In 1834, Émile Clapeyron combined the experimental laws of Boyle, Charles, and Gay-Lussac into the single equation pV = nRT. This elegant formula describes the equilibrium state of an ideal gas — a model where molecules are considered point-like and non-interacting. It works as a 'switch' between the volume, pressure, and temperature of a gas, allowing prediction of the behavior of real gases under ordinary conditions.
History
The experiments of Robert Boyle (1662) and Edme Mariotte showed the inverse proportionality of pressure and volume (pV=const at constant T). Jacques Charles (1787) and Joseph Gay-Lussac (1802) established the dependence of volume on temperature. Amedeo Avogadro in 1811 hypothesized that equal volumes of gases contain equal numbers of molecules under the same conditions. Émile Clapeyron in 1834 combined these laws into a single equation, later generalized by Dmitri Mendeleev with the inclusion of the universal gas constant.
How it works
Widely applied from internal combustion engine calculations to atmospheric modeling. Limits of applicability: the equation is not applicable at high densities and low temperatures, when intermolecular interactions and the finite size of molecules become significant — there, Van der Waals equations with corrections are used.
In practice
From inflating tires to weather forecasting: the relationship between pressure, volume, and temperature governs engines, balloons, and breathing.
Fun fact
If you leave a ball in the sun, it inflates itself — not magic, but the temperature increase raises the pressure with almost constant volume.
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