Examples: Reif
Show that CP and CV may be related to each other through quantities that may bedetermined from the equation of state (i.e. by knowing V as a function of P, T, and N)
(the result to this question is something you will need for question 2 of assignmentnumber 8).
Examples: Reif
Lecture 31– EXAM II on Friday
•Exam will cover chapters 6 through 10
•NOTE: we did do a few things outside of the text, particularly aroundchapter 10:
•Maxwell Relations
•Jacobians
•Exam will start at 13:20, and end at 14:20 (60 minutes)
•Exam will have 4 questions some with multiple parts.
•Total number of “parts will be on the order of 8 or 9.
•Most will be worth 10 points, a few will be worth 5.
•You are allowed one formula sheet (2 sides) of your own creation.
•I will provide mathematical formulas you may need (e.g. summationresult from the zipper problem, Taylor Expansions etc., Stirling’sapproximation, certain definite integrals).
•Extra Office Hours:
•Thursday 3:30 to 5:00
•Friday: 11:00 to 11:45
Review EXAM II
•Chapter 6:
•Converting sums to integrals (Density of States) for massive and masslessparticles
•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
Review EXAM II
•Chapter 7:
•Helmholtz free energy
•The exchange of particles (Chemical Potential)
•Gas columns, adsorbed layers are examples, but there are many others.
when equilibrium is established btn. A and B
Review EXAM II
•Chapter 8:
•Quantum gases and corrections to ideal gas law from “statistical” correlations.
•The occupation number formulation of many body systems
•Bose-Einstein and Fermi-Dirac Statistics and their occupation numbers
(For non-relativistic particles with finite mass;a generalization of what we saw in chpt. 4)
Review EXAM II
•Chapter 9:
•Degenerate Quantum gases.
•The occupation number formulation of many body systems.
•Applications of degenerate Fermi systems (metals, White Dwarves, NeutronStars)
•Physical meaning of the Fermi Energy (temperature) and Bose Temperature
•Bose-Einstein Condensation
•Temperature dependence of the chemical potential
Fermion ideal gas
Bosonideal gas
T < TB
Only for T<<TF
Review EXAM II
•Chapter 10:
•Natural Variables and the “fundamental relation”
•Thermodynamic potentials and manipulations
•Legendre Transformations (see next slide)
•Jacobians and their manipulations (see slide after next).
•Maxwell Relations
Keep in mind that such relations may be derived forsystems where work involves something other thanPdV, and they come from equating the second-ordermixed partial derivatives of one of the four majorthermodynamic functions (E, H, F, G)
[I copied the above formulae from Wikipedia, whereA is used for the Helmholtz free energy).
See Week 10notes!!
Key Definitions:
E=E(S,V,N) Internal energy (fundamental relation)
H=H(S, P, N) = E + PV (Enthalpy)
F=F(T, V, N) = E - TS (Helmholtz Free Energy)
G=G(T, P, N) = E + PV –TS (Gibbs Free Energy)
For hydro-static systems (volume the onlyexternal parameter).
dE = TdS – PdV + dN
dH = TdS +VdP + dN
dF = -SdT –PdV + dN
dG = -SdT + VdP + dN
Examples:
Examples:
Examples:
•What is the fundamental difference between thethermodynamics of a gas of photons (the Planckradiation law and associated physics) and thethermodynamics of latttice vibrations in a solid (Debyemodel)?
•A 50 mW Ar Ion laser (=488nm, beam diameter 5mm) is directed toward a black sphere of radius R=1.0cm in outer space. What will be the equilibriumtemperature of the sphere? Can you neglect themicrowave background?