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Exam I results

Exam I results. Low-Temperature C V of Metals (review of exam II). From: T. W. Tsang et al. Phys. Rev. B31, 235 (1985). Review EXAM II. Chapter 9: Degenerate Quantum gases. The occupation number formulation of many body systems.

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Exam I results

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  1. Exam I results

  2. Low-Temperature CV of Metals(review of exam II) From: T. W. Tsang et al. Phys. Rev. B31, 235 (1985)

  3. Review EXAM II • Chapter 9: • Degenerate Quantum gases. • The occupation number formulation of many body systems. • Applications of degenerate Fermi systems (metals, White Dwarves, Neutron Stars) • Physical meaning of the Fermi Energy (temperature) and Bose Temperature • Bose-Einstein Condensation • Temperature dependence of the chemical potential Fermion ideal gas Only for T<<TF Boson ideal gas T < TB

  4. Review EXAM II • Chapter 6: • Converting sums to integrals (Density of States) for massive and massless particles • Photon and Phonon Gases • Debye and Planck models • Occupation number for bosons • Specific heat associated with atomic vibrations (Debye model) Debye model for solids (note: this ignores Zero-point motion)

  5. CALM • What physics contributes to the “internal partition functions” (Z(int)) that appear in 11.19 and 11.20. • It's all the internal energy such as rotational and vibrational bonding energy. • The internal partition function is a representation of the part of the partition function that is engendered due to energy of the a particle that is non-translational (like vibration and spin). • Z(int) refers to the partition function for the portion of a molecule's energy due to it's internal condition, vibration, etc, i.e. everything except the overall motion of the molecular CM. • The above all sound pretty much alike, but I like the way that the third really emphasizes the idea that it is EVERYTHING aside from translation! Rotation and vibration are often emphasised most; but electronic ground state (AND EXCITED STATES SOME TIMES!), spin, etc. also contribute.

  6. Heat Capacity of diatomic gases Note: the temperature scale is hypothetical http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/x.%20Equipartion.pdf

  7. Interaction between spin and rotation for homonuclear mol. See the following applet to see the effect of nuclear statistics on the heat capacity of hydrogen: http://demonstrations.wolfram.com/LowTemperatureHeatCapacityOfHydrogenMolecules/

  8. Example 11.9 from Baierlein • A gas of the HBr is in thermal equilibrium. At what temperature will the population of molecules with J=3 be equal to the population with J=2? • (NOTE: HBr has Qr=12.2K. )

  9. Internal dynamics of diatomic molecules

  10. Hydrogen ionization; Sahaeqn

  11. CALM • Deuterium (D) is a hydrogen atom with a nucleus with spin=1 (one proton and one neutron), as opposed to the more common hydrogen atom with nuclear spin=1/2. What qualitative differences might you expect to see in the rotational partition functions of the molecules H2, D2, and HD? • Most responses focused on a quantitative aspect (difference in spin degeneracy factor), but only a few realized that the Fermion/Boson nature has a significant difference as outlined in the text on page 255.

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