Peculiar speed

Thus, for a molecule of type 1 the mean value of the peculiar speed (C i)m for a gas in the Maxwellian state yields ... 

The present form of the integral is not really defined in a consistent manner as the integrand contains the peculiar speed C, which is defined by C = C, whereas the integration is over the velocity space dc. Transforming from Cartesian coordinates... 

In kinetic theory, in accordance with the kinetic energy equipartition theorem, the kinetic temperature T of a gas at a uniform state at rest or in uniform translation is defined directly in terms of the average peculiar speeds of the molecules, by the three dimensional relation m C )M = kT obtained from (2.200) and (2.199). In accordance with (2.200) and (2.192) the static pressure p of a. gas in equilibrium is given hy p = 3px = nm C )M = nm C )M = knT. Considering the mass M of gas contained in a volume V, the number of mono-atomic molecules N in the mass M is M/m, and the number density n is therefore N/ V. The thermodynamic pressure is then given by pV = NkT. Alternatively one can write N = nNa, where n is the number of moles of gas present and is Avogadro s number. Then, the ideal gas law, yields ... 

While pressure melting may be important for snow and ice near 0°C, it is possible that even here an alternative explanation will prove important. Ice is a substance of unusual structural complexity, and it has been speculated that a liquidlike surface layer is present near the melting point [17,18] if this is correct, the low /t values observed at low sliding speeds near 0°C may be due to a peculiarity of the surface nature of ice rather than to pressure melting. 

In all other cases the observed result will depend upon both the speed of mixing and the speed of nitration. The relative rate will be greater than unity by an amount peculiar to the conditions of the experiment. Again, if the alkylbenzene is sufficiently reactive to be nitrated upon encounter, whilst benzene is not, the relative rate will be greater than unity and, for the experimental conditions, will be a limiting upper value no matter what aromatic is used. 

What can be said of local topology dependence in larger (and infinite) systems (for which direct calculation of global measures becomes clearly impractical) How does the average information transmission speed depend on local peculiarities of structure ... 

The rotating-disk CVD reactor (Fig. 1) can be used to deposit thin films in the fabrication of microelectronic components. The susceptor on which the deposition occurs is heated (typically around lOOOK) and rotated (speeds around 1000 rpm). A boundary layer is formed as the gas is drawn in a swirling motion across the spinning, heated susceptor. In spite of its three-dimensional nature, a peculiar property of this flow is that, in the absence of buoyant forces and geometrical constraints, the species and temperature gradients normal to the disk are the same everywhere on the disk. Consequently, the deposition is highly uniform - an especially desirable property when the deposition is on a microelectronic substrate. 

The depth in the sample surface from which the PA signal comes depends on the beam chopping frequency. At low chopping frequencies spectral information comes from greater depths in the sample. In other words, if one speeds up the motor of the device, such as a fan blade, that is chopping the incident light beam, not only will S/N diminish, but the sample will also be probed at a shallower depth below its surface. This ability to yield subsurface spectral and thermal information is a peculiar advantage of PAS over reflectance and transmission spectroscopies that still remains to be widely exploited (5). 

Both large-scale motion (mass flow) and small-scale motion (turbulence) are usually required to bring about effective mixing (R5). Different ratios of mass flow to turbulence can be obtained for a given impeller type for the same power input large ratios for large values of d/T and slow speed, small ratios for small values of d/T and high speed. The requirements peculiar to batch liquid extraction have not been established, but for other services d/T = 0.2 to 0.5 is usually recommended for baffled tanks. 

Tire speed of the reaction is thus proportional to the concentration of arsenious acid and to the square of the concentration of nitrous acid present. The effect of the presence of mercuric salts on the velocity of this oxidation is peculiar 8 at a concentration of 7-7 x 10 6 mol. per litre the reaction is completely inhibited, but with diminishing concentration the inhibiting effect becomes less marked until, at 7-7 x 10-9 mol. per litre, there is a definite positive catalytic effect which becomes more marked at the extremely low concentration of 7-7 x 10 u mol. per litre. The retarding effect of the mercuric salt may be overcome by the addition of a small amount of halogen acid to the nitric acid.9 The... 

The first difference in a detonation wave which is favorable for stability is the fact that due to the decrease in the speed of sound (added to the mass velocity) to less than the propagation velocity, independence is achieved from the conditions behind the wave. On the other hand, application of small perturbations also leads to variation in the rate of the chemical reaction. It is impossible now to foresee the result of a calculation of stability with respect to small perturbations which might prove dependent on peculiarities of the chemical kinetics (autocatalysis, activation heat). 

In Figure 5.11d, we show the electron density up to 700 Bohr radii at t = 14.51 fs after the pump pulse. It consists of distinct wave fronts spreading out with virtually constant speed in other words, the metastable wave packet decays by ejecting electrons in isolated bursts. This peculiar behavior... 

Lanthanide(III) Pc doubledecker complexes, LnPc2, possess peculiar electronic properties which make them the first molecular semiconductors [287]. Applications in the field of high speed thin film electronics have been discussed (by Simon et al.). Like the silylamides, they are also sublimable. The radical... 

Also consider all the operating factors related to the particular pump. These factors include the type of service (continuous or intermittent), operating-speed preferences, future load expected and its effect on pump head and capacity, maintenance facilities available, possibility of parallel or series hookup, and other conditions peculiar to a given job. 

Silica-M handling in an MLC pump at 5000 rpm does not show the peculiar increase in LPC seen for 8000 rpm tests, suggesting that pump speed and wt %... 

Indeed, considering that photons are rather peculiar particles in that they have zero rest mass and can exist only when travelhng at the speed of fight, it seems reasonable that the wave associated with the motion of any particle should become more and more apparent as the mass decreases, rather than the wave coming into existence suddenly when the rest mass vanishes. 

FYom this formula it is seen that to calculate /i we need to determine the mean molecular speed ( ci )m- For real systems the average molecular speed is difficult to determine. Assuming that the system is sufficiently close to equilibrium the velocity distribution may be taken to be Maxwellian. For molecules in the absolute Maxwellian state the peculiar velocity equals the microscopic molecular velocity, i.e., Ci = ci, because the macroscopic velocity... 

B being the static virial coefficient, A — (1 — vp)tt> (b — a )/2RT, p the solvent density, and to the angular velocity. This speed dependence effect can be minimized by low speeds and short solution columns. A problem peculiar to absorption optics (applicable to protein systems in general) is the difficulty in obtaining an accurate baseline due to, for example, anomalous absorption onto cell windows this difficulty is often ignored in the literature. 

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