{"id":1896,"date":"2026-09-16T14:49:56","date_gmt":"2026-09-16T14:49:56","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=1896"},"modified":"2026-09-16T14:49:58","modified_gmt":"2026-09-16T14:49:58","slug":"gay-lussacs-law","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/gay-lussacs-law\/","title":{"rendered":"Gay-Lussac’s Law (P1\/T1 = P2\/T2)"},"content":{"rendered":"\n
Definition<\/div>

\nGay-Lussac’s law states that the pressure of a fixed quantity of gas in a rigid sealed container rises in direct proportion to its absolute temperature, so P1\/T1 = P2\/T2 with every temperature in kelvin. Heating the gas gives it no room to expand into, so the whole effect appears as pressure.\n<\/p><\/div>\n\n

Every aerosol can carries a line telling you not to leave it in the sun. It is not decoration. The can is a sealed steel box that cannot grow, so warming the propellant inside has only one outlet: the pressure pushing outwards on the walls.<\/p>\n\n

The same physics shows up in a duller place \u2014 the tyre pressure gauge on the forecourt. Check your tyres after half an hour on the motorway and every one of them reads high, not because air has been added, but because the air inside is hotter than it was on the driveway. One short equation covers both cases.<\/p>\n\n

What Is Gay-Lussac’s Law?<\/h2>\n\n

Gay-Lussac’s law is the rule that the pressure of a fixed amount of gas held at constant volume is directly proportional to its absolute temperature. Heat the gas by a certain fraction on the kelvin scale and the pressure rises by exactly that fraction.<\/p>\n\n

Three conditions have to hold, and each one earns its place. The container must keep the same volume, so there is nowhere for the expansion to go. The amount of gas must stay the same, which rules out leaks. And the temperature must be measured on an absolute scale, in kelvin.<\/p>\n\n

Put like that, the law is a statement about a ratio. Divide the pressure by the absolute temperature at any moment and you get the same number every time, however hot or cold the gas becomes. That number is fixed by how much gas you sealed in and how big the container is.<\/p>\n\n

You will meet the same law under two other names. Some textbooks call it the pressure-temperature law, which says what it does; others call it Amontons’s law, which is closer to who found it. All three names describe one behaviour: a sealed, rigid container of gas whose pressure tracks its absolute temperature.<\/p>\n\n

The Gay-Lussac’s Law Formula<\/h2>\n\n

Written for two states of the same sealed gas \u2014 before and after a temperature change \u2014 the law takes this form:<\/p>\n\n

P1<\/sub> \/ T1<\/sub> = P2<\/sub> \/ T2<\/sub><\/div>\n\n
\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\nNotes<\/th>\n<\/tr>\n<\/thead>\n
P1<\/sub><\/td>absolute pressure in the starting state<\/td>Pa<\/td>measured from a vacuum, not from the surrounding air; kPa, bar, atm and psi all work provided both pressures use the same unit<\/td><\/tr>\n
T1<\/sub><\/td>absolute temperature in the starting state<\/td>K<\/td>kelvin only; T\/K = temperature in \u00b0C + 273.15<\/td><\/tr>\n
P2<\/sub><\/td>absolute pressure in the final state<\/td>Pa<\/td>the quantity you usually want<\/td><\/tr>\n
T2<\/sub><\/td>absolute temperature in the final state<\/td>K<\/td>kelvin only, again<\/td><\/tr>\n
V, n<\/td>volume and amount of gas<\/td>m3<\/sup>, mol<\/td>do not appear in the formula because both are held fixed<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Rearranged for the pressure you are usually chasing, it reads:<\/p>\n\n

P2<\/sub> = P1<\/sub> \u00d7 T2<\/sub> \/ T1<\/sub><\/div>\n\n

So the working is short: convert both temperatures to kelvin, form the ratio T2<\/sub>\/T1<\/sub>, and multiply the starting pressure by it. If you would rather have the arithmetic and the unit conversions done for you \u2014 including solving backwards for a temperature \u2014 the Gay-Lussac’s law calculator<\/a> takes pressures in Pa, kPa, atm, bar or psi and temperatures in K, \u00b0C or \u00b0F.<\/p>\n\n

One habit will save you marks. Keep the temperature ratio in full during the calculation and round only the final answer, because rounding the ratio first can shift the result by a whole digit. Problem 1 below shows exactly where that goes wrong.<\/p>\n\n

The lab underneath lets you build the experiment instead of imagining it. You choose the pressure and the temperature at which the vessel was sealed, then move the current temperature and watch what happens.<\/p>\n\n

Two things are worth staring at. The vessel outline never changes size at any setting, because the volume is fixed by the walls, and the pressure-temperature graph beside it stays a single straight line that runs back to zero pressure at -273.15 \u00b0C, whichever starting state you choose.<\/p>\n\n

<\/span>Gay-Lussac's Law Lab<\/span><\/div>