The series on the right-hand side of the equation of state of a gas:
where is the pressure, is the temperature, is the specific volume, and is the Boltzmann constant. The term of the series which contains the -th virial coefficient describes the deviation of the gas from ideal behaviour due to the interaction in groups of molecules. can be expressed in terms of irreducible repeated integrals :
summed over all natural numbers , , subject to the condition
is the volume of the gas, the integration extends over the total volume occupied by the gas, and is the interaction potential. There is a rule for writing down for any in terms of . The expression obtained after simplification is:
In practice, only the first few virial coefficients can be calculated.
Power series in , with coefficients expressed in terms of , can be used to represent equilibrium correlation functions for particles; a corollary of this fact is that the equation of state can be obtained in a simple manner .
There exists a quantum-mechanical analogue of the virial decomposition.
|||J.E. Mayer, M. Goeppert-Mayer, "Statistical mechanics" , Wiley (1940)|
|||R. Feynman, "Statistical mechanics" , M.I.T. (1972)|
|||N.N. Bogolyubov, "Problems of a dynamical theory in statistical physics" , North-Holland (1962) (Translated from Russian)|
|||G.E. Uhlenbeck, G.V. Ford, "Lectures in statistical mechanics" , Amer. Math. Soc. (1963)|
Virial decomposition. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Virial_decomposition&oldid=16492