Lecture 4 - Chem 338 Distributions: Bosons and Fermions 1....

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Chem 338 C h em 3 3 8 L e c t u r e 4 Distributions: Bosons and Fermions 1. Entropy - Boltzmann a. S = k B ln Ω = k B ln Σ k W k 2. Distributions. a. Bosons b. Fermions c. Boltzons d. Comparison 1 exp 1 exp 1 = = T k g N T k g N B r r r B r r r μ ε or 1 exp 1 exp 1 + = + = T k g N T k g N B r r r B r r r or = = T k g N N T k g N N B r r r B r r r exp exp 1 / or
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Chem 338 Boltzmann: S = k B ln Ω
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Chem 338
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Chem 338
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Chem 338
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Chem 338
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Chem 338 The Maxwell-Boltzmann Distribution Function The thermodynamic probability for each macrostate is: If we remove one particle from energy level, r, this becomes: The ratio in the limit of large N is: or: so: and: ! ! jk N j k j jk g WN N = () 1 1 1 ' ! !! jk rk N N j r rk jr rk jk g g NN =− 1 11 1 ' ! ! rk rk N rk rk rk rk r N kr k r r r N N g N N N g N g g == = ' rk k r rk NW gNW = '' rr k k r r k r kk W g N W g N Ω= = = Ω ∑∑ ' ' r rB B N S SS Ng k k ⎡⎤ Ω −Δ = ⎢⎥ Ω ⎣⎦ ln ln
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Chem 338 exp r r rB N N gk T μ ⎡⎤ = ⎢⎥ ⎣⎦ E The definition of internal energy must be modified to account for open
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Lecture 4 - Chem 338 Distributions: Bosons and Fermions 1....

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