CMBStatisticsEP2SolnME501F2011

CMBStatisticsEP2SolnME501F2011 - 1 ME 501 Example Problem:...

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1 ME 501 Example Problem: CMB Statistics The system shown below has energy levels of jB k c h 0 K, 5 K, 10 K, 150K, and 200K. The degeneracy of each of three lower levels is 10 8 and the two upper levels is 10 10 . The system has only these energy levels; there are no translational, rotational, or vibrational modes. The number of particles in the assembly is 10 5 . (a) Calculate the energy and entropy of the assembly at a temperature of 50 K, assuming corrected Maxwell-Boltzmann statistics. Why is CMB statistics a good assumption? (b) Now re-calculate the energy and entropy of the assembly at a temperature of 50 K, assuming that the degeneracies of the upper levels j =3 and j =4 are 10 8 instead of 10 10 . Comment on the results. Solution: j j /k B (K) g j 3 150 10 10 2 10 10 8 1 5 10 8 0 0 10 8 4 200 10 10
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2  : 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       
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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 University-West Lafayette.

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CMBStatisticsEP2SolnME501F2011 - 1 ME 501 Example Problem:...

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