The microscopic model and its limits

Why does this simple law work? Because, under the name "ideal gas", lies a clear microscopic model. We picture the gas as a swarm of tiny molecules that:

   - are point-like (their own volume is negligible)
   - do not interact at a distance (no force between them)
   - bounce without loss off the walls and off each other

Two macroscopic quantities then take on a concrete meaning:

   PRESSURE     = the effect of billions of molecular impacts on the walls
   TEMPERATURE  ∝ the average kinetic energy of the molecules (their agitation)

Pressure is the ceaseless drumming of molecules on the walls: the more numerous or fast they are, the greater the pressure. Temperature, for its part, directly measures agitation: heating a gas means speeding up its molecules. At absolute zero, they would be at rest — hence the existence of a minimum temperature.

   low T  : slow molecules  ·  ·   ·      (few impacts, low pressure)
   high T : fast molecules  ·´·`·´·`·´·   (violent impacts, high pressure)

This model has its limits. It assumes molecules with no size and no interaction — which is false. At high pressure (molecules packed together, their volume counts) or at low temperature (attractive forces become noticeable, the gas tends to liquefy), real gases deviate from PV = nRT. The "ideal gas" is thus an idealization: excellent for ambient air, defeated at extreme conditions. It is a fine example of a physical model — simple, powerful, and aware of its domain of validity.