At first it sounds a bit odd. An ideal gas sounds like a gas that does not exist. Actaully, we can treat any gas as an ideal gas in the limit of low density (low pressure). Since the assumptions of an ideal gas are: 1. no intermolecular interactions and 2. no finite size of the molecules, these properties are observed for all gases at sufficiently low pressure. In fact, the gases in the atmosphere behave as ideal gases at 1 atm of pressure and 298 K. The crucial thing to understand is that an ideal gas only has kinetic energy. When we speak of the "energy" of an ideal gas we mean kinetic energy by definition since there is no potential energy. In a later section we will consider what happens at high pressure where there are deviations from ideality. However, in this section we are concerned with the definitions of microscopic energy levels and how they relate to macroscopic properties. We consider the definition of pressure as a force per unit area in order to understand the effect of the kinetic energy of the gas on the properties that we can measure. These issues are considered in the segment below.
We can derive the ideal gas equation starting with a one-dimensional equation of motion for a single particle. We then generalize the motion to N particles in three dimensions and show the relationship between the kinetic theory of gases and the ideal gas equation of state.
