How it works
The ideal gas law ties together the four things that describe a gas — pressure, volume, amount and temperature — in one compact equation, PV = nRT. Fix any three and the fourth is determined. Here we solve for pressure, but the same relationship explains why a warm tyre reads higher, why a sealed bottle crushes as it cools, and how a balloon swells in the sun.
R is the universal gas constant, 8.314 J per mole per kelvin — the fixed exchange rate between energy and gas behaviour. Temperature must be in kelvin (never Celsius), because the law is built on absolute temperature: at 0 K the pressure genuinely goes to zero.
As a sanity check, one mole of any gas at 0 °C (273.15 K) filling 22.4 litres comes out at about one atmosphere — the classic 'molar volume at STP'. Real gases drift from this at high pressure or low temperature, but for everyday air the ideal law is remarkably accurate.
Use it in real life
Tyre pressure: heating the air in a tyre from a cold morning to motorway warmth raises its pressure measurably — the reason you check tyres cold.
Scuba and altitude: the same amount of gas takes up more volume as pressure drops, which is why a diver never holds their breath while ascending and why crisp packets balloon on a plane.
Engines and HVAC: compressing air raises its pressure and temperature together — the working principle behind diesel ignition and refrigeration cycles.
Frequently asked questions
What are the units for the ideal gas law?
In SI: pressure in pascals, volume in cubic metres, amount in moles, temperature in kelvin, and R = 8.314 J/(mol·K). Keep everything in SI and the pressure comes out in pascals.
Why must temperature be in kelvin?
Because the law uses absolute temperature. Pressure and volume are proportional to kelvin, not Celsius — using °C would break the maths and even allow nonsensical negative values.
When does the ideal gas law stop working?
At very high pressures or very low temperatures, where gas molecules are close enough that their own volume and mutual attractions matter. Then real-gas models like van der Waals are needed, but for ordinary conditions the ideal law is excellent.