Particles gases

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... 

An electron or atomic beam of (projectile or test) particles A with density N, of particles per cm travels with speed V and energy E tln-ongh an infinitesimal thickness dv of (target or fielc0 gas particles B at rest with... 

If the gas particles interact through a pairwise potential, then the contribution to the viriai from the intermolecular forces can be derived as follows. Consider two atoms i and j separated by a distcmce r. ... 

In an ideal gas there are no interactions between the particles and so the potential ener function, 1 ), equals zero. exp(- f (r )/fcBT) is therefore equal to 1 for every gas partic in the system. The integral of 1 over the coordinates of each atom is equal to the volume, ai so for N ideal gas particles the configurational integral is given by (V = volume). T1 leads to the following result for the canonical partition function of an ideal gas ... 

Fig. 7. NO reduction using selective catalytic recovery (SCR) (a) basic principles of the SCR process where represent gas particles and (b) effect of...

After post-ionization in the 3 cm long cylindrical plasma space between sample surface and the opposite wall, SN" enter a 90° electrostatic ion energy analyzer (ion optics) suppressing ionized plasma gas particles to a degree of 10 -10 noise levels are correspondingly low (1 cps). The transmission of the electrostatic ion optics is in the range of a few per cent. 

Entrainment velocity The velocity in a jet stream that effectively entrains the dust or gas particles that surround it. 

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... 

Probably mechanisms which have been discussed may be either (a) electrochemical, with active gas particles forming unstable transient volatile A/,... 

Notice that in Table 5.2 all the deviations are negative the observed molar volume is less than that predicted by the ideal gas law. This effect can be attributed to attractive forces between gas particles. These forces tend to pull the particles toward one another reducing the space between them. As a result, the particles are crowded into a smaller volume, just as if an additional external pressure were applied. The observed molar volume, Vm, becomes less than V , and the deviation from ideality is negative ... 

An increase in molar volume above that predicted by the ideal gas law is related to the finite volume of gas particles. These particles contribute to the observed volume, making Vm greater than V . Ordinarily, this effect becomes evident only at high pressures, where the particles are quite close to one another. 

Possible Answer Perhaps the gas put in the balloon consists of a collection of small particles that rebound from the wall of the balloon just as billiard balls rebound from the cushions of a billiard table. As the gas particles rebound from the balloon wail, they push on it. When more gas particles are added, the number of such wall collisions per second increases, hence the outward push on the balloon wall increases. The balloon expands. 

In this model the gas particles are assumed to show no interactions between each other. This model can be realized or at least approached closely in a physical sense, since under conditions of low pressure and high temperatures interaction between particles becomes progressively weaker. Another example consists in the relationship between relativistic and classifical mechanics. The relativistic expression for momentum. 

Seemingly other problems arise in the treatment of the rate of adsorption, viz. the probability that a gas particle will reach on impact a free adsorption site on a partially covered surface, and the probability that it will remain attached there. Since, however, the rates of adsorption and desorption are connected by the equilibrium requirements, essentially the same problems have to be solved in a theoretical evaluation of both the rates. In practice,... 

The preexponential factor determines the rate of incidence of the gas particles onto the free surface at a unit pressure and has a dimension of (mole sec g-1 cm-1). 

The removal of C4-acetylenes may be effected by catalytic gas-phase hydrogenation in a gas-particle operation by a process similar to that widely used for removing acetylene from ethylene streams. However, in view of the strong polymerization tendency of the C4-fractions, it is desirable in this case to work at the lowest possible temperature. 

Gas-phase reactions catalyzed by solid catalysts are normally carried out in gas-particle operation in either fixed or fluidized beds. The possibility of using gas-liquid-particle operations for such reactions is, however, of interest in certain cases, particularly if the presence of a liquid medium for the transfer of heat or mass is desirable. 

A number of such processes were established before the second World War in Germany, Japan, and France for the production of hydrocarbon mixtures in the liquid fuel range (P2). This way of manufacturing automotive fuels is now uneconomical in most areas, but related processes may be utilized for the production of various chemicals, such as paraffinic waxes or oxygenated compounds. (The manufacture of methanol from carbon monoxide and hydrogen, usually by catalytic reaction in fixed-bed gas-particle operation, is an important process of this type.)... 

Commercial Fischer-Tropsch processes have been based exclusively on gas-particle operations, mainly in fixed beds (P2). The chemical reactions are highly exothermic, however, and accurate temperature control is therefore difficult to achieve in a fixed bed. Good temperature control is important because of the temperature sensitivity of the chemical reactions taking place, and several attempts have therefore been made to develop processes based on other types of operation. 

Particles are emitted Into the atmosphere from numerous natural and manmade sources and are also formed upon condensation of gases and vapors. Direct emissions of Suspended Particulate Natter (SPN) arise from a variety of human activities Including combustion. Industrial and agricultural practices the remainder Is formed from gas-particle conversions (chiefly from SOj oxidation to sulfuric acid as sulfate salts). Particles larger than about lOpm In diameter deposit In the vicinity of the sources, but smaller... 

Condensed phase interactions can be divided roughly into two further categories chemical and physical. The latter involves all purely physical processes such as condensation of species of low volatility onto the surfaces of aerosol particles, adsorption, and absorption into liquid cloud and rainwater. Here, the interactions may be quite complex. For example, cloud droplets require a CCN, which in many instances is a particle of sulfate produced from SO2 and gas-particle conversion. If this particle is strongly acidic (as is often the case) HNO3 will not deposit on the aerosol particle rather, it will be dissolved in liquid water in clouds and rain. Thus, even though HNO3 is not very soluble in... 

Heterogeneous processes play a role in several ways including gas-particle conversions, gas uptake by cloudwater and precipitation, exchange of gases into or from the oceans, and exchange of gases into or from soil. 

Based on this experience, a computerized program was further developed on related topics to examine how students solved problems in particle distribution with a different orientation of the apparatus and pressures of gas particles. Case 2 below states the major design and findings of this follow-up study. 

Liang, J. C., Chiu, M. H. (2003). Using dynamic representations to diagnose students conceptions of the behavior of gas particles. Paper presented at the International Conferenee on Seienee Mathematies Learning, Taipei, Taiwan, R.O.C. 

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