Statiaticd Physics 315
where a = po B/kT.
(b) The entropy is
= Nk[ln(e"+e-")-a:tanha:].
(c) The average energy is
- a
ap
U = --lnz = -NpoBtanh
(d) The average magnetic moment is
- M = Npo tanh (F) PO B.
For a single ion, we have
For the whole system, we have
(AM)2 = N(A~I)~
AM=*
cosh (g).
(e) We see from (b) that the entropy (T is a function of poB/kT. If
the entropy of the spin states is maintained constant, i.e., poB/lcT is kept
constant, then the temperature of the spin states can be lowered by re-
ducing the magnetic field adiabatically. In the crystal, the decrease in the
temperature of the spin states can result in a decrease of the temperature
of the crystal vibrations by 'heat transfer". Therefore, the whole crystal is
cooled by an "adiabatic reduction of the magnetic field". From
we have Tf = K.