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176-final-exam-5-04-2011

# 176-final-exam-5-04-2011 - Print your name clearly...

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Print your name clearly: Signature: “I agree to neither give nor receive aid during this exam.” Final Exam for Physics/ECE 176 Professor Greenside Wednesday, May 4, 2011 Please read the following before starting the test: 1. This exam is closed book and will last the entire exam period. 2. No calculators or other electronic devices are allowed. 3. Look over the entire exam and get a sense of its length, what kinds of questions are being asked, and which questions are worth the most points. 4. Answer the true-false and multiple choice questions on the exam itself, answer all other questions on extra blank pages. If you need extra pages during the exam, let me know. 5. Please write your name and the problem number at the top of each extra page. 6. Unless otherwise stated, you must justify any written answer with enough details for me to understand your reasoning. 7. Please write clearly: if I can not easily understand your answer, you will lose credit. 8. If you are not sure about the wording of a problem, please ask me during the exam. 1

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Problems That Require Writing 1. (8 points) A germ can be approximated as a rigid sphere of radius about a micron (10 - 6 m) that is filled with water (density 10 3 kg / m 3 ). To the nearest power of ten and in units of microns per second (i.e., body lengths per second), estimate the magnitude of the germ’s speed that arises from the germ being in equilibrium with pond water at room temperature. 2. (12 points) During the semester, you learned two paradoxical facts: that “it is not possible to boil water with boiling water” but “it is possible to boil water with ice”. Explain briefly how to demonstrate these statements experimentally, and also discuss briefly the physics that explains these facts. 3. (8 points) What is the generalization of the Gibbs factor e - β ( E s - μN s ) for the case of a small system like a porous balloon that can exchange energy E s , particles N s , and volume V s with some reservoir? 4. (a) (5 points) Describe precisely what is meant by “Einstein’s model of a solid”. (b) (20 points) Assume that an Einstein solid that consists of N identical atoms is in equilibrium with a reservoir whose temperature has the constant value T . Derive an expression for the heat capacity C ( T ) of the Einstein solid. Next, plot C/ ( Nk ) qualitatively versus kT/ , where is the constant spacing between energy levels, and give some numerical values on the horizontal and vertical scales to indicate the scales involved. Also discuss briefly how your plot relates to the equipartition theorem and to the third law of thermodynamics. (c) (10 points) Motivated by Einstein’s model, the Dutch scientist Peter Debye obtained a more accurate description of the heat capacity C ( T ) of a solid by using more realistic assumptions than those of Einstein. His theory led to the following result for the thermal energy U of a solid consisting of N atoms in a volume V at temperature T : U = 9 NkT 4 T 3 D Z T D /T 0 x 3 e x - 1 dx, (1) where the so-called Debye temperature T D is given by T D = hc s 2 k 6 N πV 1 / 3 , (2) where c s is the speed of sound waves in the solid, and is assumed to be a constant.
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