Virial expansion

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The classical virial expansion expresses the pressure of a many-particle system in equilibrium as a power series in the number density. The virial expansion, introduced in 1901 by Heike Kamerlingh Onnes, is a generalization of the ideal gas law. He wrote that for a gas containing atoms or molecules,

where is the pressure, is the Boltzmann constant, is the absolute temperature, and is the number density of the gas. Note that for a gas containing a fraction of (Avogadro's number) molecules, truncation of the virial expansion after the first term leads to , which is the ideal gas law.

Writing , the virial expansion can be written as


The virial coefficients are characteristic of the interactions between the particles in the system and in general depend on the temperature . Virial expansion can also be applied to aqueous ionic solutions, as shown by Harold Friedman.

Comparison with Van der Waals equation[edit]

The Van der Waals equation can be used to derive the approximation with the Van der Waals constants a and b.

And when then , see Boyle temperature.

According to Van der Waals constants (data page) the constants for hydrogen gas are for example a = 0.2476 L2bar/mol2 and b = 0.02661 L/mol and therefore the estimation of the Boyle temperature for hydrogen is . (The real value for hydrogen is 110 K.[2] In nitrogen the difference is bigger.)

See also[edit]

Notes and references[edit]

  1. ^ Chang, Raymond (2014). Physical Chemistry for the Chemical Sciences. University Science Books. p. 14. ISBN 978-1-891389-69-6. 
  2. ^ Real Gases and the Virial Equation Table 1.2