Gay-Lussac’s Law describes one of the most practically important relationships in chemistry and thermodynamics: the pressure of a fixed mass of gas held at constant volume is directly proportional to its absolute temperature. Every time a car tyre warms up on a long drive, every time a pressure cooker builds steam, and every time an aerosol can is left in sunlight, Gay-Lussac’s Law is at work.
The formula
The law is expressed as:
P1 / T1 = P2 / T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature. Temperatures must be in Kelvin — the scale anchored at absolute zero. Rearranging gives four solve-for variants:
- P2 = P1 × T2 / T1 — find the new pressure after heating or cooling.
- T2 = T1 × P2 / P1 — find the temperature needed to reach a target pressure.
- P1 = P2 × T1 / T2 — back-calculate the original pressure.
- T1 = T2 × P1 / P2 — back-calculate the original temperature.
The ratio P/T is the constant of proportionality for that particular gas sample in that container.
How the calculator works
Select the variable you want to find, choose whether you prefer Kelvin or Celsius for temperature input, then enter the three known values. Temperatures entered in Celsius are converted to Kelvin automatically (K = °C + 273.15) before the formula is applied, and the result is converted back if you are working in Celsius. The tool also displays the computed P/T ratio when solving for P2, giving you a sanity-check constant to compare against your own workings.
Worked example
A sealed autoclave contains air at 101.325 kPa and 25 °C (298.15 K). The autoclave is sterilised at 134 °C (407.15 K). What is the final pressure?
P2 = 101.325 × 407.15 / 298.15 = 138.37 kPa
The P/T constant is 101.325 / 298.15 = 0.33985 kPa/K, and 0.33985 × 407.15 confirms 138.37 kPa. This is why autoclave safety valves and steam-rated seals are essential — pressures rise by roughly 35% during a standard sterilisation cycle.
| P1 (kPa) | T1 | T2 | P2 result |
|---|---|---|---|
| 101.325 kPa | 0 °C | 100 °C | 138.4 kPa |
| 200 kPa | 20 °C | 80 °C | 240.9 kPa |
| 300 kPa | -40 °C | 25 °C | 383.6 kPa |
Physical constants and assumptions
Gay-Lussac’s Law is a limiting ideal-gas law. It holds exactly only for ideal gases — point-like particles with no intermolecular forces — but provides excellent approximations for real gases at low to moderate pressures and temperatures well above their condensation points. For high-precision engineering work near critical points or at very high pressures, use a real-gas equation of state (van der Waals, Peng-Robinson, etc.).
The law is a direct consequence of the kinetic theory of gases: raising temperature increases the average kinetic energy of molecules, which increases the frequency and force of collisions with container walls, which raises pressure. Because volume is fixed, there is no expansion to absorb the energy — all of it translates into higher pressure.
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