# 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.

References in periodicals archive ?
An excess temperature in the isobaric processes readily follows from the Clapeyron equation,
The relationship between the press and temperature under the condition of phase equilibrium can be expressed by Clapeyron equation .
On the basis of conservation of energy, conservation of mass, Darcy's law, and Clapeyron equation, this paper derived water migration equation, heat transfer equation, and solute transport equation and established the coupled model of hydrothermal-salt for saturated salinized soil under the freezing condition.

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