Average density

Although density does not directly involve the use of moles, an expression for the average density of a mixture may be expressed in terms of moles and an equation of state. The density of a mixture may be defined in terms of z, and the pure component densities as follows  

This is suitable when pure component densities are available, which are a function of the system temperature and pressure. The average density of a mixture may also be expressed in terms of the total mass and volumetric flow rates 

If a suitable equation of state is available, then Qtot may be expressed in terms of G and W yglz) as in Section 9.2.2.2. For example, assuming the mixture is in the gas phase, this simplifies to the following  

This is a useful expression for conversions from total volumetric flow rates to total mass flow rates. 

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A2.2.146). The average density N )/V= is the thennodynamic density. At low and high T one expects many more accessible smgle-particle states than the available particles, and (A) = means that each n.p... 

One should also note that the unfolding procedure makes the average density of levels unifomi over the entire energy range. Thus, the difference... 

Silicates. In 1990, a continuous hydrothermal production plant was started up in Sulitjehna, Norway for manufacture of 9000 m /yr of calcium sihcate [10101-39-0] having average density of 0.255 g/cm. The calcium siUcate is of the xonodite [12141 -77-4] form, Ca Sig02y(0H)2, which can easily be... 

He then recommends that the following relationships be used to estimate the mixture average density and viscosity for trie power calculations ... 

In calciilating the power required for mixers, a reasonable estimate of the average density and viscosity for a two-phase system is satisfactoiy. 

Many times solids are present in one or more phases of a solid-hquid system. They add a certain level of complexity in the process, especially if they tend to be a part of both phases, as they normally will do. Approximate methods need to be worked out to estimate the density of the emulsion and determine the overall velocity of the flow pattern so that proper evaluation of the suspension requirements can be made. In general, the solids will behave as though they were a fluid of a particular average density and viscosity and won t care much that there is a two-phase dispersion going on in the system. However, if solids are being dissolved or precipitated by participating in one phase and not the other, then they will be affected by which phase is dispersed or continuous, and the process will behave somewhat differently than if the solids migrate independently between the two phases within the process. 

To determine the compression-zone requirement in a thickener, a test should be run in a deep cylinder in which the average settling pulp depth approximates the depth anticipated in the full-scale basin. The average density of the pulp in compression is calculated and used in Eq. (18-47) to determine the required compression-zone volume ... 

Fig. 12. Laboratory OSB board density profile as a function of board thickness when the board average density of the panel is different (590 kg/nv and 690 kg/m ). Note the much higher peaks of surface density for the panel of higher average density, and the more even density profile for the panel of lower average density.

Another example of phase transitions in two-dimensional systems with purely repulsive interaction is a system of hard discs (of diameter d) with particles of type A and particles of type B in volume V and interaction potential U U ri2) = oo for < 4,51 and zero otherwise, is the distance of two particles, j l, A, B] are their species and = d B = d, AB = d A- A/2). The total number of particles N = N A- Nb and the total volume V is fixed and thus the average density p = p d = Nd /V. Due to the additional repulsion between A and B type particles one can expect a phase separation into an -rich and a 5-rich fluid phase for large values of A > Ac. In a Gibbs ensemble Monte Carlo (GEMC) [192] simulation a system is simulated in two boxes with periodic boundary conditions, particles can be exchanged between the boxes and the volume of both boxes can... 

In order to develop integral equations for the correlation functions, we consider the system composed of N polydisperse spheres. The average density of particles with diameter <7, is given by... 

We would like to recall that Xa p) is the fraction of molecules not bonded at an associative site now it is a function of the averaged density p(r). A generalization of the perturbational theory allows us to define Xa p) similar to the case of bulk associating fluids. Namely... 

The prescription proposed in the original Meister-Kroll-Groot [138,139] theory for hard spheres requires the determination of the local density and the averaged density as two independent variational variables by minimizing the grand potential with respect to these variables. The modification introduced by Rickayzen et al. [143,144] arises from another definition of the average density... 

Fig. 16 presents a eomparison of the phase diagrams for eonfined (sohd lines) and bulk fluids (dashed lines). The average density in the pore Pp is defined as... 

Abbreviations N is the total number of particles Pdim is the average density of dimers in each of the parts I and III is the average density of monomers in each of the parts II and IV p is the average density at the middle of parts II and IV this value has been used to calculate the excess chemical potential from Eq. (148). All remaining symbols are explained in the text. 

FIG. 21 Dependence of the average density on the configurational chemical potential. The solid line denotes the grand canonical Monte Carlo data, the long dashed fine corresponds to the osmotic Monte Carlo results for ZL = 40, and the dotted line for ZL = 80. (From Ref. 172.)... 

For the electronic structure calculations in a disordered system, f is chosen to be the Green function (zI-H( n )) where H is the Hamiltonian of the system and n are the random site occupation variables. According to ASF configuration averaged density of states (DOS) is given by ... 

To calculate the conductivity of the whole liquid, one has to average the obtained function for the configurations of an MD trajectory, which corresponds to an ensemble average. The corresponding averaged density-of-states (DOS) was computed considering the same configurations as described above for each case. 

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