Compressibilities partial compressibility factor

The value of z from the general equation of state and its derivative with respect to u, is substituted in the partial compressibility factor equation to give... 

Chueh s method for calculating partial molar volumes is readily generalized to liquid mixtures containing more than two components. Required parameters are and flb (see Table II), the acentric factor, the critical temperature and critical pressure for each component, and a characteristic binary constant ktj (see Table I) for each possible unlike pair in the mixture. At present, this method is restricted to saturated liquid solutions for very precise work in high-pressure thermodynamics, it is also necessary to know how partial molar volumes vary with pressure at constant temperature and composition. An extension of Chueh s treatment may eventually provide estimates of partial compressibilities, but in view of the many uncertainties in our present knowledge of high-pressure phase equilibria, such an extension is not likely to be of major importance for some time. 

Equation 163, written as liu = (f- / RT, clearly shows that In (j) is a partial molar property with respect to GR/ RT. MultipHcation of equation 175 by n and differentiation with respect to at constant 7, P, and in accord with equation 116 yields, after reduction, equation 179 (constant 7, .x), where Z, is the partial molar compressibility factor. This equation is the partial-property analogue of equation 178. 

During the operation with gas ballast, such an amount of air will enter the pump house (after the pump house is separated from the vacuum chamber) that the water vapor at the operating temperature of the pump cannot condense during the compression phase of the pump. Consider an example water vapor is pumped at a partial pressure of 0.5 mbar and the temperature of the pump is +70 °C. Under these conditions, the water vapor will condense if the compression exceeds -310 mbar. If the pressure in the pump house is increased by air from 0.5 mbar to e.g. 50 mbar, the compression needs only to be 1000/50 = 20. The original water vapor at 0.5 mbar is compressed by a factor of 20, and the water vapor pressure reaches only 0.5 X 20 = 10 mbar. No condensation can take place at 70 °C in the pump house. 

Xt partial molar property y mole fraction, gas phase z mole fraction, solid phase z electrical charge on ion Z compressibility factor... 

Graphical integration requires simple plots of both (dZ/6T)P/P and (Z - 1)/P vs. P. Values of (Z - l)/P are calculated directly from the given compressibility-factor data at 360 K, The quantity (dZ/dT)P/P requires evaluation of the partial derivative... 

Component (i) Yi Partial pressure (Pi =PYi) Reduced pressure (Pi /Pc.i) Reduced temperature (T/Tc,i) Compressibility factor (Zj) ZiYi... 

Real gas behavior can be partially accounted for by including the compressibility factor ... 

Explain in your own words and without the use of jargon (a) the three ways of obtaining values of physical properties (b) why some fluids are referred to as incompressible (c) the liquid volume additivity assumption and the species for which it is most likely to be valid (d) the term equation of state (e) what it means to assume ideal gas behavior (f) what it means to say that the specific volume of an ideal gas at standard temperature and pressure is 22.4 L/mol (g) the meaning of partial pressure (h) why volume fraction and mole fraction for ideal gases are identical (i) what the compressibility factor, z, represents, and what its value indicates about the validity of the ideal gas equation of state (j) why certain equations of state are referred to as cubic and (k) the physical meaning of critical temperature and pressure (explain them in terms of what happens when a vapor either below or above its critical temperature is compressed). 

X = linear coordinate in direction opposite to flow In the above notation, the units of Di will be distance /time, and the permeability Pi may be expressed in the same units. If different units are to be adopted for Pi then the form of the gas law or equation of state may be introduced, whereby (Pyi) V = z iii RT, where Pyt is the partial pressure (or absolute activity) of component i, iii is the moles of component i, and z is the compressibility factor (which in general is applicable to singlephase liquids as well as gases). Accordingly,... 

For mechanical pumps, the potential condensation of vapours from the work chamber can cause problems for the pumps, especially for a CVD process. The compression of the vapour leads to condensation, which forms liquid droplets, if the partial pressure of a gaseous vapour reaches its saturated vapour pressure of a liquid. These condensed liquid droplets may contain water, HC1 and some chlorosilanes. They mix with the pump oil and result in corrosion of pump parts. For example, the vapour pressure of methyltrichlorosilane (a kind of precursor for SiC deposition) at 28°C is about 200 Torr. If this gas is compressed by a factor of 107 by a two-stage pump, methyltrichlorosilane will be condensed if its partial pressure in the reaction chamber is more than 2 x 10 5 Torr. 

The partial molar volume or compressibility factor is evaluated from an equation of state or from experimental data. 

A general equation of state may be written as PV=zRT or z = PV/RT, where V is the molar volume and z is the compressibility factor. In accordance with the partial property equation, the partial molar volume and the partial compressibility factor are expressed as follows ... 

Here, quantity 2, is a partial molar compressibility factor evaluated at constant temperature and total volume ... 

Here, pis molar density, and is a partial molar compressibility factor given by... 

To interpret Eq. (5.186), we first note that this expression describes a scaling of the pressure. The system of JV particles is (virtually) separated into NjK subsystems, every one of which contains K interacting particles. Each of these subsystems occupies the entire volume V and contributes a partial pressure p K g,k T/V). If it were permissible to neglect interactions among particles assigned to different subsystems, the total pressure would equal N/K)p K g,k T/V). However, particles belonging to different subsystems do indeed interact with one another, so that it is necessary to introduce a corrective factor, namely, the renormalized compressibility factor functional equation, expressing the requirement that the value of the pressure be unaltered by the virtual subdivision of the system. 

Based on Eurocode 2, the design compressive strength equals the characteristic strength ft divided by the partial safety factor for concrete. This design value corresponds to a sensitivity factor ay = 0.8 in a level 11 method (Konig Hosser 1982). 

Effective area Design compressive force Design compression resistance of the cross section Buckling resistance of member Partial safety factor for material resistance... 

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