Per unit volume

The V/L ratio is a volatility criterion seldom used in France but is used in Japan and in the United States where it has been standardized as ASTM D 2533. At a given temperature and pressure, the V/L ratio represents the volume of vapor formed per unit volume of liquid taken initially at 0°C. 

Measured in MJ/m or Btu/ft, the Wobbe Index has an advantage over the calorific value of a gas (the heating value per unit volume or weight), which varies with the density of the gas. The Wobbe Index Is commonly specified in gas contracts as a guarantee of product quality. A customer usually requires a product whose Wobbe Index lies within a narrow range, since a burner will need adjustment to a different fuel air ratio if the fuel quality varies significantly. A sudden increase in heating value of the feed can cause a flame-out. 

This structure is called close packed because the number of atoms per unit volume is quite large compared with other simple crystal structures. 

Since the absorption spectrum is a ratio it is amenable to other interpretations. One such interpretation is that the absorption spectrum is the ratio of energy absorbed to energy incident. From this perspective, the quantity /)co(d/d0< li 0l f 0) is interpreted as the rate of energy absorption (per unit volume), since d E/d t = /)co(d AVd t) while tire quantity E dha is interpreted as the incident energy flux, which depends only on the field intensity and is independent of frequency. 

The quantity introduced above is the spectral density defined as the energy per unit volume per unit frequency range and is... 

For an electrolyte solution containing both anions and cations, with the tennmal velocity of the cations being and the number of ions of charge z Cq per unit volume being Et, the product corresponds just... 

Figure A2.5.9. (Ap), the Helmholtz free energy per unit volume in reduced units, of a van der Waals fluid as a fiinction of the reduced density p for several constant temperaPires above and below the critical temperaPire. As in the previous figures the llill curves (including the tangent two-phase tie-lines) represent stable siPiations, the dashed parts of the smooth curve are metastable extensions, and the dotted curves are unstable regions. See text for details.

Now, again, we use a probabilistic argument to say that the number of particles with velocity in this total volume is given by the product of the total volume and the number of particles per unit volume with velocity Vp that is, 8v(v,Uj) To complete the calculation, we suppose that the gas is so dilute that each of the... 

Our first result is now the average collision frequency obtained from the expression, (A3.1.10). by dividing it by the average number of particles per unit volume. Here it is convenient to consider the equilibrium case, and to use (A3.1.2) for f. Then we find that the average collision frequency, v, for the particles is... 

Stosszahlansatz. The total number of (Vj, v)-collisions taking place in bt equals the total volume of the (Vj, v)-collision cylinders times the number of particles with velocity per unit volume. 

Another important characteristic of the late stages of phase separation kinetics, for asynnnetric mixtures, is the cluster size distribution fimction of the minority phase clusters n(R,z)dR is the number of clusters of minority phase per unit volume with radii between R and + cW. Its zeroth moment gives the mean number of clusters at time r and the first moment is proportional to die mean cluster size. 

For a general dimension d, the cluster size distribution fiinction n(R, x) is defined such that n(R, x)dR equals the number of clusters per unit volume with a radius between andi + dR. Assuming no nucleation of new clusters and no coalescence, n(R, x) satisfies a continuity equation... 

The central quantity of interest in homogeneous nucleation is the nucleation rate J, which gives the number of droplets nucleated per unit volume per unit time for a given supersaturation. The free energy barrier is the dommant factor in detenuining J J depends on it exponentially. Thus, a small difference in the different model predictions for the barrier can lead to orders of magnitude differences in J. Similarly, experimental measurements of J are sensitive to the purity of the sample and to experimental conditions such as temperature. In modem field theories, J has a general fonu... 

A completely analogous derivation leads to the rate coefficient for bimolecular reactions, where dare partition fiinctions per unit volume. ... 

Consider an ensemble composed of constituents (such as molecules) per unit volume. The (complex) density operator for this system is developed perturbatively in orders of the applied field, and at. sth order is given by The (complex). sth order contribution to the ensemble averaged polarization is given by the trace over the eigenstate basis of the constituents of the product of the dipole operator, N and = Tr A pp... 

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... 

Each of the species A transfers energy e g to each species B. The amount of energy transferred per unit volume in unit time from ensemble A to ensemble B is... 

The number of translational states per unit volume dR with directed energies E = (E, p) in the range [E, E +... 

Efficient use of a catalyst requires high rates of reaction per unit volume and, since reaction takes place on the surface of a solid, catalysts have high surface areas per unit volume. Therefore, tlie typical catalyst is porous, witli... 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

The rate of storage of chemical potential (in other words, the power P carried by the chemical reaction) isypg, where j = d/j/dt = the net flux per unit volume (here, as elsewhere, lower case letters denote concentrations,... 

Now the force per unit volume exerted on the porous medium by the pressure gradient in the gas is -grad p, where p, as distinct from is the physical pressure of the gaseous mixture. This is the force which must be balanced in our model by the external forces acting on the dust particles, so... 

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