Lecture Notes2

6 ideal diatomic gas 1 hhtrans hrot hvib helec hnucl q

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Unformatted text preview: ∂ ln Ξ λe − βε k =∑ N = ∑ nk = kT , − βε k ∂µ k k 1 ± λe V ,T λε k e − βε k E = ∑ nk ε k = ∑ , − βε k k k 1 ± λe nk = λe − βε k 1 ± λe − βε k ( pV = kT ln Ξ = ± kT ∑ ln 1 ± λe − βε k k 3. At high T & low density, F - D & B - E statistics goes to Boltzmann ∞ 4. Math formula : ∑x j = (1 − x) −1 where x < 1 j =0 Ch. 5 Ideal Monatomic Gas H = Htrans + H elect + Hnucl ∞ qtrans = ( ∑ exp(− n =1 q trans V = 3, Λ βh 2 n 2 3 )) 8ma 2 where h2 Λ= 2πmkT 1/ 2 ) 5 qelect = ∑i welect −i e − βεi qnucl = wnucl Ch. 6 Ideal Diatomic Gas 1. H=Htrans+ Hrot+ Hvib+ Helec+ Hnucl, (q q q q q ) N 2. Q(V,N,T)= trans rot vib elec nucl N! 2 η J ( J + 1) 3. Erot,J= =BJ(J+1) 2I E =Etrans+Erot+Evib+Eelec+Enucl ∞ a) For heteronuclear molecule, qrot= ∑ (2 J + 1)e -BJ(J+1)/kT J =0 ∞ = ∑ (2 J + 1)e −ΘrJ(J+1)/T J =0 8π IkT , w=1 for hetero-, 2 for home-nuclear dia-molecule wh 2 2 b) At Θr<<T, qrot≈ c) fn= NJ N d) Jmax = ∝ (2J+1)e − ΘrJ(J+1)/T kT 2B 1 1 5. Evib=(n + 2 )hv n=0,1,2,…v= 2π a) qvib= ∑ e −βεn = n -βhv(n+1/2) b) fn∝e k µ e − hv / 2kT e − Θv / 2T = − hv / kT − Θv / T 1− e 1− e Ch. 7 Classical Statistical Mechanics 1. Formulas for classical and indistinguishable system s 1 − βε q = ∑ e j → s ∫ ⋅ ⋅ ⋅ ∫ e − βH ∏dp ji dq ji j =1 h j qN 1 − βE = ∑e j → ⋅ ⋅ ⋅ e − βH ( p , q ) dpdq . N! N ! h Ns ∫ ∫ j Where s is the...
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