Particle Model and Pressure [H]

This lesson provides a deeper exploration of how the particle model explains gas pressure and how changes in temperature and volume affect pressure, as required by the AQA GCSE Physics specification (4.3.3). This is Higher Tier only content, labelled [H]. You need to be able to explain pressure changes in terms of the motion and collisions of gas particles, linking kinetic energy, temperature, volume, and pressure together.

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The Particle Model of a Gas

The particle model (sometimes called the kinetic theory of gases) describes gas behaviour in terms of the motion of its particles. The key assumptions are:

1. A gas consists of a very large number of tiny particles (atoms or molecules) in constant random motion.
2. The particles move in straight lines between collisions.
3. The collisions between particles, and between particles and the walls, are elastic — no kinetic energy is lost.
4. The volume of the particles themselves is negligible compared to the volume of the container.
5. There are no forces of attraction between gas particles (except during collisions).
6. The pressure of the gas is caused by the collisions of the particles with the walls of the container.

graph TD
    A["Gas particles in<br/>constant random motion"] --> B["Particles collide with<br/>container walls"]
    A --> C["Particles collide<br/>with each other"]
    B --> D["Each collision exerts<br/>a tiny force on the wall"]
    D --> E["Billions of collisions<br/>per second create<br/>measurable PRESSURE"]
    C --> F["Collisions are elastic:<br/>no KE lost"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#3498db,color:#fff
    style D fill:#e67e22,color:#fff
    style E fill:#e74c3c,color:#fff
    style F fill:#27ae60,color:#fff

Exam Tip: When explaining gas pressure using the particle model, always include these key phrases: "particles in constant random motion", "collisions with the walls", and "force per unit area". These are the phrases examiners look for. Do NOT say particles "push" against the walls — they COLLIDE with the walls.

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Factors That Affect Gas Pressure [H]

The pressure of a gas depends on three factors:

Factor	Effect on Pressure	Explanation Using Particle Model
Temperature (at constant volume)	Higher temperature = higher pressure	Particles move faster, collide with walls more frequently and with more force
Volume (at constant temperature)	Smaller volume = higher pressure	Same number of particles in a smaller space = more frequent collisions with walls
Number of particles (at constant T and V)	More particles = higher pressure	More particles = more collisions with the walls per second

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Explaining Pressure Changes with Temperature [H]

When a gas in a sealed container (fixed volume) is heated:

graph LR
    subgraph Before_Heating["Before Heating<br/>(Lower Temperature)"]
        BH1["Particles move slowly"]
        BH2["Fewer collisions"]
        BH3["Less forceful collisions"]
        BH4["Lower pressure"]
    end
    subgraph After_Heating["After Heating<br/>(Higher Temperature)"]
        AH1["Particles move faster"]
        AH2["More frequent collisions"]
        AH3["More forceful collisions"]
        AH4["Higher pressure"]
    end

    Before_Heating -->|"Heat<br/>energy<br/>added"| After_Heating

    style Before_Heating fill:#3498db,color:#fff
    style After_Heating fill:#e74c3c,color:#fff

Step-by-step explanation (for a 6-mark answer):

1. The gas is heated, so energy is transferred to the gas particles.
2. The kinetic energy of the particles increases — they move faster.
3. The faster-moving particles collide with the walls of the container more frequently (more collisions per second).
4. Each collision is more forceful because the particles have greater momentum (momentum = mass x velocity, and velocity has increased).
5. The total force exerted on the walls increases.
6. Since pressure = force / area, and the area of the walls is constant (the container is rigid), the pressure increases.

Exam Tip: In a 6-mark "explain" question about gas pressure and temperature, you need to provide a CHAIN OF REASONING. Start with the energy input, explain the effect on particles (faster speed, more kinetic energy), link to collisions (more frequent, more forceful), then conclude with the effect on pressure. Each link in the chain can earn a mark.

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Explaining Pressure Changes with Volume [H]

When the volume of a gas is decreased at constant temperature:

Step-by-step explanation:

1. The same number of gas particles are now contained in a smaller space.
2. The temperature has not changed, so the particles still have the same average kinetic energy and move at the same average speed.
3. However, the particles now have less distance to travel before hitting a wall.
4. This means the particles collide with the walls more frequently (more collisions per second).
5. Each collision has the same force (because the speed is unchanged).
6. But the total force per second on the walls increases because of the higher collision frequency.
7. Since pressure = force / area, and the increased collision frequency increases the force, the pressure increases.

Key Distinction

When Temperature Increases (constant volume)	When Volume Decreases (constant temperature)
Particles move faster	Particles move at the same speed
Collisions are more frequent AND more forceful	Collisions are more frequent but the same force per collision
Both effects increase pressure	Only frequency effect increases pressure

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Combining Temperature and Volume Effects [H]

In real situations, both temperature and volume might change simultaneously. The general gas relationship combines both effects:

For a fixed mass of gas:

p1 x V1 / T1 = p2 x V2 / T2

(This is the combined gas law, though at GCSE you are more likely to deal with one variable at a time.)

Quick Reference: Gas Laws Summary [H]

Law	Constant	Relationship	Equation
Pressure-Temperature	Volume and mass	p is proportional to T	p1 / T1 = p2 / T2
Boyle's Law (Pressure-Volume)	Temperature and mass	p is inversely proportional to V	p1 x V1 = p2 x V2
Charles's Law (Volume-Temperature)	Pressure and mass	V is proportional to T	V1 / T1 = V2 / T2

Exam Tip: At GCSE, you are most likely to be tested on Boyle's Law (p x V = constant) and the pressure-temperature relationship (p / T = constant) separately. However, you should be aware that both involve the same gas particles and the same particle model explanation. The key difference is whether kinetic energy changes (temperature change) or remains constant (volume change).

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Pressure and the Weight of the Atmosphere

Atmospheric pressure is caused by the weight of the air above the surface. At sea level, the atmospheric pressure is approximately 101,325 Pa (about 100,000 Pa or 100 kPa).

Altitude	Atmospheric Pressure	Explanation
Sea level	~101,000 Pa	Maximum column of air above
Mountain top (e.g. 3000 m)	~70,000 Pa	Less air above — thinner atmosphere
Edge of space (~100 km)	~1 Pa	Almost no air above

As altitude increases:

• There are fewer air molecules above the surface.
• The weight of the air column above is less.
• The atmospheric pressure decreases.

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Particle Model Explains Atmospheric Pressure [H]

The particle model explains atmospheric pressure as follows: