Law

Ideal gas law

P V = n R T

Statement

The relationship between pressure, volume, amount of substance, and absolute temperature for an ideal gas.

Symbols and units

$P$	pressure	Pa
$V$	volume	m³
$n$	amount of substance	mol
$R$	gas constant	8.314 J/(mol·K)
$T$	absolute temperature	K

When it applies

A gas dilute enough that molecular size and intermolecular forces are negligible.

Don't use when

Not accurate for real gases at high pressure or low temperature, where molecular size and intermolecular attraction become significant — a real-gas equation of state (e.g. van der Waals) is needed there.

Derivation

Combines three separately observed regularities: pressure inversely proportional to volume at fixed temperature, volume proportional to temperature at fixed pressure, and volume proportional to the amount of gas present.

P V = n R T

Worked examples

Heating a sealed container

At fixed volume, P is directly proportional to T:

\frac{P _{2}}{P _{1}} = \frac{T _{2}}{T _{1}}

Doubling the absolute temperature of a sealed, fixed-volume container doubles its pressure.

Watch out for

T must be in kelvin. The 'ideal' model neglects molecular size and intermolecular forces — real gases deviate noticeably at high pressure or low temperature.