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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 ...
Pitzer equations[1] are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. [2][3][4] They were first described by physical chemist Kenneth Pitzer. [5] The parameters of the Pitzer equations are linear combinations of parameters, of a virial expansion of the excess Gibbs free ...
In these equations, the subscript A is for analyte (the solution) and T is for the toluene with the Rayleigh ratio of toluene, R T being 1.35×10 −5 cm −1 for a HeNe laser. As described above, the radius of gyration, R g, and the second virial coefficient, A 2, are also calculated from this equation.
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 interactions can be interpreted in terms of a second virial coefficient B(T) for the mixture. 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 ...
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.
This is the virial equation of state and describes a real gas. Since higher order virial coefficients are generally much smaller than the second coefficient, the gas tends to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature (or when c = 1 V m {\textstyle c={\frac {1}{V_{m}}}} or P ...