One law for three variables
For a fixed amount of gas, pressure, volume and temperature are linked. The combined gas law brings together three classic laws:
- Boyle’s law (constant temperature): P₁V₁ = P₂V₂
- Charles’s law (constant pressure): V₁/T₁ = V₂/T₂
- Gay-Lussac’s law (constant volume): P₁/T₁ = P₂/T₂
Combined: P₁V₁/T₁ = P₂V₂/T₂, with temperatures in kelvin.
Solving for each unknown
- V₂ = P₁V₁T₂ ÷ (T₁P₂)
- P₂ = P₁V₁T₂ ÷ (T₁V₂)
- T₂ = P₂V₂T₁ ÷ (P₁V₁)
Pressure and volume can use any unit, as long as both states use the same one; the calculator converts for you. Temperature must be absolute: K = °C + 273.15, or K = (°F − 32) × 5/9 + 273.15.
Worked example
A syringe holds 2.00 L of air at 1 atm and 25 °C. It is compressed to 2 atm and heated to 100 °C.
- T₁ = 298.15 K and T₂ = 373.15 K.
- V₂ = 1 × 2.00 × 373.15 ÷ (298.15 × 2) = 1.252 L.
Doubling the pressure alone would halve the volume to 1.00 L; heating by 75 °C expands it back by 25%.
Everyday examples
- Tire pressure: a tire filled to 35 psi at 70 °F drops to about 30 psi at 20 °F, because pressure falls with absolute temperature (Gay-Lussac).
- Balloons: a helium balloon taken from a warm room into the cold shrinks visibly (Charles).
- Scuba diving: air in a diver’s lungs doubles in volume rising from 10 m depth (2 atm) to the surface (1 atm), which is why divers must never hold their breath while ascending (Boyle).
- Aerosol cans: heating a sealed can raises its pressure, hence the warnings against storing them above 120 °F.
Why kelvin
The gas laws describe proportionality to absolute temperature. At 0 °C, a Celsius-based calculation would divide by zero, and at −10 °C it would predict a negative volume. Kelvin starts at absolute zero, where an ideal gas would have no pressure.
Limits
The law assumes an ideal gas and a constant amount of gas. It works well for air and common gases near room conditions, but deviates at high pressures, very low temperatures and near condensation. If gas is added or removed, use the ideal gas law PV = nRT instead.