The history
From a tube of mercury in Florence to a number fixed forever in 2019: 400 years of learning how gases push, stretch and move.
People once thought air had no weight at all. Then glass tubes, mercury and balloons showed that a gas pushes back when you squeeze it, swells when you heat it, and does both in the same way whatever it is made of. In the end all the rules fitted into one short equation, PV = nRT, and scientists found out why: a gas is a crowd of molecules hitting the walls.
1643
Lasting vacuum made in a lab
Evangelista Torricelli, Florence, Italy
1662
Law linking pressure and volume
Robert Boyle and Robert Hooke, Oxford, England
21 November 1783
People fly (hot-air balloon)
Pilâtre de Rozier and the Marquis d'Arlandes, Paris
1 December 1783
Crewed hydrogen balloon flight
Jacques Charles and Nicolas-Louis Robert, Paris
1834
Gas law in one equation
Émile Clapeyron, Paris, France
1860
First law of physics based on chance
James Clerk Maxwell, Aberdeen, Scotland
1874
One gas constant for every gas
Dmitri Mendeleev, St Petersburg (Horstmann in 1873)
1910
Nobel Prize for a gas equation
Johannes Diderik van der Waals, Netherlands
1643 – 1738
Mercury tubes prove air has weight, Boyle finds that squeezed air pushes back, and the first thinkers link pressure to heat and to tiny moving particles.
1643
1643 (tested on a mountain in 1648)
Torricelli filled a glass tube with mercury and turned it upside down in a bowl. The mercury fell to about 76 cm and stopped, leaving empty space above it. The weight of the air outside was holding it up. In 1648 Pascal's brother-in-law carried the same tube up the Puy de Dôme in France, and the mercury stood lower at the top.
Why it mattered. It proved that air has weight and pushes on everything, which is what pressure means.
1662
Boyle trapped air in the short, closed end of a J-shaped glass tube and poured mercury into the long end. Every time he doubled the push, the trapped air shrank to half its size. Towneley and Power had spotted the same pattern, and Boyle printed the result in the second edition of his book on the "spring of the air".
Why it mattered. It was one of the first laws of nature written as a rule linking two measured numbers: pressure times volume stays the same.
1676
Mariotte, a French priest and scientist, found the same rule on his own and wrote it up in his Discourse on the Nature of Air. He added an important warning: it only works if the temperature does not change. In the same book he coined the word "barometer".
Why it mattered. His warning about temperature pointed the way to the next gas laws.
1702
Amontons, who had been mostly deaf since boyhood, built a thermometer that read temperature from the pressure of trapped air. He saw that equal drops in temperature gave equal drops in pressure. If you kept cooling, the pressure would one day reach nothing, which he put at about minus 240 °C.
Why it mattered. It was the first hint that there is a coldest possible temperature, absolute zero.
1738
In his book Hydrodynamica, Bernoulli pictured air as countless tiny particles flying in all directions. Their hits on the walls of a container make the pressure, and faster particles mean a hotter gas. He even showed why this gives Boyle's law.
Why it mattered. It was the first kinetic theory of gases, more than a hundred years before most scientists accepted it.
1783 – 1802
Paris goes balloon mad, and the scientists who fly them discover that every gas grows by the same amount when heated.
1783
21 November 1783
The Montgolfier brothers, paper makers from Annonay, built a huge cloth and paper balloon and filled it from a fire. Pilâtre de Rozier and d'Arlandes rode it about 9 km across Paris in some 25 minutes. The brothers thought smoke held a special gas with "levity". In fact, heated air simply spreads out, so the balloon holds less of it and is lighter than the cold air around it.
Why it mattered. It was the first time people flew freely, and it made the link between heat and gas volume impossible to ignore.
1783
27 August and 1 December 1783
Charles filled a silk balloon with hydrogen made from iron and acid. His first, unmanned balloon came down in the village of Gonesse, where frightened villagers attacked it with pitchforks. On 1 December, Charles and Robert flew in a hydrogen balloon themselves for about two hours, watched by a huge crowd.
Why it mattered. Gas balloons turned the study of gases into something the whole of Paris cared about.
1787
c. 1787 (never published)
Charles is said to have filled balloons with different gases and warmed them all by the same amount. Each one grew by the same fraction of its size. He never wrote it up, so we only know about it because another scientist gave him the credit later.
Why it mattered. It suggested that all gases follow one rule for heat, whatever they are made of.
1801
1801 (published 1802)
Dalton, a teacher who was fascinated by weather, studied how water vapour mixes into air. He found that in a mixture of gases, each gas pushes as if the others were not there. The total pressure is just the sum of the parts. The same year he showed that different gases expand alike when heated.
Why it mattered. It is why divers and doctors can work out how much oxygen is in each breath.
1802
31 January 1802
Gay-Lussac measured carefully how gases grow when heated at a steady pressure. He found they all grow by about 1/267 of their size at 0 °C for every degree. He also said that Charles had found this about 15 years earlier, which is why we call it Charles's law.
Why it mattered. The number 267 hid a secret: cool a gas to about minus 267 °C and its volume would, in theory, shrink to nothing.
1811 – 1874
Avogadro's idea lets gases be counted, Clapeyron joins the rules into one equation, and Mendeleev gives it one constant, R.
1811
1811 (revived at Karlsruhe in 1860)
Gay-Lussac had noticed in 1808 that gases react in simple volumes, like two litres of hydrogen to one of oxygen. Avogadro explained it with a bold guess: equal volumes of any gas, at the same temperature and pressure, hold the same number of particles. Almost nobody listened until Cannizzaro handed out a pamphlet at a big chemistry meeting in Karlsruhe, Germany, in 1860.
Why it mattered. It is the n in PV = nRT: it lets you count particles by measuring a gas.
1834
Clapeyron, an engineer who had taught in St Petersburg and built early French railways, was explaining Sadi Carnot's ideas about steam engines. To do it, he joined Boyle's law and Gay-Lussac's law into one equation, pv = R(267 + t), and drew engine cycles as loops on a pressure against volume graph. That graph is still used for every engine today.
Why it mattered. It is the ideal gas law almost as we write it now.
1874
Earlier versions of the gas law used a different constant for each gas. Mendeleev, famous for the periodic table, used Avogadro's idea to write the law for a mole of any gas as pV = RT, with one shared R. His value was within about 0.3% of today's. In Russia the ideal gas law is still called the Clapeyron–Mendeleev equation.
Why it mattered. The single R is what makes PV = nRT work for every gas.
By the numbers
Each estimate comes from asking at what temperature a gas would push or fill nothing. Better measurements closed in on minus 273.15 °C.
1845 – 1872
The gas laws are explained at last: pressure and temperature come from molecules racing about at a spread of speeds.
1845
1845 (printed 1892)
Waterston, a Scot teaching naval cadets for the East India Company in Bombay, worked out a detailed theory of gases made of moving molecules. He sent it to the Royal Society in London, and a referee wrote that it was "nothing but nonsense". It sat in the archive until Lord Rayleigh found and printed it in 1892, nine years after Waterston died.
Why it mattered. His ideas were right, and the story is still told as a warning about ignoring outsiders.
1857
A year after August Krönig in Berlin, Clausius published a fuller theory of gases as molecules racing about and bumping into things. He showed how their speed sets the pressure and the temperature, and later worked out how far a molecule travels between bumps. Together they turned Bernoulli's old picture into real physics.
Why it mattered. It explained where PV = nRT comes from: it is just molecules hitting walls.
1860
1859 talk, 1860 paper
Maxwell realised the molecules in a gas have a spread of speeds, a few slow, most in the middle, a few very fast. He worked out the shape of that spread, and it was the first law of physics based on chance. In 1872 Boltzmann in Graz showed why any gas settles into exactly this spread.
Why it mattered. It showed that a gas law is really the average behaviour of trillions of molecules.
1869 – 2019
Real gases turn out to bend the rules, van der Waals fixes the law, balloons return, and R becomes an exact number.
1869
Andrews squeezed carbon dioxide at different temperatures. Below about 31 °C, squeezing turned it into a liquid. Above that temperature, no amount of squeezing made a liquid at all. He called this the critical point and described it in the Royal Society's Bakerian Lecture.
Why it mattered. It showed real gases break the ideal gas law, and explained how to turn gases into liquids by cooling them first.
1873
14 June 1873 (Nobel Prize 1910)
Van der Waals, a former schoolteacher, fixed the ideal gas law in his PhD thesis. He added two corrections: molecules take up some space, and they pull on each other a little. His equation described gases and liquids together, and Maxwell praised it in the journal Nature.
Why it mattered. It won him the 1910 Nobel Prize in Physics and is still the first step past PV = nRT.
1960
22 October 1960
Yost flew the first modern hot-air balloon, with a plastic envelope and a propane burner he designed. The burner heats the air inside, the air expands, some spills out, and the balloon gets lighter. It flew for about 25 minutes. Almost every hot-air balloon today uses his design.
Why it mattered. It is Charles's law you can ride in.
2019
20 May 2019
The world's measurement scientists fixed the Boltzmann constant and the Avogadro constant at exact values. Since R is simply one times the other, the gas constant became exact too: 8.31446261815324 joules per mole per kelvin. The kelvin itself is now defined through the Boltzmann constant.
Why it mattered. The constant in PV = nRT is now a fixed part of how the world defines temperature and amount.
Did you know?
Boyle called air's push its "spring", because squeezed air pushes back like a squashed spring.
In France, Boyle's law is usually called Mariotte's law, after Edme Mariotte.
Jacques Charles never published Charles's law. We only know because Gay-Lussac gave him the credit in 1802.
The first hydrogen balloon was attacked with pitchforks by villagers in Gonesse, and the French government then had to tell people that balloons were not monsters.
The Montgolfier brothers thought smoke contained a special lifting gas. It was really just hot air.
The law that pressure rises with temperature is often named after Gay-Lussac, but Amontons found it about a century earlier.
R is simply the Avogadro constant times the Boltzmann constant. Since 2019 both are exact, so R is exactly 8.31446261815324 J/(mol·K).
John Dalton once settled on minus 3,000 °C as the coldest possible temperature, more than ten times too cold.
The people
1627 – 1691 · Natural philosopher and chemist · Ireland
Showed that squeezing air makes it push back harder, in exact proportion.
1635 – 1703 · Experimenter and inventor · England
Built the air pumps and glassware behind Boyle's experiments.
c. 1620 – 1684 · Priest and physicist · France
Found Boyle's law on his own and warned it only holds at one temperature.
1663 – 1705 · Physicist and instrument maker · France
Mostly deaf from boyhood, he first guessed at a coldest possible temperature.
1746 – 1823 · Physicist and balloonist · France
Flew the first crewed hydrogen balloon and found, but never published, Charles's law.
1766 – 1844 · Teacher, chemist and weather watcher · England
Showed each gas in a mixture pushes as if it were alone.
1778 – 1850 · Chemist and physicist · France
Measured how gases expand, credited Charles, and rose to about 7,000 m in a balloon in 1804.
1776 – 1856 · Physicist and lawyer · Italy
Guessed that equal volumes of gas hold equal numbers of particles.
1799 – 1864 · Engineer · France
Wrote the gas laws as one equation and drew engines as pressure and volume loops.
1811 – 1883 · Naval instructor and physicist · Scotland (worked in Bombay, India)
Wrote a correct kinetic theory of gases that was rejected as nonsense.
1831 – 1879 · Physicist · Scotland
Worked out the spread of speeds of molecules in a gas.
1837 – 1923 · Physicist, once a schoolteacher · Netherlands
Fixed the gas law for real molecules that take up space and attract.
Where it happened
Sources
Dates marked “c.” are approximate, and historians sometimes disagree about who was first. If you spot a mistake, tell us.
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