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 = –mv – mv = –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!