Gay-Lussac's law formula
At constant volume, the pressure of a fixed amount of gas is directly proportional to its absolute temperature: P1/T1 = P2/T2. Rearranged for the new pressure, P2 = P1·T2 ÷ T1. Temperatures must be in kelvin. This is why a sealed aerosol can bursts when heated. To let volume change as well, use the combined gas law calculator.
How to use this calculator
Enter the initial pressure P1 and both temperatures in kelvin (add 273.15 to Celsius). The calculator returns the final pressure P2 in the same pressure unit you used for P1. It guards against an initial temperature of 0 K. Let the volume change at fixed temperature instead and you are looking at Boyle’s law.
- Pressure units are free. atm, kPa, bar or psi all work — P2 simply comes back in whatever unit P1 used, because the units cancel in the ratio.
- Temperature units are not. Kelvin is mandatory; Celsius or Fahrenheit will silently give a wrong answer.
- Volume must be fixed. If the container can expand, this law no longer applies on its own.
Worked example
A sealed rigid tank at 1 atm and 300 K is heated to 600 K. P2 = (1 × 600) ÷ 300 = 2 atm. Doubling the absolute temperature doubles the pressure when volume is fixed. The three simple gas laws are all special cases of the ideal gas law calculator.
Frequently asked questions
- What is Gay-Lussac's law?
- Gay-Lussac's law states that at constant volume the pressure of a fixed amount of gas is directly proportional to its absolute temperature.
- What is held constant?
- Volume and the amount of gas stay constant. Only pressure and temperature change together.
- Why use kelvin?
- The direct proportion only holds on an absolute scale, so convert any Celsius temperature to kelvin by adding 273.15 before entering it.
- What real situation does this describe?
- A sealed, rigid container being heated, such as an aerosol can or a pressure cooker, where rising temperature raises the internal pressure.
- What happens if I enter Celsius by mistake?
- You get a badly wrong answer, and often a nonsensical one. Warming a gas from 27 °C to 327 °C looks like a twelvefold pressure rise in Celsius, but in kelvin it is 300 K to 600 K — a doubling. Negative Celsius values can even produce a negative pressure.