Kinetic theory assumptions

Kolev [46] discussed the validity of these relations for fluid particle collisions considering the obvious discrepancies resulting from the different nature of the fluid particle collisions compared with the random molecular collisions. The basic assumptions in kinetic theory that the molecules are hard spheres and that the collisions are perfectly elastic and obey the classical conservation laws do not hold for real fluid particles because these particles are deformable, elastic and may agglomerate or even coalescence after random collisions. The collision density is thus not really an independent function of the coalescence probability. For bubbly flow Colella et al [15] also found the basic kinetic theory assumption that the particles are interacting only during collision violated, as the bubbles influence each other by means of their wakes. 

The kinetic theory of transport processes in gases rests upon three basic assumptions. 

Translational energy, which may be directly calculated from the classical kinetic theory of gases since the spacings of these quantized energy levels are so small as to be negligible. The Maxwell-Boltzmann disuibution for die kinetic energies of molecules in a gas, which is based on die assumption diat die velocity specuum is continuous is, in differential form. 

The kinetic theory of gases has been used so far, the assumption being that gas molecules are non-interacting particles in a state of random motion. This... 

Kinetic theory A mathematical explanation of the behavior of gases on the assumption that gases consist of molecules in ceaseless motion in space. The molecular kinetic energy depends on the temperature of the gas. 

There is a reasonable explanation for this type of deviation. The kinetic theory, which explains the pressure-volume behavior, is based upon the assumption that the particles exert no force on each other. But real molecules do exert force on each other The condensation of every gas on cooling shows that there are always attractive forces. These forces are not very important when the molecules are far apart (that is, at low pressures) but they become noticeable at higher pressures. With this explanation, we see that the kinetic theory is based on an idealized gas—one for which the molecules exert no force on each other whatsoever. Every gas approaches such ideal behavior if the pressure is low enough. Then ihe molecules are, on the average, so far apart that then-attractive forces are negligible. A gas that behaves as though the molecules exert no force on each other is called an ideal gas or a perfect gas. 

In kinetic theory, the macroscopic quantities are found as averages over the motion of many molecules each molecular event is assumed to take place over a microscopic time interval, so that a measurement that is made over a macroscopic time interval involves many molecules. The kinetic-description is, therefore, a probabilistic one in that assumptions are made about the motion of one molecule and the results of this motion are averaged over all of the molecules of the gas, giving proper weight to the probability that the various molecules of the gas can have the assumed motion. 

In its most elementary aspects, kinetic theory is developed on the basis of a hard sphere model of the particles (atoms or molecules) making up the gas.1 The assumption is made that the particles are uniformly distributed in space and that all have the same speed, but that there are equal numbers of particles moving parallel to each coordinate axis. This last assumption allows one to take averages over... 

The first characteristic equation to be proposed which gave an adequate representation of the properties of gases was the equation of van der Waals, which resulted from a revision of the deduction of the equation (1) from the kinetic theory, and the introduction of corrections in the fundamental assumptions that ... 

It has been assumed in the deduction of (1) that the solute is an ideal gas, or at least a volatile substance. The extension of the result to solutions of substances like sugar, or metallic salts, must therefore be regarded as depending on the supposition that the distinction between volatile and non-volatile substances is one of degree rather than of kind, because a finite (possibly exceedingly small) vapour pressure may be attributed to every substance at any temperature above absolute zero. This assumption is justified by the known continuity of pleasure in measurable regions, and by the kinetic theory of gases. 

We make use of the assumption which is conventional in kinetic theory of the harmonic oscillator [193] as well as in energy-corrected IOS [194]. All the transition rates from top to bottom in the rotational spectrum are supposed to remain the same as in EFA. Only transition rates from bottom upwards must be corrected to meet the demands of detailed balance. In the same way the more general requirements expressed in Eq. (5.21) may be met ... 

Conventional bulk measurements of adsorption are performed by determining the amount of gas adsorbed at equilibrium as a function of pressure, at a constant temperature [23-25], These bulk adsorption isotherms are commonly analyzed using a kinetic theory for multilayer adsorption developed in 1938 by Brunauer, Emmett and Teller (the BET Theory) [23]. BET adsorption isotherms are a common material science technique for surface area analysis of porous solids, and also permit calculation of adsorption energy and fractional surface coverage. While more advanced analysis methods, such as Density Functional Theory, have been developed in recent years, BET remains a mainstay of material science, and is the recommended method for the experimental measurement of pore surface area. This is largely due to the clear physical meaning of its principal assumptions, and its ability to handle the primary effects of adsorbate-adsorbate and adsorbate-substrate interactions. 

When the radius of an aerosol particle, r, is of the order of the mean free path, i, of gas molecules, neither the diffusion nor the kinetic theory can be considered to be strictly valid. Arendt and Kallman (1926), Lassen and Rau (1960) and Fuchs (1964) have derived attachment theories for the transition region, r, which, for very small particles, reduce to the gas kinetic theory, and, for large particles, reduce to the classical diffusion theory. The underlying assumptions of the hybrid theories are summarized by Van Pelt (1971) as follows 1. the diffusion theory applies to the transport of unattached radon progeny across an imaginary sphere of radius r + i centred on the aerosol particle and 2. kinetic theory predicts the attachment of radon progeny to the particle based on a uniform concentration of radon atoms corresponding to the concentration at a radius of r + L... 

This equation has a different temperature coefficient from that calculated from kinetic theory, and shows a shortcoming in the theory which is due to the assumption of non-interaction between the molecules. 

Kennedy and Thomas attempted to construct a formal kinetic theory to account for these phenomena. They started from the assumption, for which there is no evidence, that the propagation reaction takes place with free ions only, but that the chain breaking reactions involve ion-pairs. 

The term (pv) is a constant in the problem since there are no sources or sinks. With the further assumption from simple kinetic theory that Dp is independent of temperature, and hence of x, Eq. (6.1) becomes... 

The polymer self-assembly theory of Oosawa and Kasai (1962) provides valuable insights into the nature of the nucleation process. The polymerization nucleus is considered to form by the accretion of protomers, but the process is highly cooperative and unfavorable. Indeed, this is strongly suggested by the observation that thousands of actin or tubulin protomers are found in F-actin and microtubule structures if nucleation of self-assembly were readily accomplished and highly favorable, the consequence would be that many more fibers of shorter polymer length would be observed. The Oosawa kinetic theory for nucleation permits one to obtain information about the size of the polymerization nucleus if two basic assumptions can be satisfied in the experimental system. First, the rate of nuclei formation is assumed to be proportional to the loth power of the protomer concentration with io representing the number of protomers required to create the nucleus. Second, the treat-... 

Classical Free-Electron Theory, Classical free-electron theory assumes the valence electrons to be virtually free everywhere in the metal. The periodic lattice field of the positively charged ions is evened out into a uniform potential inside the metal. The major assumptions of this model are that (1) an electron can pass from one atom to another, and (2) in the absence of an electric field, electrons move randomly in all directions and their movements obey the laws of classical mechanics and the kinetic theory of gases. In an electric field, electrons drift toward the positive direction of the field, producing an electric current in the metal. The two main successes of classical free-electron theory are that (1) it provides an explanation of the high electronic and thermal conductivities of metals in terms of the ease with which the free electrons could move, and (2) it provides an explanation of the Wiedemann-Franz law, which states that at a given temperature T, the ratio of the electrical (cr) to the thermal (k) conductivities should be the same for all metals, in near agreement with experiment ... 

Which one of the following is NOT an assumption of the kinetic theory of gases ... 

Dr Gustav Schweikert of Bad Godesberg, described in Explosivstoffe 3, 197-200 (1955) and 4, 10-14 (1956) a theory of detonation of condensed-phase explosives, which is based on the assumption that such.detonations follow essentially the same basic laws as the combustion of colloidal propellants, and can be comprehended thru the same molecular and reaction-kinetic theories... 

Using a kinetic approach, Langmuir was able to describe the type I isotherm with the assumption that adsorption was limited to a monolayer. According to the kinetic theory of gases, the number of molecules striking each square centimeter of surface per second is given by... 

A detailed discussion of the statistical thermodynamic aspects of thermally stimulated dielectric relaxation is not provided here. It should suffice to state that kinetics of most of the processes are again complicated and that the phenomenological kinetic theories used to described thermally stimulated currents make use of assumptions that, being necessary to simplify the formalism, may not always be justified. Just as in the general case, TSL and TSC, the spectroscopic information may in principle be available from the measurement of thermally stimulated depolarization current (TSDC). However, it is frequently impossible to extract it unambiguously from such experiments. 

This kinetic-theory-based view of the Langmuir result provides no new information, but it does draw attention to the common starting assumptions of the Langmuir derivation and the BET derivation (Section 9.5a). This kinetic derivation of the Langmuir equation is especially convenient for obtaining an isotherm for the adsorption of two gases. This is illustrated in Example 9.4. 

A basic assumption of the kinetic theory was originally that the binary mixture is dilute in one component. In more recent years, the theory has been extended to mixtures of arbitrary composition [117]. 

The kinetic theory of gases is a simple model that can be used to relate the motion (kinetic energy) of molecules to some thermodynamic properties. The theory makes the following assumptions ... 

We now come to the specific application of these general ideas to tfie bimolecular reaction. The method of calculation used by Lewis will be followed, although, as will appear later, the equation he derives may be obtained rather more satisfactorily from the kinetic theory by slightly different assumptions. 

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