Gas molecules, velocity

Derive the root-mean-square (rms) gas molecule velocity. 

Once more, differential IMS resides on the directed drift component shifting the ion-gas molecule velocity distribution to the right of Maxwell-Boltzmann distribution at gas temperature (2.2.2). As ions in gases are thermalized, the increase of translational ion temperature (Th) mirrors onto vibrational (2.5) and rotational (2.6) temperatures via inelastic collisions. While this inelasticity and dismption of alignment by rotational excitation affect the mobility of a fixed geometry (2.5.1, 2.6, and 2.7.2), internal heating may change the ion structure via endothermic isomerization, dissociation, or reactions with carrier gas components. 

When the size of a particle approaches the same order of magnitude as the mean free path of the gas molecules, the setthng velocity is greater than predicted by Stokes law because of molecular shp. The slip-flow correc tion is appreciable for particles smaller than 1 [Lm and is allowed for by the Cunningham correc tion for Stokes law (Lapple, op. cit. Licht, op. cit.). The Cunningham correction is apphed in calculations of the aerodynamic diameters of particles that are in the appropriate size range. 

Electric Wind By virtue of the momentum transfer from gas ions moving in the electrical field to the surrounding gas molecules, a gas circiilation, known as the electric or ionic wind, is set up between the electrodes. For conditions encountered in electrical precipitators, the velocity of this circulation is on the order of 0.6 m/s. (2 ft/s). Also, as a result of this momentum transfer, the pressure at the collecting eleclrode is slightly higher than at the discharge electrode (White-head, op. cit., p. 167). 

The escape velocity required for gas molecules to overcome the earths gravity and go off to outer space is 1.12 X 103m/s at 15°C Calculate die molar mass of a species with that velocity. Would you expect to find He and H2 molecules in the earth s atmosphere How about argon atoms ... 

If charge exchange occurs when the incident positive ion passes the neutral gas molecule with a certain velocity, transfer of translational energy will usually take [place. This transfer of translational energy... 

The void fraction should be the total void fraction including the pore volume. We now distinguish Stotai from the superficial void fraction used in the Ergun equation and in the packed-bed correlations of Chapter 9. The pore volume is accessible to gas molecules and can constitute a substantial fraction of the gas-phase volume. It is included in reaction rate calculations through the use of the total void fraction. The superficial void fraction ignores the pore volume. It is the appropriate parameter for the hydrodynamic calculations because fluid velocities go to zero at the external surface of the catalyst particles. The pore volume is accessible by diffusion, not bulk flow. 

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... 

On the continuum level of gas flow, the Navier-Stokes equation forms the basic mathematical model, in which dependent variables are macroscopic properties such as the velocity, density, pressure, and temperature in spatial and time spaces instead of nf in the multi-dimensional phase space formed by the combination of physical space and velocity space in the microscopic model. As long as there are a sufficient number of gas molecules within the smallest significant volume of a flow, the macroscopic properties are equivalent to the average values of the appropriate molecular quantities at any location in a flow, and the Navier-Stokes equation is valid. However, when gradients of the macroscopic properties become so steep that their scale length is of the same order as the mean free path of gas molecules,, the Navier-Stokes model fails because conservation equations do not form a closed set in such situations. 

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. 

Molecules in a gas are in constant motion at speeds on the order of the speed of a rifle bullet at equilibrium there is no net flow of gas and the motion is random. This motion produces collisions of the molecules with the walls of the vessel containing the gas, with a change in momentum of the gas molecule resulting from each collision. This change in momentum produces a force per unit area, or pressure on the wall. Consider those molecules with the component of velocity in the x direction between the value of vx and vx + dvx. The x direction is defined as the direction normal to the wall. The fraction of molecules with the x component of velocity in this range, denoted dN(vx)/N, is given by the density function, f(vx), where... 

Since the rate of change of momentum with time is the force of the gas molecules on the wall, the pressure, or force per unit area, from the gas molecules of velocity vx becomes... 

The total pressure coming from all the gas molecules directed at the wall (i.e., with positive velocity) is obtained by integration of dP in Eq. (9) over all positive velocities,... 

The magnitude of the velocity of a gas molecule is related to the magnitudes of the component velocities by... 

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