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Lecture 18 — The Canonical Ensemble Chapter 6, Wednesday February 20 th

Lecture 18 — The Canonical Ensemble Chapter 6, Wednesday February 20 th. Rotational energy levels in diatomic molecules Vibrational energy levels in diatomic molecules More on the equipartition theorem. Reading: All of chapter 5 (pages 91 - 123) Homework 5 due next Friday (22nd)

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Lecture 18 — The Canonical Ensemble Chapter 6, Wednesday February 20 th

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  1. Lecture 18 — The Canonical Ensemble Chapter 6, Wednesday February 20th • Rotational energy levels in diatomic molecules • Vibrational energy levels in diatomic molecules • More on the equipartition theorem Reading: All of chapter 5 (pages 91 - 123) Homework 5 due next Friday (22nd) Homework assignments available on web page Assigned problems, Ch. 5: 8, 14, 16, 18, 22

  2. Rotational energy levels for diatomic molecules l = 0, 1, 2... is angular momentum quantum number I = moment of inertia CO2 I2 HI HCl H2 qR(K) 0.56 0.053 9.4 15.3 88

  3. Vibrational energy levels for diatomic molecules n = 0, 1, 2... (harmonic quantum number) w w = natural frequency of vibration I2 F2 HCl H2 qV(K) 309 1280 4300 6330

  4. Specific heat at constant pressure for H2 CP = CV + nR H2 boils w CP (J.mol-1.K-1) Translation

  5. More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 9 x x = L

  6. More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 18 x x = L

  7. More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = 36 x x = L

  8. More on the equipartition theorem Classical uncertainty: Where is the particle? V(x) V = ∞ V = ∞ V = 0 W = ∞ S = ∞ x x = L

  9. More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

  10. More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

  11. More on the equipartition theorem: phase space Area h Cell: (x,px) dpx px dx x

  12. More on the equipartition theorem: phase space In 3D: Uncertainty relation: dxdpx = h dpx dx

  13. Examples of degrees of freedom:

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