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The virial expansion is a model of thermodynamic equations of state. It expresses the pressure P of a gas in local equilibrium as a power series of the density . This equation may be represented in terms of the compressibility factor , Z , as Z ≡ P R T ρ = A + B ρ + C ρ 2 + ⋯ {\displaystyle Z\equiv {\frac {P}{RT\rho }}=A+B\rho +C\rho ^{2 ...
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy of a stable system of discrete particles, bound by a conservative force (where the work done is independent of path), with that of the total potential energy of the system.
The first step in obtaining a closed expression for virial coefficients is a cluster expansion [1] of the grand canonical partition function = = / Here is the pressure, is the volume of the vessel containing the particles, is the Boltzmann constant, is the absolute temperature, = [/ ()] is the fugacity, with the chemical potential.
The parameters of the Pitzer equations are linear combinations of parameters, of a virial expansion of the excess Gibbs free energy, which characterise interactions amongst ions and solvent. The derivation is thermodynamically rigorous at a given level of expansion.
A is the first virial coefficient, which has a constant value of 1 and makes the statement that when volume is large, all fluids behave like ideal gases. The second virial coefficient B corresponds to interactions between pairs of molecules, C to triplets, and so on. Accuracy can be increased indefinitely by considering higher order terms.
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The following is a derivation of this third equation (the result is Eq. 6). ... can be expressed by a power series, called a virial expansion: [80] ...
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