Velocity, molecular

For our present purpose it is convenient to reformulate equation (4.11) as a condition on the mass mean velocity. Let us write the mean axial components of molecular velocities in the form... 

This factor is reminiscent of the radial distribution function for electron probability in an atom and the Maxwell distribution of molecular velocities in a gas, both of which pass through a maximum for similar reasons. 

DP Speed Factor. Pumping-speed efficiency depends on trap, valve, and system design. For gases having velocities close to the molecular velocity of the DP top jet, system-area utilization factors of 0.24 are the maximum that can be anticipated eg, less than one quarter of the molecules entering the system can be pumped away where the entrance area is the same as the cross-sectional area above the top jet (see Fig. 4). The system speed factor can be quoted together with the rate of contamination from the pump set. Utilization factors of <0.1 for N2 are common. 

Fig. 8-3. Distribution of atomic (or molecular) velocities from ihe rotating disc.

Molecular structure, experimental determination of, 324 Molecular velocities, distribution of, 131... 

The molecular diffusivity D may be expressed in terms of the molecular velocity um and the mean free path of the molecules Xrn. In Chapter 12 it is shown that for conditions where the kinetic theory of gases is applicable, the molecular diffusivity is proportional to the product umXm. Thus, the higher the velocity of the molecules, the greater is the distance they travel before colliding with other molecules, and the higher is the diffusivity D. 

Because molecular velocities increase with rise of temperature T, so also does the diffusivity which, for a gas, is approximately proportional to T raised to the power of 1.5. As the pressure P increases, the molecules become closer together and the mean free path is shorter and consequently the diffusivity is reduced, with D for a gas becoming approximately inversely proportional to the pressure. 

For liquids the same qualitative forms of relationships exist, but it is not possible to express the physical properties of the liquids in terms of molecular velocities and... 

In the previous section, the molecular basis for the processes of momentum transfer, heat transfer and mass transfer has been discussed. It has been shown that, in a fluid in which there is a momentum gradient, a temperature gradient or a concentration gradient, the consequential momentum, heat and mass transfer processes arise as a result of the random motion of the molecules. For an ideal gas, the kinetic theory of gases is applicable and the physical properties p,/p, k/Cpp and D, which determine the transfer rates, are all seen to be proportional to the product of a molecular velocity and the mean free path of the molecules. 

The second term on the left-hand side of Eq (1) expresses the convection of gas molecules across the face of dr in physical space by the molecular velocity c. The third term on the left-hand side of Eq (1) represents the convection of... 

However, it was Maxwell in 1848 who showed that molecules have a distribution of velocities and that they do not travel in a direct line. One experimental method used to show this was that ammonia molecules are not detected in the time expected, as derived from their calculated velocity, but arrive much later. This arises l om the fact that the ammonia molecules tnterdiffuse among the air moixules by intermolecular collisions. The molecular velocity calculated for N-ls molecules from the work done by Joule in 1843 was 5.0 xl02 meters/sec. at room temperature. This implied that the odor of ammonia ought to be detected in 4 millisec at a distance of 2.0 meters from the source. Since Maxwell observed that it took several minutes, it was fuUy obvious that the molecules did not travel in a direct path. 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

The Hamiltonian is insensitive to the direction of time, 7i(T) = T L(T ), since it is a quadratic function of the molecular velocities. (Since external Lorentz or Coriolis forces arise from currents or velocities, they automatically reverse direction under time reversal.) Hence both T and I1 have equal weight. From this it is easily shown that. (xl/s) = (exlL). 

The first equality follows from time homogeneity the probability that x = x(f + x) and x = x(f) are the same as the probability that x = x(f — x) and x = x(f). The second equality follows from microscopic reversibility if the molecular velocities are reversed the system retraces its trajectory in phase space. Again, it will prove important to impose these symmetry conditions on the following expansions. 

Henry s Law constant of the chemical/ and the molecular velocity of the compound in the near-surface regions. 

If two different gases are at the same temperature, which of the following must also be equal (a) Their pressures, (b) their average molecular velocities, or (c) the average kinetic energies of their molecules. 

Since n72 is the cross-sectional area for flow, and the term under the radical is the average molecular velocity (7), equation 12.2.1 can be written in the form of Fick s first law as... 

V average molecular velocity for competitive consecutive reactions... 

Figure 6 The Maxwell-Boltzmann distribution of molecular velocities at...

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