Motion, of gas particles

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 ... 

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. 

O(a) G Draw five boxes in your notebook. Inside them, illustrate the motion of gas particles according to the kinetic molecular theory. 

Explain Dalton s law of partial pressures in terms of the motion of gas particles. 

Kinetic-molecular theory can help explain the behavior of gases. For example, the constant motion of gas particles allows a gas to expand until it fills its container, such as the flotation device in Figure 13-2. What property of gases makes it possible for an air-filled flotation device to work ... 

Look at Figure 14-3, which includes a graph of volume versus temperature for a gas sample kept at a constant pressure. Note that the resulting plot is a straight line. Note also that you can predict the temperature at which the volume will reach a value of zero liters by extrapolating the line at temperatures below which values were actually measured. The temperature that corresponds to zero volume is —273.15°C, or 0 on the kelvin (K) temperature scale. This temperature is referred to as absolute zero, and it is the lowest possible theoretical temperature. Theoretically, at absolute zero, the kinetic energy of particles is zero, so all motion of gas particles at that point ceases. 

The average kinetic energy—energy due to motion—of gas particles is proportional to the temperature of the gas in kelvins. This means that as the temperature increases, the particles move faster and therefore have more energy. 

The determining factor of the kinetic energy and rate of motion of gas particles... 

The basic operations in dust collection by any device are (1) separation of the gas-borne particles from the gas stream by deposition on a collecting surface (2) retention of the deposit on the surface and (3) removal of the deposit from the surface for recovery or disposal. The separation step requires (1) application of a force that produces a differential motion of a particle relative to the gas and (2) a gas retention time sufficient for the particle to migrate to the coUecting surface. The principal mechanisms of aerosol deposition that are apphed in dust collectors are (1) gravitational deposition, (2) flow-line interception, (3) inertial deposition, (4) diffusional deposition, and (5) electrostatic deposition. Thermal deposition is only a minor factor in practical dust-collectiou equipment because the thermophoretic force is small. Table 17-2 lists these six mechanisms and presents the characteristic... 

The properties of gas ions are of great importance for the electrical performance of an electrostatic precipitator. They also are very important for particle-charging processes. The size of gas ions is normally such that they can be regarded as gas molecules carrying a single elementary charge. It can even be assumed that ions form a gas component with a very low- partial pressure. Thus, the thermal motion of gas ions is assumed to be similar to that of gas molecules. The most important parameters describing the properties of gas ions are... 

The separation step requires (1) application of a force that produces a differential motion of the particles relative to the gas, and (2) sufficient gas-retention time for the particles to migrate to the collecting surface. Most dust-collections systems are comprised of a pneumatic-conveying system and some device that separates suspended particulate matter from the conveyed air stream. The more common systems use either filter media (e.g., fabric bags) or cyclonic separators to separate the particulate matter from air. 

As shown in Example 5.10, the average speed of an N2 molecule at 25°C is 515 m/s that of H2 is even higher, 1920 m/s. However, not all molecules in these gases have these speeds. The motion of particles in a gas is utterly chaotic In the course of a second, a particle undergoes millions of collisions with other particles. As a result, the speed and direction of motion of a particle are constantly changing. Over a period of time, the speed will vary from almost zero to some very high value, considerably above the average. 

The quantities n, V, and (3 /m) T are thus the first five (velocity) moments of the distribution function. In the above equation, k is the Boltzmann constant the definition of temperature relates the kinetic energy associated with the random motion of the particles to kT for each degree of freedom. If an equation of state is derived using this equilibrium distribution function, by determining the pressure in the gas (see Section 1.11), then this kinetic theory definition of the temperature is seen to be the absolute temperature that appears in the ideal gas law. 

The motion of a particle in the flow field can be described in the Lagrangian coordinate with the origin placed at the center of the moving particle. There are two modes of particle motion, translation and rotation. Interparticle collisions result in both the translational and the rotational movement, while the fluid hydrodynamic forces cause particle translation. Assuming that the force acting on a particle can be determined exclusively from its interaction with the surrounding liquid and gas, the motion of a single particle without collision with another particle can be described by Newton s second law as... 

Just like the walls in a squash court, against which squash balls continually bounce, the walls of the gas container experience a force each time a gas particle collides with them. From Newton s laws of motion, the force acting on the wall due to this incessant collision of gas particles is equal and opposite to the force applied to it. If it were not so, then the gas particles would not bounce following a collision, but instead would go through the wall. 

Torobin, L. B. and Gauvin, W. H. Can. J. Chem. Eng. 38 (1959) 129, 167, 224. Fundamental aspects of solids-gas flow. Part I Introductory concepts and idealized sphere-motion in viscous regime. Part II The sphere wake in steady laminar fluids. Part III Accelerated motion of a particle in a fluid. 

The motion of polydispersed particulate phase is modeled making use of a stochastic approach. A group of representative model particles is distinguished. Motion of these particles is simulated directly taking into account the influence of the mean stream of gas and pulsations of parameters in gas phase. Properties of the gas flow — the mean kinetic energy and the rate of pulsations decay — make it possible to simulate the stochastic motion of the particles under the assumption of the Poisson flow of events. 

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... 

The constant motion and high velocities of gas particles lead to some important practical consequences. One such consequence is that gases mix rapidly when they come in contact. Take the stopper off a bottle of perfume, for instance, and the odor will spread rapidly through the room as perfume molecules mix with the molecules in the air. This mixing of different gases by random molecular motion with frequent collisions is called diffusion. A similar process in which gas molecules escape without collisions through a tiny hole into a vacuum is called effusion (Figure 9.13). 

The effect of the collisional force due to the impact of particles should be included when accounting for the motion of a particle except in a very dilute gas-solid flow situation. Basic mechanisms of collision between two particles or between a particle and a solid wall are discussed in Chapter 2. The collisional force between a particle and a group of neighboring particles in a shear suspension is discussed in 5.3.4.3. In a very dense system where particle collisions dominate the flow behavior, collisional forces can be described by using kinetic theory, as detailed in 5.5. The key equations derived in other chapters pertaining to the collisional forces can be summarized in the following. 

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