Gas Pressure and Temperature

This lesson covers the relationship between gas pressure and temperature as required by the AQA GCSE Physics specification (4.3.3). Understanding how gas particles create pressure and how temperature affects gas pressure is essential for explaining everyday phenomena such as why tyres expand in hot weather and why pressure cookers work.

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What Is Gas Pressure?

Gas pressure is caused by the collisions of gas particles with the walls of their container. Gas particles are in constant random motion — they move rapidly in all directions. When these particles collide with the walls of the container, they exert a force on the walls. The total effect of billions of these tiny collisions per second creates a measurable pressure.

Pressure is defined as the force per unit area:

pressure = force / area

p = F / A

Where:

• p = pressure, measured in pascals (Pa) or newtons per square metre (N/m2)
• F = force, measured in newtons (N)
• A = area, measured in square metres (m2)

1 Pa = 1 N/m2

Exam Tip: When explaining gas pressure, always refer to COLLISIONS of gas particles with the WALLS of the container. Saying "particles push against the walls" is not precise enough — it is the collisions of the moving particles that create the force, and therefore the pressure.

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How Gas Particles Create Pressure

graph TD
    A["Gas particles move<br/>randomly at high speed"] --> B["Particles collide with<br/>the walls of the container"]
    B --> C["Each collision exerts a<br/>tiny force on the wall"]
    C --> D["Billions of collisions<br/>per second"]
    D --> E["The total force per unit area<br/>= GAS PRESSURE"]

    style A fill:#2c3e50,color:#fff
    style B fill:#2980b9,color:#fff
    style C fill:#e67e22,color:#fff
    style D fill:#27ae60,color:#fff
    style E fill:#8e44ad,color:#fff

Key points about gas pressure:

• Gas particles move in straight lines between collisions.
• The particles collide with each other and with the walls of the container.
• The collisions are elastic — no kinetic energy is lost during collisions.
• The more frequent the collisions and the harder (more forceful) each collision, the greater the pressure.

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The Effect of Temperature on Gas Pressure

When the temperature of a gas in a sealed container (constant volume) increases:

1. The particles gain kinetic energy — they move faster.
2. The particles collide with the walls more frequently (more collisions per second).
3. Each collision is more forceful because the particles are moving faster.
4. The combination of more frequent and more forceful collisions means the pressure increases.

Conversely, when the temperature decreases:

1. The particles lose kinetic energy — they move slower.
2. Collisions with the walls become less frequent and less forceful.
3. The pressure decreases.

Key Relationship

For a fixed mass of gas at constant volume:

• Increasing temperature → Increasing pressure
• Decreasing temperature → Decreasing pressure

This is a directly proportional relationship when temperature is measured in Kelvin:

p / T = constant (for a fixed mass of gas at constant volume)

or equivalently:

p1 / T1 = p2 / T2

Exam Tip: The relationship between pressure and temperature is only directly proportional when temperature is measured in KELVIN (not Celsius). If a gas at 300 K has its temperature doubled to 600 K, its pressure also doubles (assuming constant volume). Always convert Celsius to Kelvin before using this relationship.

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Temperature in Kelvin

To use the pressure-temperature relationship, temperatures must be in Kelvin (K):

K = degrees C + 273

Temperature	Celsius	Kelvin
Absolute zero	-273	0
Freezing point of water	0	273
Room temperature	20	293
Boiling point of water	100	373
Oven temperature	200	473

Why Must We Use Kelvin?

The relationship between pressure and temperature is only proportional when using the Kelvin scale because:

• At absolute zero (0 K), particles have the minimum possible kinetic energy, and the pressure would theoretically be zero (the particles would have no movement to cause collisions).
• The Kelvin scale starts at this true zero point, making it a ratio scale where "double the temperature" genuinely means "double the average kinetic energy."

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Worked Examples

Worked Example 1

A sealed container of gas is at 300 K and has a pressure of 100,000 Pa. The gas is heated to 600 K. Calculate the new pressure. (Volume remains constant.)

Step 1: Write the known values: p1 = 100,000 Pa, T1 = 300 K, T2 = 600 K

Step 2: Use p1 / T1 = p2 / T2

Step 3: Rearrange: p2 = p1 x T2 / T1

Step 4: Substitute: p2 = 100,000 x 600 / 300

Step 5: Calculate: p2 = 200,000 Pa

The temperature doubled (from 300 K to 600 K), so the pressure doubled (from 100,000 Pa to 200,000 Pa).

Worked Example 2

A gas in a sealed container has a pressure of 150,000 Pa at 27 degrees C. It is cooled to -23 degrees C. Calculate the new pressure.

Step 1: Convert temperatures to Kelvin: T1 = 27 + 273 = 300 K, T2 = -23 + 273 = 250 K

Step 2: Use p1 / T1 = p2 / T2

Step 3: Rearrange: p2 = p1 x T2 / T1

Step 4: Substitute: p2 = 150,000 x 250 / 300

Step 5: Calculate: p2 = 125,000 Pa

Exam Tip: A very common mistake in gas pressure calculations is forgetting to convert Celsius to Kelvin. ALWAYS convert temperatures to Kelvin FIRST, before substituting into any equation. If you use Celsius, your answer will be wrong and you will lose all the marks for the calculation.

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Real-Life Applications

Application	Explanation
Tyre pressure increases in hot weather	The air inside the tyre is heated by the road and friction. The particles move faster, collide more frequently and with more force, increasing the pressure.
Aerosol cans warning: do not heat	Heating the can increases the pressure of the gas inside. If the pressure becomes too great, the can may explode.
Pressure cookers	The sealed lid traps steam, increasing the pressure inside. At higher pressure, water boils at a higher temperature, so food cooks faster.
Hot air balloons	Heating the air inside the balloon causes it to expand (particles move further apart). The hot air is less dense than the cooler air outside, so the balloon rises.
Car engines	In the combustion chamber, fuel burns and rapidly heats the gas. The gas pressure increases dramatically, pushing the piston down and driving the engine.

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