- Why is the average energy per atom related to the total thermal
energy U?
A single atom can be thought of as the ``system'' and all the remaining
atoms thought of as the ``reservoir.'' We compute the average energy
for this single atom at this temperature. Then, since there was nothing
special about the atom we chose, we can conclude that all N atoms will have
the same average energy, so U = N*Eavg.
- What is the partition function for a single dipole (a "spin")
in the two-state paramagnet?
Z = ebeta*mu*B + e-beta*mu*B = 2 cosh(beta*mu*B).
- Where does the factor (2j+1) in equation (6.30) come from?
For an angular mometum vector with magnitude j there are 2j+1 different
possible orientations, all different states but having the same energy.