Gay-Lussac's Law Calculator

At a glance:Gay-Lussac's law (also called the Charles–Gay-Lussac law or the third gas law) is one of the basic empirical laws describing gas behaviour, systematically studied by the French chemist Joseph Louis Gay-Lussac around 1808. It describes this situation: for a fixed amount (constant moles) of gas, at constant volume (isochoric), its pressure is directly proportional to its absolute temperature. In formula: P₁/T₁ = P₂/T₂, or P ∝ T (at constant volume). To find the pressure after the change, rearrange to P₂ = P₁·T₂/T₁, where P₁, P₂ are the pressures before and after the change, and T₁, T₂ the absolute temperatures before and after. As with other gas laws, the temperature must use the 'absolute scale' Kelvin (K = °C + 273.15), because pressure is proportional to the kinetic energy of the molecules hitting the wall, which is proportional to absolute temperature starting from absolute zero; using Celsius would give wrong results. Using this tool's default: a gas in a sealed constant-volume container at 300 K (about 27°C) has pressure 1 atm; if heated to 600 K (about 327°C), the absolute temperature doubles, so the pressure also doubles: P₂ = 1 × 600 / 300 = 2 atm. The physical essence of Gay-Lussac's law is: heating at fixed volume makes gas molecules move more vigorously and hit the wall more frequently and forcefully; since the volume cannot expand to release, all that extra hitting shows up as a pressure rise. This law explains many safety-related phenomena: first, and most importantly — when sealed containers (spray cans, lighters, compressed-gas cylinders, cans) are heated, the internal pressure rises and overheating may cause them to burst, so such items are labelled 'avoid high temperature, do not throw into fire'. Second, car tires heat up under summer sun or long driving and tire pressure rises — which is why it is recommended to measure and inflate tires when they are cool. Third, pressure cookers use sealed heating to raise internal pressure and thus the boiling point, cooking food faster. Fourth, unopened carbonated drinks and gas cylinders both carry the risk of rising pressure at high temperature. Gay-Lussac's law is the special case of the combined gas law P₁V₁/T₁ = P₂V₂/T₂ when 'volume is constant (V₁=V₂)', and is also a consequence of the ideal gas law PV=nRT under constant volume and amount. Using Gay-Lussac's law: first, convert temperature to Kelvin — the most common error. Second, the volume must stay constant and the gas amount (moles) unchanged. Third, pressure units must be consistent on both sides (all atm or all kPa). Fourth, this law describes ideal gases; real gases deviate under extreme conditions. In short, this calculator lets you quickly find the final gas pressure at constant volume from the initial pressure, initial temperature and final temperature — a practical tool for understanding gas behaviour and container safety.