Lei de Gay-Lussac (P1/T1=P2/T2)

Gay-Lussac's law: P₁/T₁ = P₂/T₂

Hold the volume fixed and the pressure of a fixed amount of ideal gas tracks its absolute temperature directly: P/T = constant. Joseph Louis Gay-Lussac put it down around 1802, and it covers isochoric heating. Warm a sealed gas cylinder and the pressure climbs in step. Temperature has to be in Kelvin, never Celsius, because the law is anchored at absolute zero. Example: 1 atm at 273 K heated to 373 K → P₂ = 1·(373/273) ≈ 1.37 atm. A tyre at 32 psi on a 0 °C winter morning reads about 38 psi once it's been baking on 50 °C summer asphalt.

Applications

It explains why tyre pressure drifts with the seasons, why pressure cookers need safety valves, how pressurised gas cylinders for oxygen or propane get designed, how boiler relief valves are sized, and where those aerosol-can warnings come from ("do not expose to temperatures above 50 °C").

FAQ

Why must temperature be in Kelvin? The law assumes P → 0 as T → 0. With Celsius you'd get nonsense, like zero or negative pressure at 0 °C. Convert with K = °C + 273.15.

What if the volume also changes? Switch to the combined gas law, P₁V₁/T₁ = P₂V₂/T₂. Gay-Lussac is just the isochoric case where V₁ = V₂.

Does it apply to liquids or solids? No, only to gases, and even then it's an approximation that holds for ideal gases. Liquids and solids barely compress, so their pressure-temperature behaviour follows different equations of state.