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# Kinetic model of matter

## Brownian motion

Brownian motion is the random movement of particles suspended in a fluid (a liquid or a gas).

The discovery of Brownian motion served as important evidence for the kinetic model of matter:

Observation: When viewed through a microscope, particles of smoke or pollen in air do not stand still but instead are in constant motion in jerky randomly changing directions.

Explanation: The air must be made up of many tiny particles which are colliding with the smoke particles. These collisions cause the random motion of the dust particle.

Brownian motion of a big dust particle that collides with a large number of smaller air molecules.
A dust particle undergoing Brownian motion due to collisions with smaller air molecules. The random line is the path taken by the dust particle.

## Particle movement and pressure

A gas in a closed container exerts a pressure on that container.

When a particle in a gas collides with one of the walls of its container it applies a force on the wall. Many particles collide with the walls every second, each applying a small force.

Since pressure is equal to force over area, this results in pressure being applied to the wall.

The pressure on one wall of the container is equal to the $$\dfrac{\Tred{\text{sum of all the forces from collisions of particles with wall}}}{\Tblue{\text{area of wall}}}$$

Because the gas particles move about at random, the pressure exerted by the gas is the same everywhere.

The pressure is higher if:

• The particles collide with the walls of the container more frequently.

• The particles in the gas have more mass or more energy.

Particles in a gas are in constant motion.

## Change in temperature causes change in pressure

A change in temperature of a gas leads to a change in pressure (assuming mass and volume are fixed).

When water in a covered saucepan is allowed to boil, you will find it increasingly difficult to keep the lid on to avoid steam from escaping. This is because the increase in temperature leads to an increase in pressure.

Increasing the temperature of a gas means that the gas particles have more energy and so move faster:

• The gas particles will hit the walls of the container more often.
• On average, gas particle hit the walls with more force.

This increases the pressure of the gas.

Remember, this is only true if the volume and mass of gas do not change.

The pressure of a gas at a constant volume increases as the temperature is increased.

## Change in temperature causes change in volume

A change in temperature of a fixed mass of gas at constant pressure causes a change in volume of the gas.

If you put a balloon filled with air into a freezer, you will notice that it shrinks dramatically as it gets colder.

Increasing the temperature of a gas means that the gas particles move faster.

To keep the pressure constant the gas particles must hit the walls of the container with the same frequency.

This can only happen if the walls of the container are further apart - the volume is increased.

The volume of a gas increases as the temperature is increased at constant pressure.

## Change in volume causes change in pressure

A change in volume of a fixed mass of gas at constant temperature causes a change in pressure of the gas.

The bubbles exhaled by a scuba diver grow as they approach the surface of the ocean.

The pressure exerted by the water decreases nearer the surface, so the volume of the bubbles increases as they rise.

Increasing the volume of a gas means that the walls of the container are further apart.

If the temperature is constant, this means that the gas particles travel at the same speed.

This means that the gas particles will collide with the walls of the container less frequently. This leads to a decrease in pressure.

The pressure of a gas decreases as the volume is increased at constant temperature.