The Gas Laws: Boyle's, Charles's and Avogadro's Law

Long before the kinetic theory explained why gases behave as they do, three empirical laws — discovered from

careful experimental measurement — described how they behave. Each law fixes one variable and studies the

relationship between the other two.

Boyle's law (pressure-volume relationship) states that, at constant temperature and for a fixed amount of gas,

the volume of a gas is inversely proportional to its pressure: $V \propto \dfrac{1}{P}$, or equivalently

$PV = \text{constant}$. This means that for two states of the same gas sample at the same temperature,

Compressing a gas to half its volume doubles its pressure, and vice versa — a direct consequence, in kinetic-theory

terms, of the particles striking a smaller wall area more frequently when squeezed into a smaller volume.

Charles's law (temperature-volume relationship) states that, at constant pressure and for a fixed amount of

gas, the volume of a gas is directly proportional to its absolute (Kelvin) temperature: $V \propto T$, or

$\dfrac{V}{T} = \text{constant}$. For two states of the same gas sample at the same pressure,

Heating a gas at constant pressure makes it expand; cooling it makes it contract — consistent with the kinetic

theory's link between temperature and the average kinetic (and hence average speed) of the particles: faster

particles need more room, at the same pressure, to keep colliding with the walls at the same average force.

A closely related law, Gay-Lussac's law (pressure-temperature relationship), states that at constant volume,

$P \propto T$, i.e. $\dfrac{P}{T} = \text{constant}$ — heating a gas in a sealed, rigid container raises its

pressure because faster-moving particles strike the fixed walls harder and more often.

Avogadro's law (volume-amount relationship) states that, at the same temperature and pressure, equal volumes of

any gas contain equal numbers of molecules (and hence equal numbers of moles): $V \propto n$, or

$\dfrac{V}{n} = \text{constant}$. This is a striking and non-obvious result — it says nothing about the identity

of the gas matters, only how many particles are present, under these conditions. It follows that $2\ \text{L}$ of

nitrogen and $2\ \text{L}$ of oxygen, at the same temperature and pressure, contain exactly the same number of …