- 2.17: Hint: use ln(N+q) = ln[N(1+q/N)] = lnN + ln(1+q/N)
- 2.24 (a) Ωmax= 2N/√ πN/2
(b) Ω = Ωmax e-2x2/N
(c) x± = ±√ N/2
- 2.25 (a) Most likely to be at the starting point
(b) Expected root-mean-square deviation: √ <d2> = ℓ√ N
(c) (Cannot be solved before taking Sec 1.7.)
- 2.26+2.32 Ω = (Aπ 2mU/h2)N/(N!)2
S = kBN (ln[Aπ 2mU/h2N2]+2) - 2.34 Use Q=-W, the expression for W when the volume changes from Vi to Vf and similarly the expression for ΔS.
- 2.35 I got T<0.012 K (not sure if that is correct)
- 2.37 Use VB=xV, VA=(1-x)V, NB=xN, and NA=(1-x)N in formulas for Δ S
- 3.5 Hint: Half-way through you should have 1/T=(kB/ε)ln(N/q)
- 3.6 Hint: Use S=kBlnΩ and 1/T=∂S/∂U
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