# Exam1ME501F2007wPartialAnswers - 1 Name ME 501 Exam#1 Prof...

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1 Name___________________________ October 16, 2007 Prof. Lucht ME 255 1. POINT DISTRIBUTION Problem #1 30 points _________________ Problem #2 30 points _________________ Problem #3 40 points _________________ 2. EXAM INSTRUCTIONS Write your name on each sheet. This exam is closed book and closed notes. Three equation sheets are attached. When working the problems, list all assumptions, and begin with the basic equations. If you do not have time to complete evaluation of integrals or of terms numerically, remember that the significant credit on each problem will be given for setting up the problem correctly and/or obtaining the correct analytical solution. ME 501 Exam #1

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2 ME 501 Exam #1 10/16/2007 Name___________________________ 1. (30 points) The system shown below has available energy levels of zero, one, two, and three units. The degeneracies of the four levels are 1, 2, 3, and 4, respectively. The thermodynamic state has five particles (N = 5) and a total system energy of eight units (E = 8). (a) For bosons, what are the available macrostates? (There are 6.) How many microstates are associated with each of these macrostates and what is the most probable macrostate? What is the entropy of the system? For Bose-Einstein statistics, the number of microstates for a given macrostate {N j } is given by:    ,, 1! !1 ! jj mBE jBE Ng WW    Answer: 201  (b) For fermions, what are the available macrostates? How many microstates are associated with each of these macrostates and what is the most probable macrostate? What is the entropy of the system? For Fermi-Dirac statistics, the number of microstates for a given macrostate {N j } is given by: ! !! j mFD jFD jjj g N Answer: 31 j j g j 3 3 4 2 2 3 1 1 2 0 0 1
3 ME 501 Exam #1 10/16/2007 Name___________________________ Problem #1 Extra Page

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4 ME 501 Exam #1 10/16/2007 Name___________________________ 2. (30 points) An electron is confined on the surface of a copper crystal by a square wall of iron atoms to a region 0 x L , 0 y L . The normalized wavefunction for the electron is given by   12 22 2 (, ,) s i n s i n e x p f o r0
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Exam1ME501F2007wPartialAnswers - 1 Name ME 501 Exam#1 Prof...

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