Lecture06A - Partition Functions (17.3, 4, 5) (Believe it...

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Lecture 6 1 Partition Functions (17.3, 4, 5) (Believe it or not) There is more to life than monatomic ideal gases. In Chapter 18 we will derive the details, but for now let’s consider an ideal diatomic molecule (rigid rotor – harmonic oscillator approx.). The molecular partition function has 3 parts: () 3/2 2/ 2 22 28 , 1 hv hv mI e qV V hh e β ππ ββ ⎛⎞ =⋅ ⎜⎟ ⎝⎠ ⎝⎠ Our old friend: translation for an ideal gas molecule of mass m. I = moment of inertia v = harmonic frequency ( ) , As before: , , ! N QQ N V N ⎡⎤ ⎣⎦ == Lecture 6 2 2 ln ln ln ! 33 2 ln ln ln 1 ln ... 2 hv QNq N Nh v m NN Ne N h βπ =− + + ⎝⎠ other terms without , ln 3 1 hv hv NV Q NNN h vN h v e EU e = + + + = ∂− / / 3 1 B B hv k T BB hv k T Nhv Nhve UN k T N k T e =+ + + AA / / For N=N (1 mole), and N 3 1 B B B hv k T hv k T kR v v e UR T R T e = + + Translational energy Rotational energy Zero-point energy Vibrational (beyond zero-point) energy As we might have anticipated, Energy is distributed among the available degrees of freedom.
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Lecture 6 3 Measuring absolutes (total energy) is difficult, but differences are easier.
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This note was uploaded on 04/01/2012 for the course CHEM 444 taught by Professor Gruebele,m during the Spring '08 term at University of Illinois, Urbana Champaign.

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Lecture06A - Partition Functions (17.3, 4, 5) (Believe it...

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