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Virial coefficients appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law. They are characteristic of the interaction potential between the particles and in general depend on the temperature. The second virial coefficient depends ...
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 This equation was first proposed by Kamerlingh Onnes. [1] The terms A, B, and C represent the virial ...
Both phase equilibrium properties and homogeneous state properties at arbitrary density can in general only be obtained from molecular simulations, whereas virial coefficients can be computed directly from the Lennard-Jones potential. [36] Numerical data for the second and third virial coefficient is available in a wide temperature range.
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. The parameters may be derived from various experimental data such as the ...
For polydisperse samples, the resulting molecular mass from a static light-scattering measurement will represent an average value. An advantage of the Debye plot is the possibility to determine the second virial coefficient. This parameter describes the interaction between particles and the solvent.
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.
In statistical 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. Mathematically, the theorem states ...
For two components, the second virial coefficient for the mixture can be expressed as = + +,, where the subscripts refer to components 1 and 2, the X i are the mole fractions, and the B i are the second virial coefficients. The cross term B 1,2 of the mixture is given by