Ideal Gas and Real Gas

A gas that obeys the ideal gas equation $PV = nRT$ at every pressure and every temperature is called an ideal gas. A defining feature of the ideal gas model is that intermolecular interactions are completely absent -- the molecules are treated as not attracting or repelling one another at all except during the instant of a collision.

No real gas is truly ideal in this strict sense, because real molecules genuinely do interact with each other. However, if the molecules of a real gas are far enough apart that these interactions become negligible, the real gas is said to be in the ideal state, and it then behaves essentially like an ideal gas. This happens at sufficiently low density -- in practice, at low pressure or high temperature, where molecules are spread far apart and rarely feel each other's presence, provided the temperature stays well above the gas's liquefaction point. The ideal gas is therefore best thought of as a model, useful for predicting the properties of a real gas whenever that real gas happens to be in its ideal state (deviations of real gases from this ideal behaviour are studied in more detail in Chemistry).

Physically, the molecules of a gas are dispersed essentially uniformly throughout whatever volume contains them (Fig. 3.1(a)), and each molecule executes continuous, random motion, tracing out a jagged, unpredictable path (Fig. 3.1(b)). As one molecule approaches another, a short-range repulsive force acts between them, so that -- to a good approximation -- the molecules behave like small, hard, elastic spheres: when they meet, they undergo an elastic collision, in which both the speed and the direction of each molecule can change abruptly, but the total kinetic energy of the colliding pair is conserved. Molecules also collide with the walls of their container. Crucially, molecules exert force on one another only during the brief instant of a collision -- between two successive collisions, a molecule travels in a straight line at constant velocity. …