Lecture 14 - Classical Statistical mechanics...

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Classical Statistical mechanics (Maxwell-Boltzmann or MB ) is recovered when a =0:   / i kT i ne   Note than the effect of a is negligible when   / 1 i kT e 1 i n (Low density) Now you can see why Gibbs’ fix works. If you treat them as distinguishable you get an extra degeneracy factor of ! ! i i N n in the partition function. But this degeneracy factor becomes just ! N as !1 i i n  when 1 i n (recall that 0! 1 ). Also since   / 1 i kT e for all values of i , it follows that // 1 1 1 kT kT e e z   Consistency Check : Ideal Gas 33 or, NN kT n n V kT V  3 3 Or, 1 1 density N V N n n number V  Another way of looking at it:   1/3 1/3 13 1 3 3 3/2 mean interparticle distance 3d 1 1 1 small conditions for recovering Classical or Maxwell-Boltzmann Statistics. large V N n n n n nT n T   
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Ideal Bose Gas     1 i i i PV kT n e            1 1 ; z i i ii PV n e n z e kT  
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Lecture 14 - Classical Statistical mechanics...

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