CHAPTER 6 THE THIRD LAW AND CRYOGENICS
6.3 CRYOGENICS 156
(a)! T^0 ;p^0 V 10 V 100 T^00 ;p^00!(b)! T^0 ;p^0 V 20 V 200 T^00 ;p^00!Figure 6.2 Joule–Thomson expansion of a gas through a porous plug. The shaded
area represents a fixed-amount sample of the gas (a) at timet 1 ; (b) at a later timet 2.capacity can be measured, so that the crystals are not perfectly ordered. The random struc-
ture is established as the crystals form from the liquid, and becomes frozen into the crystals
as the temperature is lowered below the freezing point. This tends to happen with almost-
symmetric molecules with small dipole moments which in the crystal can have random
rotational orientations of practically equal energy. In the case of solid H 2 O it is the ar-
rangement of intermolecular hydrogen bonds that is random. Crystal imperfections such
as dislocations can also contribute to the residual entropy. If such crystal imperfection is
present at the lowest experimental temperature, the calorimetric value ofSmfor the gas at
298:15K is the molar entropy increase for the change at 1 bar from the imperfectly-ordered
solid at 0 K to the ideal gas at298:15K, and the residual entropySm,0is the molar entropy
of this imperfectly-ordered solid.
6.3 Cryogenics
The field of cryogenics involves the production of very low temperatures, and the study of
the behavior of matter at these temperatures. These low temperatures are needed to evaluate
third-law entropies using calorimetric measurements. There are some additional interesting
thermodynamic applications.
6.3.1 Joule–Thomson expansion
A gas can be cooled by expanding it adiabatically with a piston (Sec.3.5.3), and a liquid
can be cooled by pumping on its vapor to cause evaporation (vaporization). An evapora-
tion procedure with a refrigerant fluid is what produces the cooling in an ordinary kitchen
refrigerator.
For further cooling of a fluid, a common procedure is to use a continuousthrottling
processin which the fluid is forced to flow through a porous plug, valve, or other con-
striction that causes an abrupt drop in pressure. A slow continuous adiabatic throttling of
a gas is called theJoule–Thomson experiment, or Joule–Kelvin experiment, after the two
scientists who collaborated between 1852 and 1862 to design and analyze this procedure.^5
The principle of the Joule–Thomson experiment is shown in Fig.6.2. A tube with
thermally insulated walls contains a gas maintained at a constant pressurep^0 at the left
(^5) William Thomson later became Lord Kelvin.