Collisions average collision frequency

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... 

In a recent study, Huan et al. [25] performed NM R experiments in vibrofluidized beds of mustard seeds in which the small sample volume allowed pulses short enough that displacements in the ballistic phase were distinguishable from those in the diffusion phase. In this case, the average collision frequency is measured directly, bypassing the uncertainty of the multiplicative factor mentioned above. These workers also measured the height dependence of the granular temperature profile. 

There is a Maxwell-Boltzmann distribution of collision velocities, given by Eq. 10.27, so to obtain the average collision frequency integrate Eq. 10.46 over all possible collision... 

We now compute as before the flow of molecules through the surface element A>S. Let us consider a volume element in the gas dr, whose spherical coordinates with respect to AS are 0, and r dr = r- sin dO d4> dr). In this volume element there will be Z dr collisions per second, where Z is the average collision frequency previously calculated (Sec. VII.8E). 

As for the collision density in the macroscopic model formulation, the average collision frequency of fluid particles is usually described assuming that the mechanisms of collision is analogous to collisions between molecules as in the kinetic theory of gases. The volume average coalescence frequency, ac d d, Y), can thus be defined as the product of an effective swept volume rate hc d d, Y) and the coalescence probability, pc d d, Y) (e.g., [16, 92, 114, 39, 46, 118]) ... 

Now that we know roughly how far a gas particle typically travels between collisions, we can determine an average collision frequency, which tells us about how many times a gas particle comes in contact with another gas particle each second. 

For a given sample of gas (which has a certain molar mass, collision diameter, and so on), what variable(s) does the average collision frequency depend on ... 

The vapor pressure of Hg at room temperature (taken as 22.0° C) is 0.001426 mmHg. What is the average collision frequency of gaseous Hg atoms in a system that contains only Hg Used = 2.4 A, and use the ideal gas law to determine the density of Hg vapors under these conditions. 

A 1.00-mol sample of Xe gas is kept at a temperature of 298 K.What volume must it have in order to have an average collision frequency of 1 per second Assume that the collision diameter is 4.00 A. 

Determine (a) the mean free paths, (b) the average collision frequencies, and (c) the total number of collisions between nitrogen and oxygen molecules in air. Assume standard thermodynamic conditions (273 K and 1 atm) and use d = 3.15 and 2.98 A for nitrogen and oxygen, respectively. 

For a given gas, density and temperature are the only variables needed to determine an average collision frequency. 

We start from a model in which collision cross sections or rate constants for energy transfer are compared with a reference quantity such as average Leimard-Jones collision cross sections or the usually cited Leimard-Jones collision frequencies [54]... 

All of these time correlation functions contain time dependences that arise from rotational motion of a dipole-related vector (i.e., the vibrationally averaged dipole P-avejv (t), the vibrational transition dipole itrans (t) or the electronic transition dipole ii f(Re,t)) and the latter two also contain oscillatory time dependences (i.e., exp(icofv,ivt) or exp(icOfvjvt + iAEi ft/h)) that arise from vibrational or electronic-vibrational energy level differences. In the treatments of the following sections, consideration is given to the rotational contributions under circumstances that characterize, for example, dilute gaseous samples where the collision frequency is low and liquid-phase samples where rotational motion is better described in terms of diffusional motion. 

The change of average z projection of the angular momentum per unit time is its change for a single collision A/ = (D — l)Jo(t) multiplied by the collision frequency Tq 1 ... 

Let us consider first quantum J-diffusion. It is carried out by purely non-adiabatic collisions realized for anc is the average rotational frequency. A semiclassical analogue of the infinite-order sudden... 

For N2 molecules in the air at room temperature cr(d is of the order of the speed of sound, 370 ms-1, a is 0.43 nm2 and Z = 5 x 1028 cm-3 s 1. This is a very large number, which means that collisions between molecules occur very frequently and the energy can be averaged between them, ensuring the concept of local thermal equilibrium. Each molecule collides ZAK/NA times per second, which is about 5 x 109 s x once every 0.2 ns. However, in the diffuse ISM where the molecule density is of order 102 cm3 the collision frequency is 5 x 10-8 s-1 or a collision every 1.5 years. 

This damping function s time scale parameter x is assumed to characterize the average time between collisions and thus should be inversely proportional to the collision frequency. Its magnitude is also related to the effectiveness with which collisions cause the dipole function to deviate from its unhindered rotational motion (i.e., related to the collision strength). In effect, the exponential damping causes the time correlation function <% I Eq ... 

Kinetic Theory of Gases Velocity Distribution Speed Distribution Collision Frequency Meen Free Path Determine average and RMS speeds from data Plot radial distribution functions... 

Counting molecules, collision frequency, collision density MB speed distribution and averages... 

Let us first consider the case where only single scattering is responsible for the charge transfer. The electric current, ib, measured by the ball probe is proportional to the product of the collision frequency, fc, and the averaged charge transfer per impact, QbP, as given by... 

As the volume of a fixed sample of gas is decreased at a constant temperature, the pressure increases. Since the temperature is constant, the average velocity of the gas particles remains constant. Constrained to a smaller volume, the collision frequency of the molecules with the walls of the container increases. Therefore, the pressure increases. 

Mean free path (/). With the large number of gas particles present in a volume of gas at a given pressure, a large number of collisions can occur. Calculation of the collision frequency allows the mean free path (/) of the particles to be determined. This is the average distance travelled by a particle between collisions. 

Let us focus our attention on one such mobile adatom. In unit time, it will travel on average a distance c, and it will collide with all the adatoms whose centres are within a distance o, of the line defining its path. Since there is a total of (A/a), adatoms per unit area, each mobile adatom will have a collision frequency of 2 o, c, (Na),. Further, since it takes two adatoms to make a collision and there are (m A/a), mobile adatoms eligible per unit area, the total collision frequency per unit area is [2o, c, (Na) ]... 

Fig. 10. The densities obtained at different cooling rates at T = 0 and p = 1 for the Lennard-Jones glass. The cooling rate is the value of the stochastic collision frequency per particle, v. The number of runs employed to obtain the reported average is shown inside each point. (From Fox and Andersen (67).)...

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