{"id":2005,"date":"2026-09-20T10:02:42","date_gmt":"2026-09-20T10:02:42","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=2005"},"modified":"2026-09-20T10:02:44","modified_gmt":"2026-09-20T10:02:44","slug":"combined-gas-law","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/thermodynamics\/combined-gas-law\/","title":{"rendered":"The Combined Gas Law: When Pressure and Temperature Both Move"},"content":{"rendered":"\n
Definition<\/div>

\n\nThe combined gas law states that for a fixed amount of gas, the pressure times the volume divided by the absolute temperature keeps the same value through any change: P1V1\/T1 = P2V2\/T2. Hand it any five of those six quantities and it returns the sixth. Temperatures go in kelvin, pressures are absolute.\n\n<\/p><\/div>\n\n

A sealed bag of crisps carried up a mountain road arrives looking like a pillow. The air outside thinned as you climbed, the air trapped inside had nowhere to go, and the packet stretched to take up the slack. Meanwhile the temperature fell, quietly pulling the other way.<\/p>\n\n

That tug-of-war is the whole subject. Boyle’s law handles a squeeze at a steady temperature, Charles’s law a warming at a steady pressure \u2014 but a balloon, a tyre and a crisp packet rarely hold anything steady. One equation covers the case where two things move at once.<\/p>\n\n

What Is the Combined Gas Law?<\/h2>\n\n

The combined gas law says that for a sealed sample of gas, the group PV\/T keeps the same value no matter how the three quantities inside it change. Move two of them and the third has to shift so the group stays put.<\/p>\n\n

Think of it as a budget. The gas is handed a fixed allowance at the start; spend some of it on a higher pressure and something has to give, either the volume or the temperature. Nothing is created and nothing is lost, because the allowance was set by how much gas is in there.<\/p>\n\n

Fixed amount<\/strong> is the condition that does all the work. The same molecules have to be present at the end as at the beginning \u2014 no leak, no gas dissolving into a liquid, no reaction quietly eating or making them. Break that and the law has nothing to say.<\/p>\n\n

The name is literal. Three older relations each pinned one quantity and let the other two move; this one refuses to pin anything, which is why it is the version that survives contact with a real balloon.<\/p>\n\n

The Combined Gas Law Formula<\/h2>\n\n

Written for two states of the same sample, the law is a single equality between two groups.<\/p>\n\n

P1<\/sub>V1<\/sub> \/ T1<\/sub> = P2<\/sub>V2<\/sub> \/ T2<\/sub><\/div>\n\n

Subscript 1 is the state before, subscript 2 the state after. Rearranged for the quantity people usually want, the volume at the end, it becomes one multiplication over another.<\/p>\n\n

V2<\/sub> = P1<\/sub>V1<\/sub>T2<\/sub> \/ (T1<\/sub>P2<\/sub>)<\/div>\n\n

Any of the six can be the unknown, so there are six rearrangements and no one of them is more fundamental than the others. If you would rather not do the algebra by hand, the combined gas law calculator<\/a> takes any five values, in kilopascals, litres, kelvin, Celsius or Fahrenheit, and returns the sixth with the working shown.<\/p>\n\n