Gases particle theory

We will almost always treat the case of a dilute gas, and almost always consider the approximation that the gas particles obey classical, Flarniltonian mechanics. The effects of quantirm properties and/or of higher densities will be briefly commented upon. A number of books have been devoted to the kinetic theory of gases. Flere we note that some... 

Most microscopic theories of adsorption and desorption are based on the lattice gas model. One assumes that the surface of a sohd can be divided into two-dimensional cells, labelled i, for which one introduces microscopic variables Hi = 1 or 0, depending on whether cell i is occupied by an adsorbed gas particle or not. (The connection with magnetic systems is made by a transformation to spin variables cr, = 2n, — 1.) In its simplest form a lattice gas model is restricted to the submonolayer regime and to gas-solid systems in which the surface structure and the adsorption sites do not change as a function of coverage. To introduce the dynamics of the system one writes down a model Hamiltonian which, for the simplest system of a one-component adsorbate with one adsorption site per unit cell, is... 

It was known from gas chromatographic theory that efficiency could be improved if the particle size of the stationary phase materials used in lc could be reduced. High performance liquid chromatography developed steadily during the late 1960s as these high efficiency materials were produced, and as improvements in instrumentation allowed the full potential of these materials to be realised. As hplc has developed, the particle size of the stationary phase used has... 

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... 

The kinetic-molecular theory (KMT) represents the properties of gases by modeling the gas particles themselves at the microscopic level. The KMT assumes that ... 

A gas that obeys these five postulates is an ideal gas. However, just as there are no ideal students, there are no ideal gases only gases that approach ideal behavior. We know that real gas particles do occupy a certain finite volume, and we know that there are interactions between real gas particles. These factors cause real gases to deviate a little from the ideal behavior of the Kinetic Molecular Theory. But a non-polar gas at a low pressure and high temperature would come pretty close to ideal behavior. Later in this chapter, we ll show how to modify our equations to account for non-ideal behavior. 

Before we leave the Kinetic Molecular Theory (KMT) and start examining the gas law relationships, let s quantify a couple of the postulates of the KMT. Postulate 3 qualitatively describes the motion of the gas particles. The average velocity of the gas particles is called the root mean square speed and is given the symbol rms. This is a special type of average speed. 

Zhou, L. 1993. Theory and numerical modeling of turbulent gas-particle Bows and combustion. Boca Raton, FL CRC Press. 

Pankow, J. F., and T. F. Bidleman, Interdependence of the Slopes and Intercepts from Log-Log Correlations of Measured Gas-Particle Partitioning and Vapor Pressure—I. Theory and Analysis of Available Data, Atmos. Environ., 26A, 1071-1080 (1992). 

Values recommended by Mackay et al. (1992) and Mackay and Callcott (1998) for the vapor pressures of a number of PAHs of atmospheric interest and several properties used in theoretical calculations of their gas-particle partitioning in ambient air are given in Table 10.6 for examples of their use, see discussion of gas-particle partitioning theory in Chapter 9.D and references cited above. 

Dunkle also stated that Fay (Ref 12), as quoted from Nicholls (Ref 13), correlated the phenomenon of spin with the natural vibration of the gas particles behind the detonation front. Using the linearized theory of sound as an approximation, Fay developed an equation for spin frequency. For transverse vibrations in a rectangular tube ... 

Kinetic energy is the energy of motion. Gas particles have a lot of kinetic energy and constantly zip about, colliding with one another or with other objects. The picture is complicated, but scientists simplified things by making several assumptions about the behavior of gas pcirticles. These assumptions are called the postulates of the kinetic molecular theory. They apply to a theoretical ideal gas ... 

Chapter 10 sets down the basic assumptions of the kinetic molecular theory of gases, a set of ideas that explains gas properties in terms of the motions of gas particles. In summary, kinetic molecular theory describes the properties of ideal gases, ones that conform to the following criteria ... 

All gas particles have some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But imperfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon the kinetic molecular theory of ideal gases. In this chapter, you re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called gas laws. ... 

One of the more important conclusions from kinetic-molecular theory comes from assumption 5—the relationship between temperature and EK, the kinetic energy of molecular motion. It can be shown that the total kinetic energy of a mole of gas particles equals 3RT/2 and that the average kinetic energy per particle is thus 3RT/2Na, where NA is Avogadro s number. Knowing this relationship makes it possible to calculate the average speed u of a gas particle. To take a helium atom at room temperature (298 K), for example, we can write... 

Before ending this discussion of gases, it s worthwhile expanding on a point made earlier The behavior of a real gas is often a bit different from that of an ideal gas. For instance, kinetic-molecular theory assumes that the volume of the gas particles themselves is negligible compared with the total gas volume. The assumption is valid at STP, where the volume taken up by molecules of a typical gas is only about 0.05% of the total volume, but the assumption is not valid at 500 atm and 0°C, where the volume of the molecules is about 20% of the total volume (Figure 9.14). As a result, the volume of a real gas at high pressure is larger than predicted by the ideal gas law. 

The connection between temperature and kinetic energy obtained from the kinetic-molecular theory makes it possible to calculate the average speed of a gas particle at any temperature. An important practical consequence of this relationship is Graham s law, which states that the rate of a gas s effusion, or spontaneous passage through a pinhole in a membrane, depends inversely on the square root of the gas s mass. 

Pankow JF, Bidleman TF (1992) Interdependence of the slopes and intercepts from log-log correlations of measured gas-particle partitioning and vapor pressure-I. Theory and analysis of available data. Atmos Environ 26A(6) 1071-1080... 

Three types of theoretical approaches can be used for modeling the gas-particles flows in the pneumatic dryers, namely Two-Fluid Theory [1], Eulerian-Granular [2] and the Discrete Element Method [3]. Traditionally the Two-Fluid Theory was used to model dilute phase flow. In this theory, the solid phase is being considering as a pseudo-fluid. It is assumed that both phases are occupying every point of the computational domain with its own volume fraction. Thus, macroscopic balance equations of mass, momentum and energy for both the gas and the solid... 

B. A. Cosgrove and J. Walkley, Can.]. Chem., 60,1896 (1982). Scaled Particle Theory of Gas Solubility and Inclusion of the Temperature Dependent Hard Sphere Term. 

The physical condition of the kinetic theory of gases can be described by elastic collisions of monodispersed spheres with the Maxwellian velocity distribution in an infinite vacuum space. Therefore, for an analogy between particle-particle interactions and molecular interactions to be directly applicable, the following phenomena in gas-solid flows should not be regarded as significant in comparison to particle-particle interactions the gas-particle... 

Zhang, J., Nieh, S. and Zhou, L. (1992). A New Version of Algebraic Stress Model for Simulating Strongly Swirling Turbulent Flows. Numerical Heat Transfer, PartB Fundamentals, 22,49. Zhou, L. (1993). Theory and Numerical Modeling of Turbulent Gas-Particle Flows and Combustion. Boca Raton, Fla. CRC Press. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

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,... 

As we have seen, when X-rays are passed through a gas, only a very few of the electrons in the atoms are knocked out. This is difficult to explain on the wave theory, but follows at once from the particle theory. On the wave theory we should expect all the electrons to be affected by the waves because the waves are continuous and pass over all the electrons present. On the particle theory a photon traveling through the gas goes on between the electrons until it hits one. The small number hit can be attributed to the extremely small size of the electrons and photons. 

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