Kinetic Theory of Ideal Gases

The simplest system in which useful products are obtained by thermochemical processing involves the evaporahon of an element or elements in vacuum in order to produce thin hlms on a selected substrate. This process is usually limited to the production of thin hlms because of the low rates of evaporation of the elements into a vacuum under conditions which can be controlled. These rates can be calculated by the application of the kinetic theory of ideal gases. 

Example 2.1. To estimate the number of gas molecules hitting the liquid surface per second, we recall the kinetic theory of ideal gases. In textbooks of physical chemistry the rate of effusion of an ideal gas through a small hole is given by [12]... 

In order to calculate kad we remember the kinetic theory of ideal gases and Eq. (2.1) of example 2.1. Equation (2.1) tells us how many gas molecules of mass m hit a certain area A per second. If we take the area to be the active area of one binding site aA the number of molecules hitting one binding site per second is... 

Entropy always increases with increasing temperature. From the kinetic theory of ideal gases in Chapter 9, it is clear that increasing the temperature of the gas increases the magnitude of the average kinetic energy per molecule and, therefore, the range of momenta available to molecules. This, in turn, increases O for the gas and, by Boltzmann s relation, the entropy of the gas. 

In analogy to the kinetic theory of ideal gases, the statistical theory of rubber elasticity is often called the kinetic theory of rubber elasticity. Reflect upon the similarities and differences between the basic philosophies of these two theories. 

In contrast, the reaction rate r mainly is derived from the kinetic theory of ideal gases and depends on the difference between the actual conditions and the equilibrium state. It can be expressed by a power law expression, where denotes a prefactor and is the activation energy of the reaction. Apart from the commonly... 

KINETIC THEORY OF IDEAL GASES 3.1.1 Introductory remarks... 

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. ... 

SIDEBAR 2.7 KINETIC MOLECULAR THEORY OF IDEAL GASES... 

Substances at high dilution, e.g. a gas at low pressure or a solute in dilute solution, show simple behaviour. The ideal-gas law and Henry s law for dilute solutions antedate the development of the fonualism of classical themiodynamics. Earlier sections in this article have shown how these experimental laws lead to simple dieniiodynamic equations, but these results are added to therniodynaniics they are not part of the fonualism. Simple molecular theories, even if they are not always recognized as statistical mechanics, e.g. the kinetic theory of gases , make the experimental results seem trivially obvious. 

For example, the measurements of solution osmotic pressure made with membranes by Traube and Pfeffer were used by van t Hoff in 1887 to develop his limit law, which explains the behavior of ideal dilute solutions. This work led direcdy to the van t Hoff equation. At about the same time, the concept of a perfectly selective semipermeable membrane was used by MaxweU and others in developing the kinetic theory of gases. 

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... 

Section 5.6 considers the kinetic theory of gases, the molecular model on which the ideal gas law is based. Finally, in Section 5.7 we describe the extent to which real gases deviate from the law. ... 

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. 

In the previous section, the molecular basis for the processes of momentum transfer, heat transfer and mass transfer has been discussed. It has been shown that, in a fluid in which there is a momentum gradient, a temperature gradient or a concentration gradient, the consequential momentum, heat and mass transfer processes arise as a result of the random motion of the molecules. For an ideal gas, the kinetic theory of gases is applicable and the physical properties p,/p, k/Cpp and D, which determine the transfer rates, are all seen to be proportional to the product of a molecular velocity and the mean free path of the molecules. 

An expression for the absolute rate of condensation can be developed readily if the simple kinetic theory of gases and the ideal gas law are applied (S2) ... 

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 ... 

Some aspects of the kinetic molecular theory (KMT) of ideal gases were outlined in Sidebar 2.7. The simplest form of KMT refers to monatomic ideal gases, for which the internal energy U and enthalpy H=U + PV = U + nRT can be written explicitly as... 

Analogies between the three transport phenomena are evident and far-reaching [2]. For instance, consider a low pressure, ideal gas, and assume that the kinetic theory of gases holds. It is shown that ... 

The previous equations which describe the behavior of an ideal gas now will be verified using the kinetic theory of gases. This will illustrate the reasons for the previously given three conditions imposed on the molecules of an ideal gas. Also, you will gain an understanding of the meanings of pressure and temperature. 

Boyle s Equation —Charles Equation—Avogadro s Law — The Equation of State for an Ideal Gas — Density of an Ideal Gas — Kinetic Theory of Gases Mixtures of Ideal Gases 100... 

DEGENERACY. In the kinetic theory of gases, a gas that does not obey the ideal gas laws is referred to as a degenerate gas. The greater the deviation of the real gas from the ideal, the greater is its degeneracy. 

Every chemistry student is familiar with the ideal gas equation PV = nRT. It turns out that this equation is a logical consequence of some basic assumptions about the nature of gases. These simple assumptions are the basis of the kinetic theory of gases, which shows that the collisions of individual molecules against the walls of a container creates pressure. This theory has been spectacularly successful in predicting the macroscopic properties of gases, yet it really uses little more than Newton s laws and the statistical properties discussed in the preceding chapters. 

For a macroscopic box (say L = 0.1 m) and realistic molecular masses, the separation between these levels is far less than ks T. As a result, the distribution of energy levels appears virtually continuous, and quantum corrections to (for example) the ideal gas law are generally extremely small. However, it is possible to use Equation 8.6 to derive the ideal gas law from quantum mechanics instead of using the kinetic theory of gases (see Problem 8-10). 

Chapter 7 covers the kinetic theory of gases. Diffusion and the one-dimensional velocity distribution were moved to Chapter 4 the ideal gas law is used throughout the book. This chapter covers more complex material. I have placed this material later in this edition, because any reasonable derivation of PV = nRT or the three-dimensional speed distribution really requires the students to understand a good deal of freshman physics. There is also significant coverage of dimensional analysis determining the correct functional form for the diffusion constant, for example. 

A correlation between surface and volume processes is described in Section 5. The atomic-molecular kinetic theory of surface processes is discussed, including processes that change the solid states at the expense of reactions with atoms and molecules of a gas or liquid phase. The approach reflects the multistage character of the surface and volume processes, each stage of which is described using the theory of chemical kinetics of non-ideal reactive systems. The constructed equations are also described on the atomic level description of diffusion of gases through polymers and topochemical processes. 

Chapter 5 gives a microscopic-world explanation of the second law, and uses Boltzmann s definition of entropy to derive some elementary statistical mechanics relationships. These are used to develop the kinetic theory of gases and derive formulas for thermodynamic functions based on microscopic partition functions. These formulas are apphed to ideal gases, simple polymer mechanics, and the classical approximation to rotations and vibrations of molecules. 

Kinetic theory of gases was given by Kronig, Clausius, Maxwell etc. to explain the behaviour of gases theoretically. This theory is applicable only to a perfect or an ideal gas. The main postulates or assumptions of the kinetic theory are ... 

In order to explain the deviations of real gases from ideal behaviour vander Waals suggested that it is necessary to modify the kinetic theory of gases. The following two postulates of the kinetic theory, according to him, do not appear to hold good under all conditions. 

In detail, Chapter 1 (Principles) reminds the reader that, in vacuum technology, gases and gas mixtures are, almost without exception, assumed to behave ideally. Information readily obtainable from the kinetic theory of gases (particle velocities, area-related flow etc.), of immense use to vacuum technologies, is also introduced. 

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