240 SOLUTIONS
c)The heat capacity may be written as the integral
Substituting into (S.4.105.8), we have
Using the heat capacity at zero magnetic field, and
(S.4.105.12) in (S.4.105.11), we obtain
The temperature may be written so for our adiabatic process
The integrand in (S.4.105.14) is found by substituting into
(S.4.105.10):
So, for a process at constant entropy, we may write
Rearranging and integrating give
and
d) A possible route to zero temperature is illustrated in FigureS.4.105.
During leg 1 the paramagnetic sample is kept in contact with a reservoir
at a low temperature, and the magnetic field is raised from 0 to The
contact with the reservoir is then removed, and the field is reduced to zero
along leg 2. The sample is thereby cooled.