Coefficients compressibility

The following example helps to illustrate the use of the equations presented up to this point. An aqueous slurry was filtered in a small laboratory filter press with a pressure drop of 0.5 atm and at a temperature of 20 C. After 10 minutes, 4.7 liters of filtrate were obtained after 20 minutes, 7.0 liters were collected. From experiments at other pressures, it was determined that the cake compression coefficient was s = 0.4. We wish to determine the volume of filtrate expected after 30 minutes from a filter press having a filtering area 10 times greater than the laboratory press if the filtration is to be performed at 1.5 atm pressure. The liquid temperature will be 55 °C. We also wish to determine the rate of filtration at the end of the process. 

The dependency of liquid volume on pressure may be expressed in terms of the coefficient of compressibility. The coefficient is constant over a wide range of pressures for a particular material, but is different for each substance and for the solid and liquid states of the same material. For liquids, volume decreases linearly with pressure. For gases volume is observed to be inversely proportional to pressure/. If water in its liquid state is subjected to a pressure change from 1 to 2 atm, then less than a 10 % reduction in volume occurs (the compressibility coefficient is very small). However, when the same pressure differential is applied to water vapor, a volume reduction in excess of 2 occurs. 

P[3 = P[ = fan input power D = fan size (impeller or wheel diameter) N = fan speed Nj = fan specific speed p = fan air density Q = fan flow rate Kp = compressibility coefficient L, = sound power level Pjt = fan total pressure Pjy = fan velocity pressure Pj-s = fan static pressure... 

Po = fan output power = total output power Q = fan flow rate, cfm Pjt = fan total pressure Kp = compressibility coefficient 7 = isentropic coefficient... 

The compressibility coefficient is the deviation from Boyle s law per unit pressure ... 

Here, V refers to the molar volume of the nonelectrolyte, V and Vs° are the intrinsic3 and apparent molar volume of the salt, respectively, and /3 is the isothermic compressibility coefficient of the solution. Although this equation is strictly valid in the limit of Vi - 0 and ca - 0, it works quite satisfactorily for small nonpolar solutes. The equation shows that the effect is greatest for nonelectrolytes of large molar volume Vi, and for salts that cause the largest electrostriction, Vs - Vs°. A difficulty with this expression is that it is not always easy to evaluate the intrinsic volume of a salt (the mere volume, without... 

We now introduce two new parameters that describe the changes in interionic distances and volume with pressure isothermal linear compression coefficient ft, and isothermal volumetric compression coefficient jiy ... 

Table 5.64 lists isobaric thermal expansion and isothermal compressibility coefficients for feldspars. Due to the clear discrepancies existing among the various sources, values have been arbitrarily rounded off to the first decimal place. 

Complexes, see also specific type in solution, structures, see X-ray diffraction n-Complexes, 4 178-184 Complex formation constant, outersphere, 43 46, 55 electrovalent interaction in, 3 269-270 Compressibility coefficient of activation, 42 9 Comproportionation constants, class II mixed-valence complexes, 41 290-292 Comproportionation equilibrium, 41 280-281 Compton effect, 3 172 Conantokins, calcium binding, 46 470-471 Concanavalin A, 36 61, 46 308 Concensus motif, 47 451 Concentration-proportional titrations of poly-metalates, 19 250, 251, 254 Condensation... 

From the interatomic distances the conclusion is to be drawn that the bonds in the hexagonal layers of atoms in these metals are stronger than those between layers. This conclusion is substantiated by the properties of the crystals, which show basal cleavage and have larger values of the compressibility, coefficient of thermal expansion, and electrical resistance in the direction perpendicular to the basal plane than in this plane. Moreover, measurements of the intensities of... 

This second step is accomplished using the coefficient of isothermal compressibility. Methods of estimating values of this compressibility coefficient will be discussed later in this chapter. However, we now will show the use of compressibility in computing density changes corresponding to pressure changes. 

The normal procedure for estimating formation volume factor at pressures above the bubble point is first to estimate the factor at bubble-point pressure and reservoir temperature using one of the methods just described. Then, adjust the factor to higher pressure through the use of the coefficient of isothermal compressibility. The equation used for this adjustment follows directly from the definition of the compressibility coefficient at pressures above the bubble point. 

It was shown that there is an empirical equation which connects the compressibility coefficient p with the free-volume fraction ... 

Compressibility coefficient 1.67 x 10-3 per ton/inch (smallest value for all the metals)... 

The compressibility coefficient, k, and reference volume, vo, are solely dependent on the composition of the guest(s) in the hydrate lattice while the thermal expansion coefficients, a, a2, ando 3 are solely dependent on the hydrate structure. 

From studies of the concentration dependence of density and isentropic compressibility coefficients, the apparent molar volume and the isentropic apparent molar compressibility may be obtained above and below the CMC. Such studies have recently been performed for several systems by Brun, Holland and Vikingstad32,39-41 who deduced the change in partial molar volume and compressibility on micelle formation. This gives information on the counterion hydration and the packing of the hydrocarbon chains in the micelles. 

Kc = compression coefficient of tested food Ks = shear coefficient of tested food A - area of punch P = perimeter of punch C = constant... 

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