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Lecture 19

# Lecture 19 - for Strongly deg enerate B-E g ases can...

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λ for , can neither be neglected nor Strongly deg approximated enerate B-E g by an expan ases sion βε βε λ λ - - = - starting with , we obtained the density 1 k k k e N e ( 29 π λ λ ρ λ = + Z - 3 2 2 2 1 mkT V h l 3 2 l =1 l ( 29 λ λ λ - = for the weakly degenerate case, 1 0 1 V λ ε < = where 0 1 (for a 0) o to find the equation of state ( 29 β ε λ - = - ln - 1 k k pV kT e ( 29 λ ρ λ - = + - Λ 3 3 2 1 g V λ ρ we first have to find from

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( 29 λ λ λ λ λ = = + + + 2 3 3 2 ... 2 3 g l 3 3 3 2 2 2 l =1 l λ λ λ λ λ λ + + + + = 2 3 4 5 6 0.3536 0.1925 0.125 0.089 +0.068 +... ( 29 ( 29 λ λ = = = = = Z ] n where we looked in a table for the Riemann zeta f 3 2 3 2 for 0 0 0 for 1 1 2.612 g g ( 29 λ g λ 1 0 2.612
π Λ = = 3 2 2 3 for a given T, constant 2 h mkT ( 29 λ λ 3 2 we can plo g t vs 1 λ 2.612 ( 29 ( 29 λ λ λ λ Λ + - 3 3 2 and g 1 vs V ( 29 λ λ λ Λ - 3 1 vs V λ λ λ Λ - 3 since V is large, 0 1 only for 1 V λ ρ what is the value for a given ? ρ Λ 3 λ ( 29 ρ ρ λ ¬ Λ < ° Λ ; 3 3 3 2 at T, 2.621 g ρ λ Λ = 8 3 (V= ) at T, 2.621 1 for V ρ Λ = 3 for 2.621, there is a singularity

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( 29 ρ ρ = Λ = 3 3 2 at a given , there is a at which 1 o o T T g ( 29 Λ - Λ = Λ 3 3 3 o o N N n ( 29 λ λ - o the term
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Lecture 19 - for Strongly deg enerate B-E g ases can...

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