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Unformatted text preview: 13.4 Dilute gases & MaxwellBoltzmann Distribution , 1 << j j g N , 1 1 1 / ) ( << = = kT j j j j e g N f For a dilute gas, the occupation number at each energy level is much smaller than the available number of quantum states, i.e., for each j. (13.27) This gives in FermiDirac or BoseEinstein distribution. It follows that (13.28) . / ) ( kT j j j j e g N f = Since (13.29) Thus, Eq(13.28) can be rewritten as (13.30) It follows that for dilute gases, both FermiDirac and Bose Einstein statistics reduce to the Boltzmann distribution. This classical limit is called MaxwellBoltzmann distribution f MB . , 1 N N n i i = = . , / 1 / / ) ( 1 Z N e g N e N e g kT n i j kT kT n i j j j = = = = = . / B kT j j j f e Z N g N f j = = In fact, there is another approach to get Eq(13.30). For dilute gases (N j <<g j ), we can have So that Similarly, we have . ) 1 )...( 2 )( 1 ( )! ( )! )( 1 )...( 2 )( 1 ( )! ( ! j N j j j j j j j j j j j j j j j j j j g N g g g g N g N g N g g g g N g g + = + = ....
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 Winter '10
 Dr.asdas
 mechanics, Energy

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