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PV = nRT is one of the most used equations in Class 11 physics and chemistry. It did not come from a single experiment. A French railway engineer wrote it down, in an early form, while trying to explain how heat engines work. This post covers who Émile Clapeyron was, what his equation looked like, and how to use the modern version without the usual unit slips.
Who was Émile Clapeyron?
His MacTutor biography from the University of St Andrews gives his dates as 26 January 1799 to 28 January 1864, both in Paris. He graduated from the École Polytechnique in 1818, trained as an engineer at the École des Mines with his friend Gabriel Lamé, and spent ten years in Russia teaching and building roads and bridges.
Back in France after 1830, he worked on the Paris to Saint-Germain railway, designed steam locomotives and later metal bridges. He became a professor at the École des Ponts et Chaussées in 1844 and was elected to the Paris Academy of Sciences in 1848.
What did he write in 1834?
His "Memoir on the Motive Power of Heat" appeared in the Journal de l'École Royale Polytechnique in 1834. An English translation was printed in 1837 in Taylor's Scientific Memoirs, volume 1. It opens by noting that the law of Mariotte (which we call Boyle's law) and that of Gay-Lussac relate "the volume, the pressure, and the temperature of a given quantity of any gas".
Later he writes: "The law enunciated by Mariotte, combined with that of Gay-Lussac, establishes between these different quantities the relation", which he simplifies to pv = R(267 + t), with t the temperature on the centigrade scale. Here R is a constant for that particular sample of gas.
The 267 came from the expansion of gases measured by Gay-Lussac, who reported in 1802 that a gas grows by 100/266.66 of its volume between the freezing and boiling points of water. Our post on Jacques Charles and the volume of a gas tells that story. The modern figure is 273.15.
Why does Clapeyron matter for heat engines?
The same memoir revives the work of Sadi Carnot, whose 1824 book Clapeyron cites. MacTutor notes that Carnot's work was virtually unknown before this paper, and that Clapeyron expressed it analytically, with graphs. In the memoir, the gas expands and is compressed on a diagram of pressure against volume, the same kind of graph you use for cycles today. MacTutor adds that this work influenced Thomson and Clausius as the second law of thermodynamics took shape.
Worked example: the modern equation
The NCERT Class 11 Physics chapter Kinetic Theory writes the perfect gas equation as PV = μRT with R = 8.314 J mol⁻¹ K⁻¹, and uses 1 atm = 1.01 × 10⁵ Pa. Find the volume of 1 mol of gas at 27 °C and 1 atm.
Convert temperature. T = 27 + 273.15 = 300.15 K.
Use SI units. P = 1.01 × 10⁵ Pa.
Solve. V = nRT/P = (1 × 8.314 × 300.15) / (1.01 × 10⁵) = 0.0247 m³ = 24.7 L.
Compare with Clapeyron's constant. With 267 + 27 = 294 in place of 300.15, the same calculation gives 24.2 L, about 2 per cent lower. His equation had the right form; only the zero of temperature was slightly off.
Which mistakes does this help you avoid?
Celsius in the equation. T must be in kelvin.
Litres with SI R. With R = 8.314, volume comes out in m³. Multiply by 1000 for litres.
Pressure in atm with SI R. Convert atm to Pa first, or use R in L atm units consistently.
For more practice, see our guide to ideal gas problems. The JEE (Main) 2026 syllabus lists the equation of state of a perfect gas. Check the current year's syllabus for your exam. MacTutor also notes that the Clapeyron relation, which gives the heat of vaporisation of a liquid, is named after him.
What can a student take from Clapeyron's way of working?
Combine what is known. Two separate gas laws became one equation once he wrote them together.
Draw it. Turning Carnot's words into a graph made the argument easier to follow and to extend.
Rescue good ideas. Carnot's work was virtually unknown until Clapeyron restated it in a clearer form.
If you can use PV = nRT but cannot see why it holds, the Fermi Concept Library covers every concept in physics, including kinetic theory, with its own lesson.
Try it now: find the volume of 0.50 mol of gas at 127 °C and 2.0 atm, and state your units at each step.
