Lecture12

2 kt 2 i 12 2 exp 2 kt normalizafon

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Unformatted text preview: Degrees of freedom Boltzmann factor (probability distribuFon for a given value of v, ω1, ω2) " mv 2 Ctrans Crot ,1Crot ,2 exp $ ! # 2 kT 2 % " I ((12 + (2 ) % ' exp $ ! ' 2 kT & # & NormalizaFon constants # I "i2 (Crot ,i ) = * exp % ! !) $ 2 kT ) !1 = 2! kT I & (d"i ' Crot ,i = I 2! kT 4 Energy contribuFon from each DOF Calculate the energy contribuFon from the 2 rotaFonal degrees of freedom: < Erot 2 2 $ I (!12 + !2 ) I (!12 + !2 ) ' >= Crot ,1Crot ,2 + + exp & " # ) "* "* 2 2 % ( 1 !" kT * * We can define the contribuFon from each DOF as: < E DOF $ I !2 I !2 >= Crot + exp & " # "* 2 2 % * 1 2! 2" I! ' I! # 1 % ) d! = 2" $ 2 ! ( < E DOF 2" I! &1 (= ' 2! 1 >= kT 2 Each DOF contributes ½ kT 5 Total energy of our rotators The total energy of 1 mole of rotators is: U total = N A < Etot > vz ! v The total translaFonal energy is: z vy M vx !1 M !2 U trans M 3 = N A kT 2 M y The total...
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