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Equations of state/History

Equations of state provide quantitative relationships between the pressure, volume and temperature of substances, particularly gases and liquids.

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Boyle's law (1662)

Boyle's Law was perhaps the first expression of an equation of state. In 1662 Robert Boyle, an Irishman, performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. In mathematical form, this can be stated as:

PV = constant

The above relationship has also been attributed to Edme Mariotte[?] and is sometimes referred to as Mariotte's law. However, Mariotte's work was not published until 1676.

Charles' law (1787)

In 1787 the French physist Jacques Charles found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 degree interval. Later, in 1802, Joseph Louis Gay-Lussac published results of similar experiments, indicating a linear relationship between volume and temperature:

V1/T1 = V2/T2

Dalton's law of partial pressures (1801)

The Ideal gas law (1834)

In 1834 Émile Clapeyron combined Boyle's Law and Charles' law into the first statement of the ideal gas law. Initially the law was formulated as PV=R(T+267) (with temperature expressed in degrees celsius). However, later work revealed that the number should actually be 273.2, giving:


van der Waals Equation of State (1873)

Amagat's law[?] (1880)

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Thomas a Kempis

... 400 different editions. De Backer (Essai, ut inf.) enumerates 545 Latin and about 900 French editions. Originally written in Latin, a French translation was made ...

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