Density volume

This equation was derived for a two-dimensional system, where the areal density, p, of the snow was used. It applies equally to a three-dimensional system, where the discontinuity is a plane instead of a line, and p is the volume density. 

Name Flashpoint °F Explosive Limits in air % by Volume Density... 

Stimulated emission is quantified by the (wavelength dependent) excited state cross-section other processes are important, stimulated emission leads directly to amplification of light. In a material with a volume density fVcxc of excited 5 -states this amplification can be described by... 

W-h/kg (LiCF)], and a volume density of 10 W-h/in. , the battery is currently marketed by Matsushita in six different capacities. The most popular of these, the BR-435, is a cylindrical cell 4 mm in diameter by 30 mm long 4 million of these cells were produced in 1977 (B31). 

Unlike mass and volume, density does not vary with the amount of a substance. Notice in Figure 1-20 that all the corks float, regardless of their sizes. Notice also that all the pieces of lead sink, regardless of their sizes. Dividing a sample into portions changes the mass and volume of each portion but leaves the density unchanged. A property that depends on amount is called extensive. Mass and volume are two examples of extensive properties. A property that is independent of amount is called intensive. Density and temperature are intensive properties. 

Fraction Boiling point (°C) Volume % Density (kg L- ) Sulfur (wt.%) (approx.)... 

Then, we can reduce each elementary volume dV — hih2dl and increase the volume density so that the elementary mass ... 

In this case the volume density S(q) tends to infinity as h, when h(q) approaches zero. Correspondingly, the expression for the field is... 

We have found that the volume density tends to infinity differently near point, linear, and surface masses, and this fact influences the field behavior in the vicinity of such places. Of course, Equation (1.6) always allows us to calculate the field of attraction g. At the same time, in many cases the use of Equation (1.15) greatly simplifies this procedure. 

Here d is the volume density at a point. For instance, at points where masses are absent div g = 0. Let us discuss the physical and mathematical content of these equations. The first one clearly shows that the attraction field does not have vortices and, correspondingly, the work done by this field is path independent. In other words, the circulation of the field is equal to zero. At the same time, the second equation demonstrates that the field g is caused by sources (masses) only. As illustration, consider the set of these equations in the Cartesian system of coordinates ... 

Besides, the potential and its first derivatives are continuous at boundaries where a volume density is discontinuous function. It is obvious that in this case the solution of the forward problem is unique. Now consider a completely different situation, when a density 5 q) is given only inside some volume V surrounded by a surface S, Fig. 1.8a. Inasmuch as the distribution of masses outside V is unknown, it is natural to expect that Poisson s equation does not uniquely define the potential U, and in order to illustrate this fact let us represent its solution as a sum ... 

The behavior of g as a function of R is shown in Fig. 1.12c, and, of course, it is a continuous function. Now let us mentally decrease the thickness h and increase the volume density so that the mass remains the same. In such a way we arrive at a distribution of masses with a surface density, and this replacement does not change the field outside the shell, but it leads to a discontinuity of the field at the surface masses. It is instructive to demonstrate why the field inside the shell, Relementary surfaces dS and dS2- By definition we have ... 

Let us consider now a transition from a layer with a finite thickness to a plane of surface masses, where z = 0. Suppose that the layer thickness tends to zero, but the volume density increases in such way that their product, a — 6h remains constant. Then, the field outside the layer does not change and equals its original value, while... 

Here is the volume density and the scalar component of the attraction field, that is, the force per unit mass. To describe the effect of surface forces, consider front- and the backsides of the volume, dS(x + dxl2,y,z) and dS x—dxl2,y,z), which are perpendicular to the v-axis. Due to the action of the neighboring part of the medium the surface force acting on backside is... 

The volume density of charge of a given type, Qyj, is dehned as Qyj = ZjFcj. A conductor is always electroneutral that is, in any part of it the combined density of all ions (and other charges, free and locahzed) is zero and hence... 

Generally, a phase transition is triggered by an external stress which most commonly is a change in temperature or pressure. Properties that can change discontinuously include volume, density, specific heat, elasticity, compressibility, viscosity, color, electric conductivity, magnetism and solubility. As a rule, albeit not always, phase transitions involve structural changes. Therefore, a phase transition in the solid state normally involves a change from one to another modification. 

VOLUME DENSITY SURFACE DENSITY SPECIFIC SURFACE MEAN INTERCEPT LENGTH MEAN FREE DISTANCE MEAN DIAMETER MEAN CURVATURE ELONGATION RATIO DEGREE OF ORIENTATION... 

The pharmaceutical industry has taken great interest of late in the study of polymorphism and solvatomorphism in its materials, since a strong interest in the phenomena has developed now that regulatory authorities understand that the nature of the structure adopted by a given compound upon crystallization can exert a profound effect on its solid-state properties. For a given material, the heat capacity, conductivity, volume, density, viscosity, surface tension, diffusivity, crystal... 

The thickness of the total disk mass distribution is dynamically measured for the first time and is found to be 390 pc in relative agreement with the old stellar disk scaleheight. All the dynamical evidences concerning the structure of the disk (its local volume density - i.e. the Oort limit-, its surface density and... 

At both 3 and 6 months, there was a two- to threefold increase in volume density of alveolar Type II cells after 6 months, lungs had foci of pneumonia, suggesting a higher susceptibility to pulmonary... 

Sometimes expressed in terms of volume density - equivalent to surface density in a uniform or exponentially... 

Fig. 12.6. Observable baryons in the Universe as a function of time. The curves represent the total mass density in stars (in Af0Mpc-3) from Rudnick et al. (2003) based on a survey of near-infrared selected galaxies in the Hubble Deep Field South, assuming a Salpeter(O.l) IMF. (For a Kennicutt (1983) IMF, the numbers would be approximately halved.) The points with error bars show the cosmic density of H I from DLAs and sub-DLAs at various redshifts, uncorrected for obscuration, while the point at bottom right shows the present-day density of H i clouds determined by Zwaan et al. (2005). The typical H I co-moving volume density corresponds to S2Hi — 0.7 x 10-3 (taking h = 0.65). After Peroux, Dessauges-Zavatsky, D Odorico et al. (2005).

The result is that when 8 is large, stars form rapidly, roughly as in a Schmidt Law in volume density with n 2, until star formation is quenched by shocks and there is a saturation conversely, when it is small, there is a much more gradual process. Figure 12.15 shows the resulting metallicity evolution with time for different <5 s, assuming a yield p = 0.02 Z . 

Let s briefly review the promising hydrogen storage methods by Figure 5, where the volume densities (Vd) vs weight densities (Wd) for each storage method are shown [16],... 

Vd, Wd, MH, SWNT, PCP, and AC mean volume density, weight density,metalhydrides, single walled carbon-nanotubes, pressurized carbon polymer, and activated carbon, respectively. 

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