P301 Lecture 8 “CMB fit to BB spectrum” 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)

P340 Lecture 18 “CMB Spectrum” BB spectrum of the cosmic background over a wide range of frequencies

P340 Lecture 18 “CMB Temperature The measured temperature of the universe as a function of frequency range used for the measurement.

Lecture 18-- Example

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. Chemistry (3 answers) Higher Debye Temperature (2 answers; but what gives them this and why does it matter?) Quantum effects are more important in this case (1 answer; again, what is it that makes these effects more important for these tow materials?).

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. Chemistry (3 answers) Higher Debye Temperature (2 answers; but what gives them this and why does it matter?) Quantum effects are more important in this case (1 answer; again, what is it that makes these effects more important for these tow materials?). Both Boron and Diamond are high-strength light weight solids. This is getting closes, but what does it really mean and why does it matter. HINT: Be is also a case where the material is well below the Dulong-Petit value at room T.

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. Chemistry (3 answers) Higher Debye Temperature (2 answers; but what gives them this and why does it matter?) Quantum effects are more important in this case (1 answer; again, what is it that makes these effects more important for these tow materials?). Both Boron and Diamond are high-strength light weight solids. This is getting closes, but what does it really mean and why does it matter. HINT: Be is also a case where the material is well below the Dulong-Petit value at room T. The maximum frequency (and therefore  D ) is set by the mimimum wavelength (related to atomic size, which does not vary a lot across the periodic table) and the speed of sound (which depends on bulk modulus and density). Materials with strong bonds and light atoms have very large sound velocities, and therefore high Debye temperatures. If T is much less than  D, then many modes do not contribute to the materials thermodynamics (and therefore the heat capacity is below the classical limit).

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.

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). A. It's the same idea as electrical or graviational potential. … (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 would flow from a region of high potential (warm) to a region of low potential (cool). (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).).