176-midterm-03-04-10-answers - Midterm Exam for Physics/ECE...

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Unformatted text preview: Midterm Exam for Physics/ECE 176: Answers Professor Greenside Thursday, March 4, 2010 The following answers are far more detailed than what was necessary to get full credit for any given problem. I include the details with the hope that they will help you to understand the thermal physics better. Problems That Require Writing 1. (30 points) The year is 2020 and you have been invited by one of your professor friends to be a guest speaker in her undergraduate thermal physics class. Using as a specific example one of the three key systems that you have studied so far this semester (Einstein solid, ideal gas, or paramagnet), discuss concisely what you would say to the class about how microstates, macrostates, multiplicity, and the second law of thermodynamics are related to one another: why does counting microstates have anything to do with thermodynamic equilibrium? Note: your goal is to show me that you understand the logical thread that ties various ideas together, in the context of a specific example. You dont need to write full sentences or give any mathematical derivations but you do need to state key definitions, assumptions, and mathematical expressions, and especially indicate through appropriate brief phrases the logic that connects the various concepts so that these future students understand what is going on. Answer: In your answer, I was looking for most of the following ideas, concepts, and equations. I have made bold certain words or phrases that were especially important to mention. (a) Thermal physics is concerned with macroscopic objects that consist of many parts. The object is isolated from the world so that its total energy U , volume V , and number of components N are conserved . Experiments then show that such isolated macroscopic objects eventually reach thermodynamic equilibrium, in which certain properties are uniform throughout the object (tem- perature, pressure, etc) and the properties are independent of how the object reached equilibrium. (b) The macroscopic object is characterized by certain macroscopic quantities such as U , V , and N , which defines the objects macroscopic state or macrostate . Many other properties could be used to characterize the object (color, geometric shape, heat capacity, resistivity, brittleness, sound speed, etc) but the most important parameters are ones for which some conservation law holds. (c) The macroscopic object may be further characterized by its microstates. A particular microstate is defined to be a list of all the states of each individual component that makes up the object at a particular time. For example, a microstate of an ideal gas would correspond to particular values of the position x = ( x,y,z ) and momentum p = ( p x ,p y ,p z ) for each atom in the gas so the microstate involves a list of 6 N numbers total if there are N atoms in the gas. For an Einstein solid with N quantum harmonic oscillators, a microstate would be a list of the N energy levels ( q 1 ,...,q N ) occupied by each oscillator, which indicates how much energy is stored in each...
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176-midterm-03-04-10-answers - Midterm Exam for Physics/ECE...

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