Download P340_2011_week10

Laser Cooling/Trapping of atoms
http://www.ptb.de/en/org/4/44/443/melcol_e.jpg
We will discuss this in more detail toward the end of the semester, but it is
possible to slow-down (cool) atoms by passing them through a region with
counter-oriented laser beams tuned to just below an optical transition [“optical
molassses”; so that atoms moving toward the laser will see photons Doppler
shifted onto the resonance and absorb the photon (along with its momentum),
and other atoms will interact minimally with the photons]. Using this technique,
along with simple evaporative cooling, you can get VERY COLD gases of
atoms in an optical/magnetic trap
U.C. Boulder group’s BEC
This is a map of the momentum distribution in the gas cloud
(measured by looking at the gas after the trap has been turned
off) for various temperatures (yes, it is O(10-7 K)). The sharp
white peak in the middle is the BEC showing up at ~ 200 nK
Bose-Einstein Condensation
There is a great applet at this web sit:
http://www.colorado.edu/physics/2000/bec/evap_cool.html
You can slowly cool a model gas down and get BEC, or
cool it down too quickly and just have all the gas leave your
trap (you can even stop the gas in some state and then
have it reestablish equilibrium in another smaller trap). The
site shows the temperature of the gas, you can watch it
cool as some molecules (the most energetic) leave the trap,
and it shows the temperature at which BEC would be
expected for the density in the trap.
See also the movie at:
http://www.colorado.edu/physics/2000/bec/images/evap2.gif
Another interesting applet (more for chapter 14 when we talk about cooling)
Is at the related website:
http://www.colorado.edu/physics/2000/bec/lascool4.html
Intended CALM Question
In dealing with systems in which the atoms or molecules possess finite
magnetic moments, it is possible to do work on a system by changing the
applied magnetic field. The infinitesimal work performed on a substance
with magnetization M could then be written (dbar)W=MdH. Should M or H
be the “natural variable for the internal energy in such a system? Show how
one might define a generalization of the Helmholtz free energy to have the
other of this pair (M,H) as its natural variable.
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 only
external parameter).
dE = TdS – PdV + mdN
dH = TdS +VdP + mdN
dF = -SdT –PdV + mdN
dG = -SdT + VdP + mdN
Examples: Baeirlein
DVB I: Show that you can compute changes in entropy for any
combination of isothermal and isobaric processes in a hydrostatic
thermodynamic system if you know the specific heat capacity at
constant pressure and the equation of state.
DVB II: Suppose you take an ideal gas from (100kPa,300K) to
(100kPa, 450K) and then to (400kPa, 450K). What is the net amount
of heat that must be transferred to the gas to accomplish this?
Jacobians
For more details and
examples see extract
from L&L as a pdf file on
the course web site under
lecture presentations.
From vol. 5 of the “Course in Theoretical Physics” by Landau and Lifshitz ;
L. M. Lifshitz and L. P. Pitaevskii “Statistical Physics 3rd Ed. Part 1 page 53)
Jacobians can be extremely useful in developing non-obvious relationships among functions
of several interdependent variables (as we are often wanting to do in thermodynamics).
CALM: CP or CV?
7 of 11 respondents knew that CP was easier to measure and CV easier
to compute.
Most could give a good explanation for the former, nobody was
convincing for the latter
Examples: DVB
Show that CP and CV may be related to each other through quantities that may be
determined from the equation of state (i.e. by knowing V as a function of P, T, and N).
Does this formula work for the case we already know (ideal gas)?
Examples: Reif
Examples: Reif
Examples: Reif