2. The kinetic theory of matter
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What is the kinetic theory? P.8
The kinetic theory of matter is, in its essence, quite a simple theory. However, like all good models in physics, it has enormous predicting power. It is so effective at predicting the behaviour of matter that it is now accepted as absolute truth.

In this unit, we will look at the basic ideas of the kinetic theory and move on to relating the model to mathematical predictions and explanations of behaviour in the gas laws.

Vibrating solid lattice
Picture 2.1 Lattice of particles. The particles vibrate.
Kinetic theory – the basics
We think that all matter is made of particles. There are forces between these particles and these forces hold the particles together (in solids and liquids). However, the particles are also moving. The higher the temperature of a material, the more its internal energy and the more energy its particles have. In a solid, this means they vibrate more vigorously; in liquids and gases, it means they move faster.
A particle oscillator
Picture 2.2 Single particle on spring oscillator

Solid energies
Particles in a solid are vibrating. It is as though each one is an oscillator on a spring. This means that a particle can have kinetic energy (because it is moving) and elastic potential energy – stored in the springy bond when it is stretched.
A simple oscillator will have its maximum kinetic energy as it moves through its equilibrium position (this is where it moves fastest). However, it will then lose this kinetic energy and gain potential energy as its bonds are stretched again. The total energy of the oscillator is the sum of its kinetic energy and elastic potential energy. At any time, the total energy is a constant (picture 2.2).
Graph of KE and PE for an oscillator
Picture 2.3 Graph of elastic potential energy for single oscillator. The EPE forms a 'potential well' that traps the particle. When the oscillator is in a lattice, the graph changes shape. As the oscillator gains total energy, the particle can eventually break free of the well.

A group of particles
However, this picture is more involved for a solid with billions of particles. They are constantly transferring energy between each other. So the total internal energy of the solid is the sum of all the kinetic energies and potential energies of all the particles. At any given time, we couldn’t say whether the energy is mainly kinetic energy or elastic potential energy. Neither could we say which particles have how much energy. The total internal energy of the solid is randomly distributed between KE and EPE and also randomly shared amongst all the particles.

As the internal energy of the solid increases, the average maximum elastic potential energy of the oscillators goes up. Eventually, they have enough EPE to break their bonds. The solid will begin to melt. Whilst it is melting, any extra internal energy is used to break bonds and the temperature stops going up.

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Question 6
a) We sometimes refer to a bond as a ‘potential well’. What do we mean by this phrase?

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b) How does a potential well bind particles in place?

Summary                                           Close
  • the kinetic theory says that all matter is made of particles
  • there are forces between the particles
  • the particles can have kinetic energy or, when bound, elastic potential energy
  • solid particles vibrate more as the solid heats up