The ideal gas equation

I did want to mention that the CarnotCycle big entry for the month is “The Ideal Gas Equation”. The Ideal Gas equation is one of the more famous equations that isn’t F = ma or E = mc2, which I admit is’t a group of really famous equations; but, at the very least, its content is familiar enough.

If you keep a gas at constant temperature, and increase the pressure on it, its volume decreases, and vice-versa, known as Boyle’s Law. If you keep a gas at constant volume, and decrease its pressure, its temperature decreases, and vice-versa, known as Gay-Lussac’s law. Then Charles’s Law says if a gas is kept at constant pressure, and the temperature increases, then the volume increases, and vice-versa. (Each of these is probably named for the wrong person, because they always are.) The Ideal Gas equation combines all these relationships into one, neat, easily understood package.

Peter Mander describes some of the history of these concepts and equations, and how they came together, with the interesting way that they connect to the absolute temperature scale, and of absolute zero. Absolute temperatures — Kelvin — and absolute zero are familiar enough ideas these days that it’s difficult to remember they were ever new and controversial and intellectually challenging ideas to develop. I hope you enjoy.



If you received formal tuition in physical chemistry at school, then it’s likely that among the first things you learned were the 17th/18th century gas laws of Mariotte and Gay-Lussac (Boyle and Charles in the English-speaking world) and the equation that expresses them: PV = kT.

It may be that the historical aspects of what is now known as the ideal (perfect) gas equation were not covered as part of your science education, in which case you may be surprised to learn that it took 174 years to advance from the pressure-volume law PV = k to the combined gas law PV = kT.


The lengthy timescale indicates that putting together closely associated observations wasn’t regarded as a must-do in this particular era of scientific enquiry. The French physicist and mining engineer Émile Clapeyron eventually created the combined gas equation, not for its own sake, but because he needed an…

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