Kinetics gas theory

The traditional unipolar diffusion charging model is based on the kinetic theory of gases i.e., ions are assumed to behave as an ideal gas, the properties of which can described by the kinetic gas theory. According to this theory, the particle-charging rate is a function of the square of the particle size dp, particle charge numbers and mean thermal velocity of tons c,. The relationship between particle charge and time according White s... 

Thus, the BLEVE theory predicts that, when the temperature of a superheated liquid is below T, liquid flashing cannot give rise to a blast wave. This theory is based on the solid foundations of kinetic gas theory and experimental observations of homogeneous nucleation boiling. It is also supported by the experiments of BASF and British Gas. However, because no systematic study has been conducted, there is no proof that the process described actually governs the type of flashing that causes strong blast waves. Furthermore, rapid vaporization of a superheated liquid below its superheat limit temperature can also produce a blast wave, albeit a weak... 

The problem has been largely worked at from both sides from the theoretical side the point of view has been almost exclusively that of the kinetic gas theory. It must be kept in mind, however, that it is possible that a purely mechanical theory may not be sufficient to cover the phenomena, as has recently appeared in the case of the specific heats of solids. 

According to the kinetic gas theory the number n of the gas molecules, referenced to the volume, is dependent on pressure p and thermodynamic temperature T as expressed in the following ... 

Model concept Gas Is pourable (fluid) and flows In a way similar to a liquid. The continuum theory and the summarization of the gas laws which follows are based on experience and can explain all the processes in gases near atmospheric pressure. Only after it became possible using ever better vacuum pumps to dilute the air to the extent that the mean free path rose far beyond the dimensions of the vessel were more far-reaching assumptions necessary these culminated in the kinetic gas theory. The kinetic gas theory applies throughout the entire pressure range the continuum theory represents the (historically older) special case in the gas laws where atmospheric conditions prevail. 

With the acceptance of the atomic view of the world - accompanied by the necessity to explain reactions in extremely dilute gases (where the continuum theory fails) - the kinetic gas theory was developed. Using this it is possible not only to derive the ideal gas law in another manner but also to calculate many other quantities involved with the kinetics of gases - such as collision rates, mean free path lengths, monolayer formation time. 

Thermal Properties of Metallic Solids. In the preceding sections, we saw that thermal conductivities of gases, and to some extent liquids, could be related to viscosity and heat capacity. For a solid material such as an elemental metal, the link between thermal conductivity and viscosity loses its validity, since we do not normally think in terms of solid viscosities. The connection with heat capacity is still there, however. In fact, a theoretical description of thermal conductivity in solids is derived directly from the kinetic gas theory used to develop expressions in Section 4.2.1.2. 

It is clear that the viscosity, thermal conductivity, and diffusion coefficients transport coefficients are defined in analogous ways. They relate the gradient in velocity, temperature, or concentration to the flux of momentum, energy, or mass, respectively. Section 12.3 will present a kinetic gas theory that allows an approximate calculation of each of these coefficients, and more rigorous theories are given later in this chapter. 

The most reliable method of obtaining the molecular interaction parameters is by fitting measured temperature-dependent transport data to the rigorous kinetic gas theory expressions, and extracting e and a. 

Comparing with Eq. 12.1 gives a kinetic gas theory expression for the viscosity ... 

Very often you will see the result in Eq. 12.48 with a leading term of 1/3 [35,178,332] rather than 1/2 [14,60], However, the simple derivations leading to the former [35,178] have about the same degree of approximation as the one given here. All such kinetic gas theory expressions are meant to be illustrative only.)... 

Comparing Eqs. 12.54 and 12.2 gives the kinetic gas theory formula for the thermal conductivity X ... 

Two reasons are responsible, for the greater complexity of chemical reactions 1) atomic particles change their chemical identity during reaction and 2) rate laws are nonlinear in most cases. Can the kinetic concepts of fluids be used for the kinetics of chemical processes in solids Instead of dealing with the kinetic gas theory, we have to deal with point, defect thermodynamics and point defect motion. Transport theory has to be introduced in an analogous way as in fluid systems, but adapted to the restrictions of the crystalline state. The same is true for (homogeneous) chemical reactions in the solid state. Processes across interfaces are of great... 

In the case of homogeneous interaction the mechanism of collisions between separate drops will show some resemblance to the collision mechanism between separate molecules, as assumed in the kinetic gas theory. In accordance with this theory, the collision rate po can be put equal to... 

Here we estimate the relative magnitude of ks and ko in an ideal gas at various pressures. An upper limit to ks, where it is assumed that every collision leads to reaction, was given by Eq. (4.14), ks = cr(v), where a = 7rd2 is the reaction cross-section and (v) = -sjHkn r/ jm) is the average velocity at the temperature T. The diffusion constant is (from kinetic gas theory) given by D = (l/3)A(v), where A = ksT/(a/2op) is the mean-free path of the molecule at the pressure p. That is,... 

In the condensed phase the AC permanently interacts with its neighbors, therefore a change in the local phase composition (as were demonstrated on Figs. 8.1 and 8.2) affects the activation barrier level (Fig. 8.6). Historically the first model used for surface processes is the analogy of the collision model (CM) [23,48,57]. This model uses the molecular-kinetic gas theory [54]. It will be necessary to count the number of the active collisions between the reagents on the assumption that the molecules represent solid spheres with no interaction potential between them. Then the rate constant can be written down as follows (instead of Eq. (6)) ... 

A discussion of vapor-phase fundamentals begins with the basic gas laws, which apply to any vapor-phase deposition technique. These techniques employ gases at low pressure (less than 1 atm) and therefore are well described by basic laws such as the ideal gas law and the kinetic gas theory, which are presented in undergraduate physical chemistry. For the purposes of vapor deposition, the critical gas parameters include (1) concentration, (2) velocity distribution, (3) flux, and (4) mean free path. The concentration of gas particles in a low-pressure gas, less than 1 atm, is given by the ideal gas law,... 

Diffusion is the process whereby matter is transported from one part of a system to another as a result of random molecular motion [22]. The random molecular motion is driven by the kinetic energy of individual molecules (i.e. thermal motion). From Eq. (61), the net rate of molecular diffusion is governed by the molecular diffusion coefficient and the concentration gradient. The molecular diffusion coefficient (Di mol) is a property of the solute-solvent system. For very simple systems Di mol can be derived from first principles. For example, the value of Di moi for an inert gas can be estimated from kinetic gas theory [21]. For more complex systems, empirical equations are often used. 

Table 1 presents several examples of unsteady-state kinetics models. These models are presented in the form of rate dependencies for catalytic reaction stages and side processes. The parameters of the models, such as reaction rate constants and activation energies, are given in references (Table 1) and were determined mainly from experimental data using transient response techniques. For the reaction of CO oxidation over a supported platinum catalyst, the kinetic gas theory was applied for estimating the adsorption constants. 

The binary molecular diffusion coefficient, DAB, can be derived from the kinetic gas theory. A more accurate empirical correlation is given by ... 

The following represents only the briefest discussion of kinetic gas theory. For more information there are many good texts on the subject [e.g., see Ladd (1986), Barrow (1973), or Daniels and Alberty (1979)]. 

A gas fulfilling Eq. (1.4) is called an ideal gas. Kinetic gas theory shows, that a gas behaves like an ideal gas, first if the he gas molecules are infinitesimally small, round, hard spheres occupying negligible volume and, secondly, if no forces exist amongst these molecules except during collisions. This holds true for most gases at low pressure and temperatures well above the critical temperature. This is the highest possible temperature at which a substance can condense. 

Metals form a class of solids with characteristic macroscopic properties. They are ductile, have a silver-white luster, and they conduct electricity and heat remarkably well. An early, but still relevant microscopic model aimed at explaining the electrical conductivity, heat conductivity, and optical properties was proposed by Drude [10]. His model incorporates two important successes of modem science the discovery of the electron in 1887 by J. J. Thomson, and the molecular kinetic gas theory put forward by Boltzmann and Maxwell in the second half of the 19th century. 

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