy

When a substance is heated, energy is transferred to its particles. This increases the internal energy of the system. However, the way the internal energy increases depends on whether the substance is changing temperature or changing state.

Heating Without a Change of State

When you heat a substance and its temperature rises (no change of state):

• The particles gain kinetic energy — they vibrate faster (in solids) or move faster (in liquids and gases).
• The kinetic energy of the particles increases.
• The potential energy of the particles stays roughly the same (the spacing between particles does not change significantly).
• The temperature increases because temperature is a measure of the average kinetic energy of the particles.

Heating During a Change of State

When you heat a substance at its melting point or boiling point (during a change of state):

• The particles gain potential energy — the energy goes into breaking or weakening the forces of attraction between particles.
• The kinetic energy of the particles stays the same.
• The temperature stays constant even though energy is being transferred to the substance.
• The spacing between particles increases as bonds are broken.

graph TD
    A["Energy is transferred<br/>to the substance"] --> B{"Is the substance<br/>changing state?"}
    B -->|"No"| C["Kinetic energy of<br/>particles increases"]
    B -->|"Yes"| D["Potential energy of<br/>particles increases"]
    C --> E["Temperature rises"]
    D --> F["Temperature stays<br/>constant"]
    C --> G["Particles move/<br/>vibrate faster"]
    D --> H["Bonds between<br/>particles break"]

    style A fill:#2c3e50,color:#fff
    style B fill:#f39c12,color:#fff
    style C fill:#27ae60,color:#fff
    style D fill:#e74c3c,color:#fff
    style E fill:#27ae60,color:#fff
    style F fill:#e74c3c,color:#fff
    style G fill:#27ae60,color:#fff
    style H fill:#e74c3c,color:#fff

Exam Tip: A favourite exam question is: "Explain why the temperature of a substance does not change during melting even though it is being heated." The key answer is that the energy supplied is used to increase the POTENTIAL energy of the particles (overcoming forces of attraction / breaking bonds between particles) rather than increasing their KINETIC energy. Since temperature is related to kinetic energy, the temperature stays the same.

---

Temperature and Kinetic Energy

Temperature is a measure of the average kinetic energy of the particles in a substance.

• When the temperature of a substance increases, the average kinetic energy of its particles increases.
• When the temperature decreases, the average kinetic energy decreases.
• At absolute zero (-273 degrees C or 0 K), the particles have the minimum possible kinetic energy — they have virtually no movement (though quantum mechanics tells us they retain some zero-point energy).

The Kelvin Temperature Scale

The Kelvin scale starts at absolute zero (0 K), where particles have the minimum kinetic energy.

Temperature	Celsius (degrees C)	Kelvin (K)
Absolute zero	-273	0
Water freezes	0	273
Water boils	100	373
Room temperature	~20	~293

To convert between the scales:

• K = degrees C + 273
• degrees C = K - 273

---

Particle Motion in Each State

State	Type of Particle Motion	Average Kinetic Energy	Forces Between Particles
Solid	Particles vibrate around fixed positions	Low	Strong forces hold particles in a regular pattern
Liquid	Particles move around each other, sliding past one another	Medium	Weaker forces than in a solid — particles are close but not in fixed positions
Gas	Particles move rapidly and randomly in all directions	High	Very weak forces — particles are far apart and move independently

Energy Distribution in Particles

At any given temperature, not all particles in a substance have the same kinetic energy. Instead, there is a distribution of energies:

• Some particles move faster than average (higher kinetic energy).
• Some particles move slower than average (lower kinetic energy).
• The temperature corresponds to the average kinetic energy of all the particles.

This distribution of energies is important for understanding evaporation — the fastest-moving particles at the surface of a liquid have enough energy to escape as gas, even below the boiling point.

---

Changes in Internal Energy During State Changes

Process	Change in Kinetic Energy	Change in Potential Energy	Change in Temperature
Heating a solid (below melting point)	Increases	No significant change	Increases
Melting (at melting point)	No change	Increases	No change (constant)
Heating a liquid (between melting and boiling point)	Increases	No significant change	Increases
Boiling (at boiling point)	No change	Increases	No change (constant)
Heating a gas (above boiling point)	Increases	No significant change	Increases
Cooling / Freezing / Condensation	Decreases / No change	No change / Decreases	Decreases / No change

---

Heating Curve Revisited with Internal Energy

graph LR
    subgraph Heating_Curve["Heating Curve"]
        A["Solid<br/>Heating<br/>(KE increases)"] --> B["Melting<br/>(PE increases,<br/>KE constant)"]
        B --> C["Liquid<br/>Heating<br/>(KE increases)"]
        C --> D["Boiling<br/>(PE increases,<br/>KE constant)"]
        D --> E["Gas<br/>Heating<br/>(KE increases)"]
    end

    style A fill:#3498db,color:#fff
    style B fill:#9b59b6,color:#fff
    style C fill:#2ecc71,color:#fff
    style D fill:#9b59b6,color:#fff
    style E fill:#e74c3c,color:#fff

During the flat sections (melting and boiling):

• Energy is supplied but temperature does not change.
• The energy is being used to overcome intermolecular forces (increase potential energy).
• The internal energy increases because the potential energy component increases.