# Kinetic Theory of Gases(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## Model of the Kinetic Theory of Gases

• Gases consist of atoms or molecules randomly moving around at high speeds
• The kinetic theory of gases models the thermodynamic behaviour of gases by linking:
• The microscopic properties of particles i.e. mass and speed
• The macroscopic properties of particles i.e. pressure and volume
• The theory is based on a set of the following assumptions:
• Molecules of a gas behave as identical (or all have the same mass)
• Molecules of gas are hard, perfectly elastic spheres
• The volume of the molecules is negligible compared to the volume of the container
• The time of a collision is negligible compared to the time between collisions
• There are no intermolecular forces between the molecules (except during impact)
• The molecules move in continuous random motion
• Newton's laws apply
• There are a very large number of molecules

• The number of molecules of gas in a container is very large, therefore the average behaviour (eg. speed) is usually considered

#### Exam Tip

Make sure to memorise all the assumptions for your exams, as it is a common exam question to be asked to recall them.

## Pressure in the Model of Kinetic Theory of Gases

• A gas is made of a large number of particles
• Gas particles have mass and move randomly at high speeds
• Pressure in a gas is due to the collisions of the gas particles with the walls of the container that holds the gas
• When a gas particle hits a wall of the container, it undergoes a change in momentum due to the force exerted by the wall on the particle (as stated by Newton's Second Law)
• Final momentum = –mv
• Initial momentum = mv

• Therefore, the change in momentum Δp can be written as:

Δp = final momentum – initial momentum

Δp = –mvmv = –2mv

• According to Newton's Third Law, there is an equal and opposite force exerted by the particle on the wall (i.e. F)

A particle hitting a wall of the container in which the gas is held experiences a force from the wall and a change in momentum. The particle exerts an equal and opposite force on the wall

• Since there is a large number of particles, their collisions with the walls of the container give rise to gas pressure, which is calculated as follows:

• Where:
• p = pressure in pascals (Pa)
• F = force in newtons (N)
• A = area in metres squared (m2)

#### Exam Tip

Momentum is a Mechanics topic that should have been covered in a previous unit. The above derivation of change in momentum and resultant force should have already been studied - if you're not comfortable with it then make sure you go back to revise this!

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