15.2 Equation of State

Main Content

1. What is an Ideal Gas?

A real gas is made up of billions of tiny molecules flying around and bumping into each other and the walls of their container. An ideal gas is a simplified, theoretical version of a gas — a model that makes the maths much easier.

An ideal gas is defined as a gas that obeys the relationship:

$pV \propto T$

This means that the product of pressure (p) and volume (V) is directly proportional to the thermodynamic temperature (T). In other words, if you multiply the pressure and volume of an ideal gas together, the answer will always scale up or down in the same way as the temperature.

2. The Three Gas Laws Behind the Ideal Gas

The relationship pV ∝ T comes from combining three simpler gas laws. You need to understand what each one says:

Boyle's Law (constant temperature): At a constant temperature, pressure and volume are inversely proportional — if one goes up, the other goes down.

Charles's Law (constant pressure): At a constant pressure, volume is directly proportional to thermodynamic temperature — if temperature doubles, volume doubles. $V \propto T$

Pressure Law (constant volume): At a constant volume, pressure is directly proportional to thermodynamic temperature — if temperature increases, pressure increases. $p \propto T$

Combining all three laws gives us: $pV \propto T$

Any gas that follows this relationship at all pressures, volumes, and temperatures is called an ideal gas.