In this chapter, we will develop one of the earliest and most successful theories of matter: the so-called ideal gas theory. This theory envisages a gas as being a collection of molecules whose average kinetic energy is so large that the potential energy of interaction between the molecules is unable to hold them together. This model will probably be familiar, but just in case it is not, Figure 4.1 shows how one imagines the motion of the molecules in a gas.

Figure 4.1. A schematic illustration of the motion of molecules in a gas. The molecules are shown as a central darkly-shaded region, where the electron charge density is high, and a peripheral lightly-shaded region. Although there is no electronic charge in this peripheral region, the electric field there will significantly affect the motion of any other molecules that enter that region. Notice that on average, the distance between the molecules is large compared with the extent of their region of influence. The arrows indicate the velocities of the molecules. Notice that the velocities are randomly oriented and that the length of the velocity vectors is varied, indicating that the molecules have a wide range of speeds.

Ideal gas theory tells us some amazing things are happening in the air around us. It predicts that the average speed of the molecules is around 500 m s-1 and that molecules collide with every square centimetre of the skin on your body roughly 1023 times every second. It also predicts that separation between the molecules is around 3.5 nm compared with the typical separation between molecules in their solid state of around 0.3 nm. As we shall see in Chapter 5, we have every reason to believe these predictions because quantitative explanations of the properties of gases based on the ideal gas model are extraordinarily successful.

§4.2 The ideal gas model: Here we outline the basic assumptions of the ideal gas theory. Importantly these assumptions are approximately true for almost every real gas that we will encounter! Then we derive from first principles an equation that relates the density of an ideal gas to its temperature and pressure

§4.3 Calculating microscopic quantities: In this section we look at some results which allow us to calculate some microscopic properties of gas.

§4.4 Beyond the ideal gas equation: Finally we look at how we can extend the ideal gas theory in order to take account of a more realistic set of assumptions than those we made in §4.2.