Kinetic Theory

Basic Assumptions of Kinetic Theory

The kinetic theory explains the behaviour of particles in gases using a simple model based on a few key assumptions:

• Particles are in constant, random motion, moving in all directions at various speeds.
• The volume of the particles themselves is negligible compared to the volume of the gas; most of the gas volume is empty space.
• Collisions between particles, and between particles and the walls of the container, are perfectly elastic. This means no kinetic energy is lost during collisions.
• The temperature of the gas is directly related to the average kinetic energy of its particles. Higher temperature means higher average kinetic energy.

These assumptions allow us to understand and predict how gases behave under different conditions.

Particle Motion and Temperature

Temperature is a measure of the average kinetic energy of particles in a substance. As temperature increases, particles move faster on average.

This means:

• At higher temperatures, particles have more energy and move more quickly.
• At lower temperatures, particles move more slowly.

The kinetic energy (KE) of a particle is proportional to the absolute temperature (measured in kelvin, K):

KE 27 Temperature (K)

Note: The average speed of particles is proportional to the square root of the absolute temperature, while kinetic energy is proportional to the temperature itself.

This explains why heating a gas causes it to expand or increase in pressure:

• If the volume is fixed, faster particles hit the container walls more often and with more force, increasing pressure.
• If the pressure is fixed, the gas expands as particles move faster and push the walls outward.

For example, when air in a bicycle tyre heats up on a sunny day, the pressure inside increases because the particles move faster and collide more forcefully with the tyre walls.

For instance, if the temperature of a gas doubles (in kelvin), the average kinetic energy of its particles also doubles, causing more energetic collisions.

Pressure and Particle Collisions

Pressure in a gas is caused by particles colliding with the walls of their container. Each collision exerts a tiny force on the wall.

The total pressure is the result of many particles hitting the walls per second. Pressure depends on:

• Number of collisions per second: More collisions mean greater pressure.
• Force per collision: Faster particles hit harder, increasing pressure.

If the volume of the container decreases, particles have less space to move, so they collide with the walls more often, increasing pressure.

If temperature increases, particles move faster, increasing both the force and frequency of collisions, so pressure rises.

This relationship between pressure, volume, and temperature is summarised by the gas laws (covered in other topics), but the kinetic theory provides the particle-level explanation.

Example: Calculating the Effect of Temperature on Particle Speed

If the temperature of a gas increases from 300 K to 600 K, by what factor does the average kinetic energy of the particles increase?

Since kinetic energy is proportional to temperature (in kelvin):

$$\frac{\text{KE}_2}{\text{KE}_1} = \frac{T_2}{T_1} = \frac{600}{300} = 2$$

The average kinetic energy doubles, so particles move faster and collide more forcefully with container walls.