Lecture12

3 2 2 u total kt kt 2 2 2 2 so whenever one can

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Unformatted text preview: rotaFonal energy is: U rot = N A kT x 6 What about vibraFons? m m m m m m fixed p relaFve momentum x 1 V = kx 2 2 KE = 12 p 2 Two more degrees of freedom added: U vib = N A kT 7 Total energy of a diatomic U total = U trans + U rot + U vib 7 !3 2 2$ U total = # + + & kT = kT 2 "2 2 2% So whenever one can write a contribuFon to the energy in terms of a quadraFc variable, each degree of freedom of this variable will contribute ½ kT to the energy Law of equiparBBon of energy Our calculaFons were all classical. When do you expect our calculaFons to break down? 8 ApplicaFon: Specific heat •  Experimental verificaFon of the equiparFFon theorum is normally done by calorimetry (measurement of heat). The specific heat is defined as: CV = For our diatomic molecule: < U tot Classical result: CV = !U !T V 7 >= kT 2 7 NAk 2 9 CV of H2 gas VibraFon RotaFons TranslaFons Classical result TranslaFons 700 K VibraFonal 60 meV acFvaFon 20 um RotaFons TranslaFons Transla...
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