Physics
Models of Gas Behaviour
Models of gas behavior are theoretical frameworks used to describe the properties and interactions of gases. The kinetic molecular theory, ideal gas law, and van der Waals equation are common models used to explain gas behavior. These models help scientists understand and predict the behavior of gases under different conditions, such as changes in temperature, pressure, and volume.
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7 Key excerpts on "Models of Gas Behaviour"
eBook - PDF- Geoffrey M. Bowers, Ruth A. Bowers(Authors)
- 2014(Publication Date)
- CRC Press(Publisher)
1 chapter one The properties and behavior of gases Gases and gas-phase chemistry play very important roles in the world around us and critical roles in several important systems in cars. Gases are often used in shock absorbers and struts, are released during combus-tion reactions, are the basis of power generation in internal combustion engines, and are critical to the efficient operation of these engines from several perspectives. In this chapter, we will introduce some of the basic concepts used to understand gas behavior and apply these concepts to gain a greater understanding of the automobile. Since gases are so per-vasive in the structure, function, and operation of cars, many of these concepts will be revisited in subsequent chapters. 1.1 Kinetic molecular theory (KMT) Chemistry Concepts : thermodynamics, statistics, gas laws Expected Learning Outcomes : • Explain the basic principles of KMT • Identify the inaccurate assumptions of KMT Gases are the least dense and most compressible state of matter. Because their density is so low, we often consider gas behavior without worry-ing about interactions between molecules. These intermolecular interac-tions significantly complicate our understanding of chemistry in liquids and solids. However, the low density of gases and the subsequent minor role of intermolecular forces in gas behavior allow us to gain significant insight about gases with relatively simple and straightforward models like the ideal-gas equation or the van der Waals gas equation. These models, particularly the ideal-gas equation, are based upon a well-established theory about gas behavior known as kinetic molecular theory (KMT). Kinetic molecular theory provides a physical rationale that explains the empirical relationships (those observed in the laboratory) between gas temperature, pressure, volume, number of molecules, etc.
eBook - PDFChemistry
The Molecular Nature of Matter
- Neil D. Jespersen, Alison Hyslop(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
Explain what this term describes and how it was used in this experiment. F. The kinetic molecular theory describes how a system of gas molecules behaves and is based on a small number of straightforward postulates. Provide arguments derived from the kinetic molecular theory that support Boyle’s law, Charles’ law, Gay-Lussac’s law, Graham’s law, and Dalton’s law. Summary Organized by Learning Objective Describe the physical properties of gases at the microscopic and molecular levels. Gases expand to fill any container, are easily compressed, have low densities, and are affected by temperature and pressure. Explain the measurement of pressure using barometers and manometers. Atmospheric pressure is measured with a barometer, in which a pressure of one standard atmosphere (1 atm) will support a column of mercury 760 mm high. This is a pressure of 760 torr. By definition, 1 atm = 101,325 pascals (Pa) and 1 bar = 100 kPa. Manometers, both open-end and closed-end, are used to measure the pressure of trapped gases. Describe and use the gas laws of Dalton, Charles, Gay- Lussac, and the combined gas law. Boyle’s Law (Pressure–Volume Law). Volume varies inversely with pressure. V ∝ 1/P, or P 1 V 1 = P 2 V 2 . Charles’ Law (Temperature–Volume Law). Volume varies directly with the Kelvin temperature. V ∝ T, or V 1 /V 2 = T 1 /T 2 . Gay-Lussac’s Law (Temperature–Pressure Law). Pressure varies directly with Kelvin temperature. P ∝ T, or P 1 /P 2 = T 1 /T 2 . Graham’s Law of Effusion. The rate of effusion of a gas varies inversely with the square root of its density (or the square root of its molecular mass). Combined Gas Law. PV divided by T for a given gas sample is a con- stant. PV/T = C, or P 1 V 1 /T 1 = P 2 V 2 /T 2 . Perform stoichiometric calculations using the gas laws and Avogadro’s Law. Stoichiometric calculations are made using the gas laws and Avogadro’s Law and the previous stoichiometric methods.
eBook - PDF- R. Prasad(Author)
- 2016(Publication Date)
- Cambridge University Press(Publisher)
1.1 Kinetic Theory of Gases Out of the three prominent states of matter, solid, liquid and gas, the kinetic theory of gases is perhaps the most developed and complete. Further, under suitable boundary conditions, the kinetic theory of gases may be applied to the solid and the liquid states as well. 1.1.1 What do we expect from a good theory of gases? Any good theory of gases must be able to explain satisfactorily all experimentally observed facts about gases, like the Boyle’s law, Charles’ law, Gay-Lussac’s law, Graham’s law of effusion, Daltons law of partial pressure, magnitudes of specific thermal capacities and their ratios for different gases, their temperature dependence, thermal conductivity and viscosities of gases, etc. The simple classical theory, called the kinetic theory of gases, detailed below, brings out the main properties of gases remarkably well. It, however, fails to explain some finer points as regards to the temperature dependence of some gas properties. It is also not expected that such a simple theory will explain all details of complex gas systems. Laws of quantum statistics, also called statistical mechanics applied to gaseous systems, explain most of the properties that remained unexplained by the kinetic theory. The first step toward the development of the kinetic theory of gases is to define an ideal gas. An ideal gas is a hypothetical or imaginary gas, properties of which are defined through the following assumptions of the kinetic theory of gases. 1.1.2 Assumptions or postulates of the kinetic theory 1. Gases are made up of molecules. In any given measurable or macroscopic volume there is large number of molecules of the gas. 2. The molecules of a gas are in state of continuous motion and the relative separation between the molecules is much larger than their own dimensions. 3. Molecules exert no force on one another except when they collide.
eBook - PDF- A. Roth(Author)
- 2012(Publication Date)
- North Holland(Publisher)
CHAPTER 2 Rarefied gas theory for vacuum technology 2.1. Physical states of matter A collection of molecules can occur either in the solid, liquid or gaseous state depending on the strength of the intermolecular forces, and the average kinetic energy per molecule (temperature). The state in which molecules are most independent of each other is called an ideal or perfect gas. This is a theoretical concept which corresponds to the assump-tions that : (a) the molecules are minute spheres; (b) their volume is very small compared with that actually occupied by the gas; (c) the molecules do not exert forces upon each other; (d) they travel along rectilinear paths in a perfectly ran-dom fashion; (e) the molecules make perfectly elastic collisions. Some real gases, such as hydrogen, nitrogen, oxygen, argon, helium, krypton, neon, xenon, approximate closely at atmospheric pressures the behavior assumed for ideal gases. At lower pressures (vacuum) many more gases approach the ideal gases. Real gases, unlike ideal ones, have intermolecular forces. At pressures and temperatures where the molecules of the gas are brought close to each other they will begin to form new structures, which will have properties very different from those of the gas. When these new structures begin to form, the gas is said to be liquefying. Figure 2.1 shows a plot of pressure versus volume for different temperatures of a real gas (e.g. carbon dioxide). Curves A and B, for which the tempera-tures are high, are hyperbolas conforming to Boyle's law, describing a behavior assumed for ideal gases. At temperature T 3 , curve C is no longer completely hyperbolic. A small bump has formed at point P. At still lower temperatures, curves D and Ε show complete departure from the hyperbola of ideal gases; a flat plateau appears. When the system has the pressure and volume associated with points 17 18 RAREFIED GAS THEORY FOR VACUUM TECHNOLOGY (CH. 2) Fig.
eBook - PDF- Giuseppe Tomassetti, Giovanni Sanna(Authors)
- 2005(Publication Date)
- ICP(Publisher)
CHAPTER 1 Gas Properties 1.1 Introduction Chapter 1 is a synthetic collection of the basic ideas and laws concerning the physical behaviour of gases. Several subjects belonging to thermodynamics and the kinetic theory are briefly reviewed. The considered subjects are propaedeutic for a complete understanding of the following chapters. Because of the wide extension of the topics taken into account, we have limited our discussion to: i) Recalling the basic ideas; ii) Reporting the results and import- ant formulas; iii) Compiling a relevant bibliography for those readers who desire to go more deeply into the considered topics. Complementary infor- mation is reported in the Appendices A. 1, A.2, A.3. 1.2 Perfect and Real Gases It is well known that the macroscopic behaviour of a gas is described by an “equation of state” that correlates the thermodynamic variables pressure p , volume V and temperature T, that is For values of pressures and temperatures well different from those for which the gas starts to liquefy, Eq. (1.2.1) can be specified as f ( p , v, 7-1 = 0 . (1.2.1) pV = NKBT, (1.2.2) where N is the total number of gas molecules and KB = 1.38.10-16 erg/K is the “Boltzmann constant”. A gas satisfying Eq. (1.2.2) is called “perfect gas”. Alternative expressions of Eq. (1.2.2) are reported in Appendix A. 1. The “isothermal compressibility” kT of a gas is generally defined by [ 13 k r = -( l / V ) ( d v / d p > T . (1.2.3) For a gas satisfying to Eq. (1.2.2), Eq. (1.2.3) becomes k T = I / p . (1.2.4) 1 2 Introduction to Molecular Beams Gas Dynamics It has been experimentally verified that at low pressures the compressibility kT of a real gas is higher than that obtained by using Eq. (1.2.4), while at a high pressure, where we have kT < 1 / p , i.e. the real gas appears to be less compressible than a perfect gas. The inadequacy of Eq. (1.2.4) is also con- firmed by the fact that, in intervals of pressures and temperatures wider than those in which Eq.
eBook - PDF- Don Shillady(Author)
- 2011(Publication Date)
- CRC Press(Publisher)
Thus, we start with the studies of gases by Sir Robert Boyle (Figure 1.1). We arbitarily assume that applied mathematics is what distinguishes modern science from medieval engineering so you should be aware that in every case we will attempt to unify a concept with some equation, often involving calculus. Thus, you need to pay attention to the worked examples in the chapters, do the assigned problems, and then try the tests at the end of chapters about where a midterm or fi nal examination usually occurs. You should pay attention to the time limits given for those tests and practice those problems until you have that material down cold within the time allowed! Of course, your teacher will give different questions on the tests in your course but if you can do the sample tests you should be ready for almost any variation of that type question: What equipment is needed here? You need a calculator with special functions but a simple $9 solar-powered calculator is adequate if it has exp( x ), sin( x ), cos( x ), log( x ), and ln( x ) with at least eight signi fi cant fi gures and scienti fi c exponen-tial notation. The next requirement is a human brain and an attitude that you can do this (!) provided you put some time and effort into the work. So let us get started! PHENOMENOLOGICAL DERIVATION OF THE IDEAL GAS EQUATION While mathematical theory often runs roughly parallel to physical science, sometimes faster and other times slower, a key strategy is a process called the ‘‘ phenomenological approach. ’’ In this method a process is studied to determine the variables on which it depends and then an equation is developed, which matches the results of the problem. Often it requires a number of data points to determine whether the result is linear, quadratic, or some higher order in a given variable but the case of the ideal gas law is an excellent starting point to illustrate this method and at the same time enter the important domain of thermodynamics.
- Frederick Bettelheim, William Brown, Mary Campbell, Shawn Farrell(Authors)
- 2019(Publication Date)
- Cengage Learning EMEA(Publisher)
These six assumptions of the kinetic molecular theory give us an ide-alized picture of the molecules of a gas and their interactions with one another (Figure 5.8). In real gases, however, forces of attraction between molecules do exist and molecules do occupy some volume. Because of these factors, a gas described by these six assumptions of the kinetic molecular theory is called an ideal gas . In reality, there is no ideal gas; all gases are real. At STP, however, most real gases behave in much the same way that an ideal gas would, so we can safely use these assumptions. 5.7 Types of Intermolecular Attractive Forces As noted in Section 5.1, the strength of the intermolecular forces (forces between molecules) in any sample of matter determines whether the sam-ple is a gas, a liquid, or a solid under given conditions of temperature and pressure. In general, the closer the molecules are to each other, the greater the effect of the intermolecular forces. For example, when the tempera-ture of a gas is high (room temperature or higher) and the pressure is low (1 atm or less), molecules of the gas are so far apart that we can effectively ignore attractions between them and treat the gas as ideal. When the tem-perature decreases, the pressure increases, or both, the distances between molecules decrease so that we can no longer ignore intermolecular forces. In fact, these forces become so important that they cause condensation (change from a gas to a liquid) and solidification (change from a liquid to a solid). Therefore, before discussing the structures and properties of liquids and solids, we must look at the nature of these intermolecular forces of attraction. In this section, we discuss three types of intermolecular forces: London dispersion forces, dipole–dipole interactions, and hydrogen bonding. Table 5.2 shows the strengths of these three forces.
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