Gay-Lussac's law says that heat a gas in a sealed, rigid container and its pressure climbs — proportionally, and predictably. Documented by French chemist Joseph Louis Gay-Lussac in the early 1800s (building on earlier unpublished work by Jacques Charles), it is one of the three simple gas laws — alongside Boyle's and Charles's — that combine into the ideal gas law. This article covers where the law comes from, why Kelvin is non-negotiable, and where the direct-proportion model breaks down.
The P/T = constant relationship
Gay-Lussac's law states that for a fixed amount of gas at constant volume, pressure is directly proportional to absolute temperature: P/T = constant, or equivalently P₁/T₁ = P₂/T₂ when comparing two states. Physically, temperature is a measure of the average kinetic energy of gas molecules — heat the gas and its molecules move faster and collide with the container walls harder and more often. Because the container's volume is fixed, the gas cannot expand to relieve that extra molecular force the way it does under Charles's law; the only place the added energy can go is into a higher pressure reading. Cool the gas and the reverse happens: the molecules slow down, collide less forcefully, and pressure falls. This is exactly why a sealed can of compressed air or a car tire shows a lower pressure reading on a cold morning even though no gas has leaked out — the pressure has simply followed the temperature down.
Why the temperature must be in kelvin
Gay-Lussac's law is a statement about direct proportion from a true zero, and only the Kelvin scale has a true zero — the point at which molecular motion (and, in the idealized limit, gas pressure) theoretically stops. Celsius and Fahrenheit are both offset scales with arbitrary zero points, so a proportional relationship that holds in kelvin does not hold in either of them. Converting is one line: K = °C + 273.15, or K = (°F − 32) × 5/9 + 273.15. The calculator above does this conversion automatically and flags it whenever you enter a Celsius or Fahrenheit value, but doing it by hand is the single step most students skip — and skipping it produces pressures that are wrong by a wide margin, sometimes even negative.
How Gay-Lussac's law fits with Boyle's and the combined gas law
Gay-Lussac's law is one of three simple gas laws, each of which holds one variable fixed. Boyle's law (PV = constant) holds temperature fixed and relates pressure and volume. Charles's law (V/T = constant) holds pressure fixed and relates volume and temperature. Gay-Lussac's law (P/T = constant) holds volume fixed and relates pressure and temperature. When volume is not actually constant — for example, a weather balloon that both expands and rises through a changing atmosphere, or a piston-cylinder system where the piston is free to move — none of the three simple laws applies cleanly on its own, and you need the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, or the full ideal gas law, PV = nRT, which folds all three simple laws together with Avogadro's law.
Where the simple model breaks down
Gay-Lussac's law describes an ideal gas — molecules with negligible size and no attraction to each other. Real gases deviate from this, especially at low temperatures approaching condensation and at high pressures where the molecules' own volume stops being negligible. It also assumes the container's volume genuinely stays fixed: a real pressure vessel flexes slightly under load, and a rigid container heated far enough can fail before the ideal-gas prediction is even reached, which is why pressure-relief valves exist on sealed tanks. For everyday temperature ranges and moderate pressures — the range most classroom, workshop, and automotive problems live in — Gay-Lussac's law's direct proportion is accurate enough to use without correction.