Partial densities

According to the state equation of ideal gas, the partial density of dry air in humid air is... 

Comparing Examples 2a and 2b we notice that the total air pressure has effects on the humidity x, partial density of dry air p total pressure or pressure of humid air, and enthalpy h. Knowing the total pressure is therefore essential in calculations of the thermodynamic properties of humid air. 

Temperature rc) Humidity kg HjO/kg dry air) Water vapor partial pressure (kPa) Water v K>r partial density (kg/m ) Water vaporization heat M/kg) Mixture enthalpy (kj/kg dry air) Dry air partial density (lKinematic viscosity (I0< mJ/s) Specific heat (kJ/K kg) Heat conductivity (W/m K) Diffusion factor water air (1 O mJ/s) Temperature rc)... 

We will consider flow through a solid element. Introducing the notations for molar flow density, partial density, and the reaction rate gives an equation for the mass balance ... 

The real density pQ is the mass of the gas divided by the volume occupied by the gas. The apparent density or partial density is the mass of the gas divided by the total volume of the solid-gas mixture. 

With the aid of the partial densities and p,., the mass flow densities can be expressed as follows ... 

I he mixture clement shown in Fig. 14.15 contains the flowing gas and solid particles. The partial densities of these two elements are pg and p. respectively. The void fraction is and this can be interpreted as the partial cross-sectional area for gas flow (see Eq. (14.13)). This means that if the pressure of the gas is p, then the pressure force per unit area of the total mixture affecting the flow of gas is (pp and the pressure force affecting the flow of solids is 1 -

[Pg.1343]

For the paramagnetic case the expre.ssion for the photo current in Eq. (2) can be simplified to a concentration weighted sum over the products of the K-resolved partial density of states (DOS) ri (F) and a corresponding matrix element that smoothly varies with energy [13]. This simple interpretation of the XPS-spectra essentially also holds for the more complex spin-resolved ca e in the presence of spin-orbit coupling as studied here. 

For comparison, we applied also a simplified LCAO-DFT method to get the conductivity by means of the Kubo-Greenwood formula. This method is a hybrid between ab initio and empirical methods and is described in detail in Ref. [12]. It allows a faster computation of the electronic properties and the consideration of larger supercells than the Car-Parrinello method. Within this scheme it is also possible to split the total DOS into fractions referring to the sodium and tin atoms, respectively, i.e. to get the partial densities-of-states. 

Figure 1. Densities-of-states and partial densities-of-states corresponding to Na and Sn for different compositions of liquid NaSn.

It is easy to show that the partial densities (p) of the components can be... 

Fig. 2.5 Total and partial densities of states forTiF Pbcm, (a) and Fm-3m (b).

Complementary to other methods that constimte a basis for the investigation of molecular dynamics (Raman scattering, infrared absorption, and neutron scattering), NIS is a site- and isotope-selective technique. It yields the partial density of vibrational states (PDOS). The word partial refers to the selection of molecular vibrations in which the Mossbauer isotope takes part. The first NIS measurements were performed in 1995 to constitute the method and to investigate the PDOS of... 

The first paper of the frontier-electron theory pointed out that the electrophilic aromatic substitution in aromatic hydrocarbons should take place at the position of the greatest density of electrons in the highest occupied (HO) molecular orbital (MO). The second paper disclosed that the nucleophilic replacement should occur at the carbon atom where the lowest unoccupied (LU) MO exhibited the maximum density of extension. These particular MO s were called "frontier MO s . In homolytic replacements, both HO and LU.were shown to serve as the frontier MO s. In these papers the "partial" density of 2 pn electron, in the HO (or LU) MO, at a certain carbon atom was simply interpreted by the square of the atomic orbital (AO) coefficient in these particular MO s which were represented by a linear combination (LC) of 2 pn AO s in the frame of the Huckel approximation. These partial densities were named frontier-electron densities . 

The coefficients, particularly for large molecules, are often more useful as the sums of products called the density matrix. If Ci p is the coefficient of the pth basis function of symmetry A in the fth molecular orbital, the element (p, q) of the (partial) density matrix for m.o. i is... 

In the LHF models, it is assumed that droplets are in dynamic and thermodynamic equilibrium with gas in a spray. This means that the droplets have the same velocity and temperature as those of the gas everywhere in the spray, so that slip between the phases can be neglected. The assumptions in this class of models correspond to the conditions in very thin (dilute) sprays. Under such conditions, the spray equation is not needed and the source terms in the gas equations for the coupling of the two phases can be neglected. The gas equations, however, need to be modified by introducing a mixture density that includes the partial density of species in the liquid and gas phases based on their mass fractions. Details of the LHF models have been discussed by Faeth.l589]... 

Fig. 5. Temperature dependence of the stoichiometry coefficient v for the homogeneous decomposition of hydrazine from shock tube data. , ps2h4 = 11.6, pt = 0.7 9, Fn2h4 = 5.0, Px 1-2 , Pn2h4 = 2.2, pt = 2.5 O, Pn2h4 = 1-2, pt = 1.2 Pn2h4 = 11 Pt = 2.5 Q, Pn2h4 = 11, Pt = 5.7, Q, pm2h4 = 7.4 px = 7.5. pn2h4 = partial density of N2H4 in 10 5 mole.l-1 pt — total density at reaction conditions in 10-2 mole.l". (From Michel and Wagner28.)...

In order to study the effects of different TBF on neutron star structure, we have to calculate the composition and the EOS of cold, catalyzed matter. We require that the neutron star contains charge neutral matter consisting of neutrons, protons, and leptons (e, p ) in beta equilibrium. Using the various TBF discussed above, we compute the proton fraction and the EOS for charge neutral and beta-stable matter in the following standard way [23, 24] The Brueckner calculation yields the energy density of lepton/baryon matter as a function of the different partial densities,... 

The partial densities and the gap equation for the up and down paired quarks can be found from the fixed points of the thermodynamic potential density Q... 

In Ref. [24] it has been investigated whether with the above three- flavor quark matter EoS of the NCQM strange quark matter can appear in the interior of compact stars. The constraints of fl equilibrium and charge neutrality have been applied (see below) in order to constrain the partial densities of electrons and up-, down-, strange quarks, see Fig. 3. It can be seen that strange... 

FIGURE 6.11 Characteristic parametric variations of dimensionless temperature T and mass fraction m of fuel, oxygen, and products along a radius of a droplet diffusion flame in a quiescent atmosphere. j is the adiabatic, stoichiometric flame temperature, pA is the partial density of species A, and p is the total mass density. The estimated values derived for benzene are given in Section 2b. 

Figure 9.5 Total and partial density of state of bulk FeSi...

Figure 9.7 presents the DOS distribution of FeS2 (100) surface. By comparing the PDOS (partial density of state) on the surface with the PDOS from the bulk, a slight narrowing and an upward shift of the Fe (3d) band can be seen because the surface Fe atom loses one neighbor S atom. However, the most important effects... 

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