21 - The Kinetic Theory of Gases

# 21 - The Kinetic Theory of Gases - Chapter 21 The Kinetic...

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Chapter 21 The Kinetic Theory of Gases CHAPTER OUTLINE 21.1 Molecular Model of an Ideal Gas 21.2 Molar Speciﬁc Heat of an Ideal Gas 21.3 Adiabatic Processes for an Ideal Gas 21.4 The Equipartition of Energy 21.5 The Boltzmann Distribution Law 21.6 Distribution of Molecular Speeds 21.7 Mean Free Path 640 ± Dogs do not have sweat glands like humans. In hot weather, dogs pant to promote evapora- tion from the tongue. In this chapter, we show that evaporation is a cooling process based on the removal of molecules with high kinetic energy from a liquid. (Frank Oberle/Getty Images)

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I n Chapter 19 we discussed the properties of an ideal gas, using such macroscopic vari- ables as pressure, volume, and temperature. We shall now show that such large-scale properties can be related to a description on a microscopic scale, where matter is treated as a collection of molecules. Newton’s laws of motion applied in a statistical manner to a collection of particles provide a reasonable description of thermodynamic processes. To keep the mathematics relatively simple, we shall consider primarily the behavior of gases, because in gases the interactions between molecules are much weaker than they are in liquids or solids. In our model of gas behavior, called kinetic theory , gas molecules move about in a random fashion, colliding with the walls of their container and with each other. Kinetic theory provides us with a physical basis for our understanding of the concept of temperature. 21.1 Molecular Model of an Ideal Gas We begin this chapter by developing a microscopic model of an ideal gas. The model shows that the pressure that a gas exerts on the walls of its container is a consequence of the collisions of the gas molecules with the walls and is consistent with the macro- scopic description of Chapter 19. In developing this model, we make the following as- sumptions: 1. The number of molecules in the gas is large, and the average separation between them is large compared with their dimensions. This means that the molecules occupy a negligible volume in the container. This is consistent with the ideal gas model, in which we imagine the molecules to be point-like. 2. The molecules obey Newton’s laws of motion, but as a whole they move ran- domly. By “randomly” we mean that any molecule can move in any direction with any speed. At any given moment, a certain percentage of molecules move at high speeds, and a certain percentage move at low speeds. 3. The molecules interact only by short-range forces during elastic collisions. This is consistent with the ideal gas model, in which the molecules exert no long- range forces on each other. 4. The molecules make elastic collisions with the walls. 5. The gas under consideration is a pure substance; that is, all molecules are identical.
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21 - The Kinetic Theory of Gases - Chapter 21 The Kinetic...

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