The virial equation of state, first proposed on an empirical basis in the nineteenth century and later found to have a solid theoretical basis in statistical mechanics, is sometimes dismissed by geochemists because it only works well at low to moderate densities (see 13.5.1), and there have not been many direct applications in the geochemical literature - Spycher and Reed ( 13.7.3) is an exception. Also it is incapable of representing vapor-liquid equilibria, as do the cubic EoS. However, it is important in any study of the thermodynamics of fluids because references to it are ubiquitous in the literature on equations of state, so an understanding of it and its limitations is fundamental. [Pg.382]

Virial Equations of State The virial equation in density is an infinite-series representation of the compressibility factor Z in powers of molar density p (or reciprocal molar volume V ) about the real-gas state at zero density (zero pressure) [Pg.355]

Virial equations of state are infinite-series representations of the gas-phase compressibility factor, with either molar density or pressure taken as the independent variable for expansion [Pg.13]

The virial equation of state for a purely 2D system can be obtained by expanding the Z value in powers of the 2D density [Pg.456]

The virial equation of state is a power series expansion for the pressure p of a real gas in terms of the amount-of-substance density p [Pg.33]

The virial equation of state, first advocated by Kamerlingh Oimes in 1901, expresses the compressibility factor of a gas as a power series in die number density [Pg.202]

The volumetric properties of a gas at low and moderate densities are best described by the virial equation of state [Pg.199]

As an alternative to using density as the independent variable in a virial equation of state, we could use pressure. Then the Taylor expansion takes this form. [Pg.158]

The same result can also be obtained directly from the virial equation of state given above and the low-density fonn of g(r). B2(T) is called the second virial coefficient and the expansion of P in powers of is known as the virial expansion, of which the leading non-ideal temi is deduced above. The higher-order temis in the virial expansion for P and in the density expansion of g(r) can be obtained using the methods of cluster expansion and cumulant expansion. [Pg.423]

In the case of real gases at low pressure that satisfy the simplified virial equation of state, i.e., PV=n[RT + BpP ], the mass density is given by the following equation [Pg.1045]

The most general of the equations of state is the virial equation, which is also the most fundamental since it has a direct theoretical connection to the intermolecular potential function. The virial equation of state expresses the deviation from ideality as a series expansion in density and, in terms of molar volume, can be written [Pg.102]

At modest vapor densities, our most useful tool for vapor-phase fugacity coefficients is the virial equation of state truncated after the second term. For real fluids, much is known about second virial [Pg.27]

In previous sections we have emphasized the importance of the virial equation of state. However, for accurate calculation of properties of real gases at high density, the virial equation of state is useful only if reliable values of the virial coefficients above the third (and their temperature derivatives) are available, which is rarely the case — that is why Douslin s calculations, referred to above, employed graphical, rather than analytical, integration. Naturally, calculation of the properties of a dilute gas can be performed to good accuracy in terms of just B T) and C T) or just B T) and C (T). For example, the real-gas constant-pressure heat capacity, Cp, and the isenthalpic Joule-Thomson coefficient, can be evaluated [Pg.202]

For a given temperature, pressure, and composition, the corresponding density and Z factor given by the equation of state is needed. The vapor root is found by solving the truncated virial equation of state (see Table 14-8) for Z, and for small values of BP/RT, the expression so obtained reduces to Z = 1 + BP/RT, that is, [Pg.543]

The mathematical relationship between pressure, volume, temperature, and the number of moles of gas at equilibrium is given by its equation of state. The best-known equ on of state is the ideal-gas law, PV = RT, where P is the pressure of the gas, V is its molar volume (V/n), n is the number of moles of gas, R is the gas constant, and T is the absolute temperature of the gas. Many modifications of the ideal-gas equation of state have been proposed so that the eqnation can fit P, V, T data of real gases. One of these equations, the virial equation of state, accounts for nonideality by utilizing a power series in the density [Pg.630]

Here, p is the amount-of-substanee density, equal to the reeiproeal molar volume. To carry out the numerical integration of these equations, initial values are required for two of the three quantities Cym,Z and (dZldT)p . For example, values for Z and (dZldT)p can be determined at evenly spaced densities along an initial isotherm when accurate gas-density data are known. Then, (dZldp )T can be calculated and combined with speed of sound data to give values for Cy at each density from the first of the equations above, and then f < Z/dT )p can be determined from the second equation. A simple predictor-corrector method is then used to determine Z and dZ/dT)p at a temperature AT from the reference isotherm. This process is then repeated to cover the range of thermodynamic states of the speed of sound measurements. Accurate coefficients in the virial equation of state can then be derived from the compression factors. [Pg.10]

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