This Gay-Lussac’s law calculator solves P₁/T₁ = P₂/T₂ — how a gas’s pressure changes with temperature when its volume is held fixed (a sealed, rigid container). Enter any three values, temperatures in kelvin.
What Is Gay-Lussac’s Law?
Gay-Lussac’s law states that at constant volume, a gas’s pressure is directly proportional to its absolute temperature. Molecules move faster when hot and strike the container walls harder and more often — with nowhere to expand, that shows up purely as pressure. It completes the trio of simple gas laws with Boyle’s Law and Charles’s Law, all slices of the Ideal Gas Law, in our Physics Calculators collection.
Worked Example (Verified)
A sealed steel can holds gas at 2.0 atm and 300 K (27 °C). Heat it to 600 K (327 °C):
P₂ = P₁ × T₂/T₁ = 2.0 × 600/300 = 4.0 atm. Doubled absolute temperature, doubled pressure — and the reason you never heat a sealed aerosol can: its rated pressure can be exceeded exactly this way.
Gay-Lussac’s Law in Real Life
- Tire pressure: a tire filled to 32 psi on a 20 °C day drops measurably on a freezing morning and climbs on a hot highway — volume nearly fixed, so pressure tracks kelvin temperature.
- Pressure cookers: sealed volume + rising temperature = high pressure, which raises water’s boiling point and cooks faster.
- Aerosol can warnings (“do not expose above 50 °C”) and ammunition storage guidance are this law written as safety labels.
- Autoclaves and industrial sterilizers are engineered directly around the P–T relationship.
The Kelvin Rule Again
Like Charles’s law, this proportionality only works on the absolute scale: K = °C + 273.15. Heating from 27 °C to 327 °C looks like a 12× jump in Celsius but is exactly 2× in kelvin (300 → 600 K) — and 2× is what the pressure does.
Related Tools
- Charles’s Law Calculator — volume ↔ temperature
- Boyle’s Law Calculator — pressure ↔ volume
- Ideal Gas Law Calculator — the parent law
Frequently Asked Questions
What is the formula for Gay-Lussac’s law?
P₁/T₁ = P₂/T₂ at constant volume and amount of gas, temperatures in kelvin.
Why does pressure increase with temperature at fixed volume?
Hotter molecules move faster, hitting the walls harder and more frequently. With the volume fixed, that molecular energy has only one outlet: pressure.
What is an everyday example of Gay-Lussac’s law?
Tire pressure rising on a hot day and falling on a cold one, and the pressure inside a pressure cooker as it heats.
How does Gay-Lussac’s law differ from Charles’s law?
Charles links volume to temperature at constant pressure; Gay-Lussac links pressure to temperature at constant volume. Same proportionality shape, different held quantity.
Can this law predict when a sealed can bursts?
It predicts the pressure at any temperature; compare that with the can’s rated burst pressure to find the dangerous temperature — one reason the T₂ solve mode exists.
Is this Gay-Lussac’s law calculator free?
Yes — free, instant, no sign-up.