# Clapeyron Equation

## Clapeyron equation

[kla·pā·rōn i′kwā·zhən]
(thermodynamics)

## Clapeyron Equation

(Clapeyron-Mendeleev equation), a relation found by B. P. E. Clapeyron (1834) between the physical quantities defining the state of an ideal gas: the gas pressure p, the volume of the gas V, and the absolute temperature T.

The Clapeyron equation is written in the form pV = BT, where the proportionality coefficient B depends on the mass of the gas. D. I. Mendeleev used Avogadro’s law in 1874 to derive the equation of state for 1 mole of ideal gas pV = RT, where R is the universal gas constant. For a gas having a total mass of M and a molecular mass of µ,

pV = (M/µ)RT or pV = NkT

where N is the number of gas particles and k is Boltzmann’s constant. The Clapeyron equation is an equation of state of an ideal gas, which combines the Boyle-Mariotte law (relation between p and V at T = const), Gay-Lussac’s law (dependence of V on T at p = const), and Avogadro’s law (according to which gases contain the same number of molecules N at the same values of p, V, and T).

The Clapeyron equation is the simplest equation of state that is applicable with a certain degree of accuracy to real gases at low pressures and high temperatures (for example, atmospheric air, combustion products in gas engines) when these gases are close in their properties to an ideal gas.

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