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P340 Exam 2 HistogramAverage 34/65 = 52%

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Low-Temperature CV 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.• 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

Boson ideal gas

T < TB

Only for T<<TF

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)

(note: this ignores Zero-point motion)

Debye model for solids

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.

Heat Capacity of diatomic gases

http://www.phys.unsw.edu.au/COURSES/FIRST_YEAR/pdf%20files/x.%20Equipartion.pdf

Note: the temperature scale is hypothetical

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/

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. )

Internal dynamics of diatomic molecules

Hydrogen ionization; Saha eqn

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.