Compressibility factor defined

For pure organic vapors, the Lydersen et al. corresponding states method is the most accurate technique for predicting compressibility factors and, hence, vapor densities. Critical temperature, critical pressure, and critical compressibility factor defined by Eq. (2-21) are used as input parameters. Figure 2-37 is used to predict the compressibihty factor at = 0.27, and the result is corrected to the Z of the desired fluid using Eq. (2-83). 

Adsorbed phase compressibility factor, defined by Eq. (14.104) Elevation above a datum level... 

Show that by the use of the compressibility factor defined by PV = kRT it is possible to express equation (20.16) in the reduced form applicable to any gas. Describe the construction of a generalized chart for determining the (approximate) change of entropy of any gas with pressure at constant temperature. 

AZv Difference of vapor and liquid compressibility factors defined in Eq. (2-55) ... 

Figure 1 shows the measured sample density as a function of 1/a, where a is a compression factor defined by a-V/V with V the compressed sample volume and V the volume of loose powder that was compacted. By least-squares fitting to p—Pg/a, we found p -0.0296 g/cc (loose powder density). 

No specific mixing rules have been tested for predicting compressibility factors for denned organie mixtures. However, the Lydersen method using pseudocritical properties as defined in Eqs. (2-80), (2-81), and (2-82) in place of true critical properties will give a reasonable estimate of the compressibihty faclor and hence the vapor density. 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

An alternate to equation (6.15) is an equation that relates In

compressibility factor of the gas, that is defined as... 

A chart which correlates experimental P - V - T data for all gases is included as Figure 2.1 and this is known as the generalised compressibility-factor chart.(1) Use is made of reduced coordinates where the reduced temperature Tr, the reduced pressure Pr, and the reduced volume Vr are defined as the ratio of the actual temperature, pressure, and volume of the gas to the corresponding values of these properties at the critical state. It is found that, at a given value of Tr and Pr, nearly all gases have the same molar volume, compressibility factor, and other thermodynamic properties. This empirical relationship applies to within about 2 per cent for most gases the most important exception to the rule is ammonia. 

Equations 4.55 and 4.57 are the most convenient for the calculation of gas flowrate as a function of Pi and Pi under isothermal conditions. Some additional refinement can be added if a compressibility factor is introduced as defined by the relation Pv -= ZRT/M, for conditions where there are significant deviations from the ideal gas law (equation 2.15). 

Equation (I.IS) Is valid for open tubular columns under all normal conditions and for packed columns at low mobile phase velocities. The average carrier gas velocity is calculated from the outlet velocity by correcting the latter for the pressure drop across the column, and is simply given by u - ju, where j is the gas compressibility correction factor, defined In equation (1.2). 

Hence there must be one relation involving pc, Tc and Vc which is independent of the parameters a and b. This relation defines the critical compressibility factor Zc ... 

Nonequilibrium Extension of Omega Method The omega method HEM tends to produce discharge rates that are low, particularly for short pipes. To correct this deficiency, Diener and Schmidt proposed a modification they term the nonequilibrium compressibility factor N, defined by... 

Figure 1 shows the Rule Sheet for a TKISolver model REALGAS.TK (12. The first rule is the van der Waals equation of state. The second defines the gas constant, and the third rule defines Ae number density. The fourth defines the compressibility factor z, a dimensionless variable which measures the amount of... 

Using the Compressibility Factor. The behavior of most pure gases can be represented adequately by a single chart of the compressibility factor Z, which has been defined above in Equation (5.55). 

The volumetric properties of fluids are conveniently represented by PVT equations of state. The most popular are virial, cubic, and extended virial equations. Virial equations are infinite series representations of the compressibility factor Z, defined as Z PV/RTy having either molar density, p( = V-1), or pressure, P, as the independent variable of expansion ... 

As a first step toward improved description of real gases, we define the compressibility factor Z by the equation... 

Notice that the shapes of the isotherms of compressibility factors for the three gases given in Figures 3-2, 3-3, and 3-4 are very similar. The realization that this is true for nearly all real gases led to the development of the Law of Corresponding States and the definition of the terms reduced temperature and reduced pressure. Reduced temperature and reduced pressure are defined as... 

One way of exploring intermolecular forces is to measure the compression factor, Z, which is defined as... 

PI 1.5 Start with the defining equations for the fugacity / and the fugacity coefficient equations (11.36), (11.37), and (11.38), along with the relationships given in Table 11.1, and show that 4> is related to the compressibility factor z by equation (11.44)... 

The compressibility factor Z is defined to be PV/RT. Based on the detailed investigation of Miller (1964), Grain (1982) assumed the change of compressibility factor on vaporization, AZ for a number of chemicals at pressures below one atmosphere suggests that a value of 1 is more reasonable. Consequently, AZ = 1 is used here. 

The following table provides the Martin-James compressibility factor, j,1 and the Giddings plate height correction factor, f,2 for chromatographically useful pressures. These quantities are defined as... 

A more systematic way of approaching deviations from ideal gas behavior is by means of the compression factor, Z, defined as the ratio of the volume of the gas to that of an ideal gas at the same temperature and pressure ... 

This quantity is often called the compressibility factor, a name that is easy to confuse with the isothermal compressibility, defined in Eq. (9).] Z is obviously unity for an ideal gas. At the other extreme, when the pressure or density is very large, excluded volume effects become dominant, V > Vig, and Z > 1.0. 

Variables 2 and Zj are charges of ions i and j Ay is the Pauling factor defined as Ay = (1 + zjnx + z-Jn i, where nK and nj represent the numbers of electrons in the outermost shell of ions i and j, respectively Cy = (3/2) aiajEiEj/(Ei + Ej) and dy = (9/4e2)Cy(a, 1/Ar1 + atjE/Nj), where a denotes the polarizability of ions, N is the number of the total electrons of an ion, and E is the first ionization potential, evaluated from the Equation Ef = Nle2h2I Tr2mai for ion i, where h and m are the Planck constant and the mass of the ion, respectively. Values of p, b, and cr are estimated from isothermal compressibilities and thermal expansion coefficients of 17 rock-salt-type crystals of alkali halides by Fumi and Tosi (15). 

Critical properties of gaseous compounds are useful in determining the P-V-T Pressure-Volume-Temperature) properties at nonideal conditions. The compressibility factor Z is defined by the following relationship ... 

Lydersen, Greenkom, and Hougenl developed a general method for estimation of liquid volumes, based on the principle of corresponding states. It applies to liquids just as the two-parameter compressibility-factor correlation applies to gases, but is based on a correlation of reduced density as a function of reduced temperature and pressure. Reduced density is defined as... 

The departure from ideality (perfection) is chronicled, inter alia, by how much the compressibility factor Z, defined by ... 

The compressibility factor Z is calculated by solving the following cubic equation (whose symbols are as defined above) ... 

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