1. P301 Lecture 8 “CMB fit to BB spectrum” http://www.astro.ucla.edu/~wright/CMB.html The plot on the right shows data from the FIRAS instrument on the original COBE satellite experiment. The measurement of interest here was the set of residuals (i.e. the lower plot of the differences between the measured spectrum and that of a true black body) The curves correspond to various non-ideal BB spectra: 100 ppm reflector (  ) 60 ppm of extra hot electrons adding extra 60ppm of energy just about 1000 yrs after the big bang (  before, y after this time)

2. P340 Lecture 18 “CMB Spectrum” http://aether.lbl.gov/www/projects/cobe/CMB_intensity.gif BB spectrum of the cosmic background over a wide range of frequencies

3. P340 Lecture 18 “CMB Temperature http://aether.lbl.gov/www/projects/cobe/CMB_temp.GIF The measured temperature of the universe as a function of frequency range used for the measurement.

4. Lecture 18-- Example We know peak is proportional to temperature, so just work out the relationship with temperature.

5. Lecture 18-- CALM Explain why you think that of all the materials listed in table 6.3 or Baierlein, Carbon (Diamond) and Boron show the largest deviations of their specific heat values at room temperature from the classical “duLong-Petit” limiting value of 3NkB. Carbon (diamond) and Boron are not electrically conducting like the other substances in the table. (3 answered like this, this makes a difference at low temperatures, as we’ll see in chpt. 9, but it doesn’t really affect room T). I have no good idea. Maybe because their Debye temperatures are very large. But this reasoning seems circluar. Please explain this. (this it the mathematical reason, but I’m glad to see a thirst for more!) The Dulong-Petit law fails to account for substances which have low molecular mass but strong bonding. (this is why the Deby temperature is high. Strong bonds and light atoms give high frequencies, and if hf>>kT, then there are modes which are not excited at that temperature so they don’t contribute to the heat capacity (the classical duLong-Petit limit assume all modes are contributing).

6. Debye Model This plot for solid Argon shows clearly that the low-temperature limit behaves like T 3. Below and to the left we see that the model shows departures from T 3 above about 0.1  D, and is up to 80% of the Dulong-Petit limit by about 0.5  D.

7. Lecture 19-- CALM What is the physical meaning/significance of the chemical potential Suppose you have a copper wire, and that the chemical potential for electrons in that wire varies with temperature. Describe briefly and qualitatively what you would expect to happen if you put the two ends of that wire in contact with temperature baths at different temperatures (assume that the end at the higher temperature has the larger chemical potential). The most popular answers were: A. Chemical potential is a measure of the likeliness of a particle to diffuse. (11 answers; the book’s explanation, but what does it mean? Many others suggested it is the free energy per particle, but again what does that mean; Chemical potential governs particle diffusion JUST like temperature governs thermal diffusion; Particles move from regions of high chemical potential to regions of low chemical potential.) B. Electrons will move from the high potential to the low potential. (what are the consequences of this, and what potential do you mean? An electric field is created since there is now excess negative charge at one end and excess positive charge at the other; this is the origin of the thermoelectric effect).).