Volumes, partial

To estimate the density at 25 C of pure hydrogen peroxide and to calculate the partial volumes of both components in aqueous hydrogen peroxide of mass fraction 0.40 at 25 C. 

Precise measurements of the density of aqueous hydrogen peroxide have been made by Easton, Mitchell, and Wjmne-Jones (Trans. Faraday Soc. 1952, 48, 796). Their results at 25 C have been fitted by least squares (Francis, Reading University) to the alternative formulae 

The extrapolated value for the denaty of pure hydrogen peroxide is obtained by setting w = 1 in fonnula (2). 

The partial volumes V-n and Vp of water and hydrogen peroxide are given by the formulae 

The partial molar volumes are obtained from the partial volumes per gram by multiplication by the molar masses. 

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Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

A partially filled horizontal tank requires the determination of the partial volume of the heads. The Lnkens catalog gives approximate volumes for partially filled (axis horizontal) standard ASME and ellipsoidal heads. A formula for partially filled heads, by Doolittle [Ind. 

The terms zonal model and flow element are also used for the simplified characterization of the flow field in a single enclosure. There, a zone represents a partial volume of air in the enclosure, whereas in the multizone models described here, a zone represents a specific enclosure which is connected to other enclosures by air conductances (see The Airflow Network later). 

Isokinetic Sampling I he sample gas partial volume flow must be extracted isokinetically to avoid aerodynamic separation effects and to ensure correct particle size distribution. Isokinetics means that the velocity and direction of the sample gas partial flow at the sample nozzle are the same as at the main gas stream. ... 

Particle Collection Particles in the extracted partial volume flow are retained in the collector filter. Tlie particle mass emitted is determined by the weight difference of the filter before and after the collection. Factors crucial to the measuring precision and the smallest measuring range of particle concentration are ... 

A differential volume element dV in the flow field contains a mass of gas dm and a mass of solids dni. The corresponding volumes taken by gas and solids are denoted by tiV and dY. The sum of these partial volumes is the total volume of the mixture. 

This is similar to Dalton s law, but states that the volume of a mixture of idea gases is equal to the sum of the partial volumes that the constituent gases would occupy if each existed alone at the total pressure and temperature of the mixture. As a formula this becomes ... 

If we truncate Eqs. (63) and (64) after the first terms, and assume as before that the partial volume of the solute is a function of temperature only, we obtain the equation of Krichevsky and Ilinskaya (K5) 5... 

In spatial dimensions or in partial volumes of compact solids, or... 

Additional information on the solvation layer around the polymers was obtained by PPC (Sect. 2.1), a technique that allows one to evaluate the changes in the partial volume of the polymer throughout the phase transition, and to obtain information on the temperature-dependant relative hydrophilicity/hydrophobicity of a polymer in solution [210]. Particular interest in the PPC studies was focused on the effect of the amphiphilic grafts on the volumetric properties of the polymers. 

Finite resolution and partial volume effects. Although this can occur in other areas of imaging such as MRS, it is particularly an issue for SPECT and PET because of the finite resolution of the imaging instruments. Resolution is typically imaged as the response of the detector crystal and associated electron to the point or line source. These peak in the center and fall off from a point source, for example, in shapes that simulate Gaussian curves. These are measures of the ability to resolve two points, e.g. two structures in a brain. Because brain structures, in particular, are often smaller than the FWHM for PET or SPECT, the radioactivity measured in these areas is underestimated both by its small size (known as the partial volume effect), but also spillover from adjacent radioactivity... 

Another issue for quantification is the effect of the finite resolution of PET/SPECT relative to small structures being imaged. This can result in the so called Partial Volume Effect which is characterized by an underestimation of the true radioactivity. This is an area of increasing research, but is not a major limitation when there is not a large difference between patients and controls in the volume of... 

By analogy, we can consider an interrelation between the partial volumes of partitions ... 

In all cases, v, can be substituted with v, if definition or measurement of the latter is easier. This again means the simple rule that both partial volume of a partition and its addition are expressed using partial volumes of other partitions. 

In all cases, the porosity of bidisperse PS increases when one or both packings begin to demonstrate nondense packings. Typical dependences of s on partial volume of the large globules, X, and the ratio K=Dl/D2 is shown in Figure 9.19 [61], The min values decrease with an increase in K. 

Figure 9.19 Typical dependence of the porosity, s, of a bidisperse PS with loose random packing of globules size of on partial volume of the larger particles X, and K=D ID2.

Consider a nonporous catalyst having an active component of a complex (unknown) composition, deposited over a known support (known parameters the true density of a support and its partial mass, ms). We have no information on the type of active component, only its partial mass, mc= 1 —ms. Also known is the density of solid phase of a catalyst as a whole. Allocate the partitions for this PS, and determine (a) a partial volume of the active component (b) the hue density of the active component. 

Let us complicate Problem 5 assuming that the supported catalyst is porous. Allocate the partitions for this PS, and determine (a) a partial volume of the active component and (b) the true density of the active component. 

TABLE 18.1. Densities and Partial Volumes of Ethanol-Water Mixtures"... 

From this definition of the shape function the partial volume of the solute is given by... 

Theoretically, only fuel beds which have a significant net flow of solid phase through a partial volume of the conversion system (reactor) can be classified according to the three basic configurations. In other words, all continuous fuel beds have a net flow and can be categorised, whereas certain batch beds cannot in principle be defined. 

Figure 44 Two partial volumes at two different times (t) and (t) at the same position inside an idealised and simplified overfired updraft homogeneous batch bed. The partial volumes show the differentiated thermochemical processes both on micro and macro scale.

According to Hildebrand, the heat of mixing a solute and a solvent is proportional to the square of the difference in solubility parameters, where is the partial volume of each component, namely solvent -yj and solute 2. Since typically the entropy term favors solution and the enthalpy term acts counter to solution, the objective is to match solvent and solute so that the difference between their 8 values is small, resulting in a small enthalpy acting against solubility ... 

The following amounts of 2,2 -azobisisobutyronitrile (AIBN) are weighed into 4 graduated 25-ml flasks 35,110,180, and 250 mg (0.21,0.67,1.10, and 1.52 mmol).The flasks are filled to the mark with destabilized styrene (at 20 °C) and the amount of styrene divided by 25 ml gives the density at 20 °C (neglecting the partial volume of AIBN). 

The durability of polymers may also be improved by the addition of reinforcing fillers and fibrous reinforcements (F) to the polymer matrix (M). The modulus of a composite is a function of the distribution (amount and orientation) of the fibers,/, the modulus of each component, G, and the partial volume of the fiber, C, as shown by the following equation ... 

C Partial volume Capacity Concentration Compliance Stress-optical coefficient... 

Amagat postulated that the total volume occupied by a gas mixture is equal to the Sum of the volumes that the pure components would occupy at the same pressure and temperature. This is sometimes called the law of additive volumes. Amagat s law of partial volumes is analogous to Dalton s law of partial pressures. 

The volumes occupied by the individual components are known as partial volumes. This equation is correct only if the mixture and each of the components obey the ideal gas equation. 

Again consider a gas mixture consisting of nA moles of component A, nB moles of component B, and so on. The partial volume occupied by each component can be calculated using the ideal gas equation. 

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