Statistical and Low Temperature Physics - University of Liverpool

More documents

Recommendations

Info

Insulators The overall behaviour of the heat capacity due to phonons is shown in the left figure. In the lectures on phonons, we have learnt that it reaches a constant at high temperature, and goes to zero at low temperature. C. Kittel: Introduction to Solid State Physics, 8th edn. (Wiley-VCH, Weinheim 2004) L. Finegold, N.E. Phillips: Phys. Rev. 177, 1383 (1969) We have also seen that at low temperatures, the heat capacity is proportional to T 3 . Plotting C against T 3 would give a straight line, as shown on the right. Statistical Physics 29 Oct - Dec 2009
Insulators For T much smaller than the Debye temperature θ D, the heat capacity is T 3 53v3 C = 2V π2 k 4 B We have also seen that the Debye temperature is related to the Debye frequency by k Bθ D = ω D and the Debye frequency is given by ω D = 6Nπ2v 3 1/3 Substituting into the above formula for the heat capacity, we would get C = 12 5 π4 3 T NkB . Statistical Physics 30 Oct - Dec 2009 V θ D . .
Page 1 and 2: Statistical and Low Temperature Phy
Page 3 and 4: Aim To understand the basic techniq
Page 5 and 6: Uses of low temperatures The branch
Page 7 and 8: Pobell (2007) The history of low te
Page 9 and 10: Refrigeration techniques Three refr
Page 11 and 12: 7.2 Liquids at low temperatures Sta
Page 13 and 14: To liquefy Air Air is first compres
Page 15 and 16: The Joule-Thomson (or Joule-Kelvin)
Page 17 and 18: A note about liquid hydrogen At roo
Page 19 and 20: http://en.wikipedia.org/wiki/Helium
Page 21 and 22: Helium-3 Helium-3 is only a fractio
Page 23 and 24: Kapitza’s helium liquefier http:/
Page 25 and 26: Liquid helium specific and latent h
Page 27 and 28: 7.3 Solids at low temperatures Stat
Page 29: Insulators For non-magnetic, crysta
Page 33 and 34: Insulators This is a log-log plot o
Page 35 and 36: Metal Th Pauli principle means that
Page 37 and 38: Superconducting metals Many metals
Page 39 and 40: Magnetic specific heats Recall that
Page 41 and 42: Magnetic specific heats This figure
Page 43 and 44: Magnetic specific heats In the pres
Page 45 and 46: How to measure heat capacity: Calor
Page 47 and 48: A low temperature calorimeter At lo
Page 49 and 50: Superconducting Heat switch The the
Page 51 and 52: Superconducting heat switch In orde
Page 53 and 54: What do we use for storing liquid g
Page 55 and 56: Storing liquid helium is more trick
Page 57 and 58: Pobell (2007) The helium-4 cryostat
Page 59 and 60: The helium-3 evaporation refrigerat
Page 61 and 62: Exercise 1 Show that at room temper
Page 63 and 64: We can calculate the proportion of
Page 65 and 66: Exercise 2 At room temperature, nor
Page 67 and 68: For normal hydrogen at 20 K, 75% wo
Page 69 and 70: Exercise 3 Calculate the Debye temp
Page 71 and 72: Exercise 4 At which temperature do
Page 73 and 74: We can find γ and A from the graph
Page 75 and 76: On the higher temperature side of p

Statistical and Low Temperature Physics - University of Liverpool

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?