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Concept
Virial expansion
Summary
The virial expansion is a model of thermodynamic equation of state. This model 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, , as
This equation was first proposed by Kamerlingh Onnes. The terms A, B and C, represent the virial coefficients. The leading coefficient, A, is defined as the constant value of 1, which enforces that the equation reduces to the ideal gas expression as the gas density approaches zero.
The second, B, and third, C, virial coefficients have been studied extensively and tabulated for many fluids for more than a century. Two of the most extensive compilations are in the books by Dymond. and NIST Thermo Data Engine Database and its Web Thermo Tables. Tables of second and third virial coefficients of many fluids are included in these compilations.
The second and third virial coefficients as functions of temperature are shown in the following figure for argon. Reduced temperature and reduced virial coefficients, scaled by respective critical properties, are all dimensionless. Notice in the figure that the second virial coefficient decreases monotonically as temperature is lowered. However, the third virial coefficient has a bell shape. It increases as temperature is lowered to the critical temperature, then it passes through a peak and decreases rapidly to zero as temperature is lowered from the critical point to the triple point. It is physically unreasonable for it to decrease below the critical temperature. This is because the third virial coefficient theoretically represents the repulsive force among molecules, which is expected to increase at a lower temperature, as molecules are pressed together. The behaviors just described are similar to many other gases, as shown in the figure below.
The reason why the third virial coefficient decreases below the critical temperature is as follows. Generally, the PρT isotherms are measured in the gaseous phase.
Official source
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