P404-Midterm1-S08

P404-Midterm1-S08 - Physics 404: First Midterm Test Name...

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Physics 404: First Midterm Test Name ( print ): "I pledge on my honor that I have not given or received any unauthorized assistance on this examination." March 11, 2008 Sign Honor Pledge: Don't get bogged down on any problem you find difficult. Skip ahead and go through all 4 pages, then come back to it afterwards!! If you find a question ambiguous, ask the TA and/or write a short explanation of why.) 1. Short answer or multiple choice (in which case, circle the correct answer): a) What is the probability that a particle has not scattered by time 2 τ ? 0 1/2 1/4 e -1 e -2 e -4 < 0.00001 b) What is k B T (to one significant digit) for T = 100 K? Indicate clearly which unit of energy you are using! c)) Rewrite the thermal conductivity κ in terms of τ rather than λ . 2. Suppose a system has 3 possible energies: 0, ε , and 2 ε . a) Write the general expression for E in this case. (No derivation needed.) b) Evaluate ⟨β E if exp(- βε ) = 0.1, or equivalently βε = 2.3.
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3. Using Stirling's approximation, show that ln [N!/(N/2)!] can be written as (N/2) times some
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P404-Midterm1-S08 - Physics 404: First Midterm Test Name...

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