CMBStatisticsEPSolnME501F2011

CMBStatisticsEPSolnME501F2011 - ME 501 Example Problem:...

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ME 501 Example Problem: Corrected Maxwell-Boltzmann Statistics Consider an assembly of N = 10 5 particles distributed over the five available energy levels, j = 0, 1, 2, 3, and 4 shown in the diagram. The energy of each level (in units of Joules) is given by j = j (100 K) k B , and the degeneracy of each level is g j = 10 8 . What is the population distribution, the total assembly energy E (J), and the assembly entropy S (J/K) at a temperature of 100 K? Is the assumption of CMB statistics for the analysis a good one? Solution:  : exp exp exp exp j j j B jj j B j B B j j j BB B j B j for CMB statistics Ng kT NZ T g ZT kN ENk N g kZ T k k T Let g Z T E Z T k          j 4 3 2 1 0 j / k B (K) 400 300 200 100 0
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Fill in the table below for T = 100K: j j g j B k j  jj B K k  0 10 8 0 10 8 0 1 10 8 100 3.679x10 7 3.679x10 9 2 10 8 200 1.353x10 7 2.706x10 9 3 10 8 300 4.979x10 6 1.494x10 9 4 10 8 400 1.832x10 6 7.326x10 8 8 5 44 00 8 1 11 4 22
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This note was uploaded on 12/26/2011 for the course ME 501 taught by Professor Na during the Fall '10 term at Purdue.

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CMBStatisticsEPSolnME501F2011 - ME 501 Example Problem:...

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