Thermodynamics and Chemistry

CHAPTER 6 THE THIRD LAW AND CRYOGENICS

6.3 CRYOGENICS 158

bc

bc bc

B A

T

S

Figure 6.3 Adiabatic demagnetization to achieve a low temperature in a paramag-

netic solid.

not much greater than room temperature,JKis positive. Under these conditions, a Joule–
Thomson expansion to a lower pressure has a cooling effect, becauseTwill decrease asp
decreases at constantH. Hydrogen and helium, however, have negative values ofJKat
room temperature and must be cooled by other means to about 200 K and 40 K, respectively,
in order for a Joule–Thomson expansion to cause further cooling.
The cooling effect of a Joule–Thomson expansion is often used to cool a gas down to its
condensation temperature. This procedure can be carried out continuously by pumping the
gas through the throttle and recirculating the cooler gas on the low-pressure side through a
heat exchanger to help cool the gas on the high-pressure side. Starting at room temperature,
gaseous nitrogen can be condensed by this means to liquid nitrogen at77:4K. The liquid
nitrogen can then be used as a cooling bath for gaseous hydrogen. At77:4K, hydrogen
has a positive Joule–Thomson coefficient, so that it in turn can be converted by a throttling
process to liquid hydrogen at20:3K. Finally, gaseous helium, whose Joule–Thomson coef-
ficient is positive at20:3K, can be converted to liquid helium at4:2K. Further cooling of
the liquid helium to about 1 K can be carried out by pumping to cause rapid evaporation.

6.3.2 Magnetization

The work of magnetization of an isotropic paramagnetic phase can be written∂w^0 D
Bdmmag, whereBis the magnitude of the magnetic flux density andmmagis the mag-
nitude of the magnetic dipole moment of the phase. The total differential of the internal
energy of a closed isotropic phase with magnetization is given by

dUDTdSpdV CBdmmag (6.3.4)

withS,V, andmmagas the independent variables.
The technique ofadiabatic demagnetizationcan be used to obtain temperatures be-
low 1 K. This method, suggested by Peter Debye in 1926 and independently by William
Giauque in 1927, requires a paramagnetic solid in which ions with unpaired electrons are
sufficiently separated that at 1 K the orientations of the magnetic dipoles are almost com-
pletely random. Gadolinium(III) sulfate octahydrate, Gd 2 .SO 4 / 3
8H 2 O, is commonly used.
Figure6.3illustrates the principle of the technique. The solid curve shows the tem-
perature dependence of the entropy of a paramagnetic solid in the absence of an applied