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Instructors_Guide_Ch18

# Instructors_Guide_Ch18 - 18 The Micro/Macro Connection...

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18 The Micro/Macro Connection Recommended class days: 2 Background Information The kinetic theory of gases is the centerpiece of the micro/macro connection. There are two important aspects to emphasize to students. First, the microscopic view of gases helps us understand the mechanism of how pressure is established, energy is transferred, systems reach equilibrium, and so on. Second, the macroscopic predictions of kinetic theory, such as the values of specific heats, are strong evidence for the atomic theory of matter. Much of this chapter is fairly traditional—kinetic theory is kinetic theory, and there’s not much leeway for alternative presentations. Note that the root-mean-square speed, which plays an impor- tant role in kinetic theory, will be a new concept for most or all students. For most students, it seems an unnecessary and confusing idea. It’s important to spend some time introducing v rms . The main point is that v rms , for practical purposes, is just about the same as the average speed, but it is easier to calculate and it arises naturally in the analysis of molecular motions. Students who had difficulty with kinematics, and who have forgotten that v is a signed quantity, may need some help recognizing that the average velocity (as distinct from the average speed) is zero. Student Learning Objectives To recognize the connection between temperature, thermal energy, and the average translational kinetic energy of the molecules in the system. To understand the molecular basis for pressure and the ideal-gas law. To use the micro/macro connection to predict the molar specific heats of gases and solids. To understand how heat is transferred via molecular collisions and how thermally interacting systems reach equilibrium. To obtain a qualitative understanding of entropy, the second law of thermodynamics, and some of the implications of the second law. Pedagogical Approach The kinetic theory introduction of mean free path, pressure, and the root-mean-square speed are all fairly standard. A main point to emphasize is the underlying reasoning: each molecular collision with a wall exerts a small force on it, and pressure is due to the vast number of collisions that occur each second in a macroscopic system. The derivations are straightforward once students understand the reasoning. It’s more important to emphasize the results and their consequences than the details of the derivations. 18-1

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18-2 Instructor’s Guide Along the way, students find that the average translational kinetic energy per molecule is 2 3 1 rms B 2 2 ( ) . m v k T ε = = This is an important result because it establishes the meaning of temperature. You want to call explicit attention to the fact that ε depends only on the temperature. Two different gases at the same temperature have the same average translational kinetic energy per molecule, regardless of their masses. This will be an important point for understanding the thermal interaction of two systems.
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Instructors_Guide_Ch18 - 18 The Micro/Macro Connection...

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