Page 173 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN004D-156 June 8, 2001 15:28

16 Cryogenic Process Engineering

has a higher thermal conductivity than orthohydrogen gas decreased. For these two exceptions, the thermal conduc-
because of the higher specific heat of the parahydrogen tivitydecreaseswithadecreaseintemperature.Thekinetic
gas. theory of gases correctly predicts the decrease in thermal
In contrast to other cryogens, liquid oxygen is slightly conductivity of all gases as the temperature is lowered.
magnetic. It is also chemically very reactive with hydro-
carbon materials. It thus presents a safety problem and
3. Thermal Expansivity
requires extra precautions in handling.
Fluorine is characterized by its high toxicity and ex- The expansion coefficient of a solid can be estimated with
treme reactivity. The fatal concentration range for animals theaidofanapproximatethermodynamicequationofstate
is 200 ppm × hr, while the maximum allowable dosage for for solids that equates the thermal expansion coefficient
humans is usually considered to be 1 ppm × hr. β with the quantity γ C ν ρ/B, where γ is the Gr¨uneisen
dimensionless ratio. C ν the specific heat of the solid, ρ
B. Thermal Properties the density of the material, and B the bulk modulus. For
face-centered cubic (fcc) metals, the average value of the
The thermal properties of most interest at low tempera-
Gr¨uneisen constant is ∼2.3. However, there is a tendency
tures are specific heat, thermal conductivity, and thermal
for this constant to increase with atomic number.
expansivity.
C. Electrical and Magnetic Properties
1. Specific Heat
1. Electrical Resistivity
Specific heat can be predicted fairly accurately by mathe-
matical models through statistical mechanics and quantum The electrical resistivity of most pure metallic elements
theory. For solids, the Debye model gives a satisfactory at ambient and moderately low temperatures is approxi-
representation of the specific heat with temperature. Diffi- mately proportional to the absolute temperature. At very
culties, however, are encountered when the Debye theory low temperatures, however, the resistivity (except that of
is applied to alloys and compounds. Plastics and glasses superconductors) approaches a residual value almost in-
are other classes of solids that fail to follow this theory. dependent of temperature. Alloys, on the other hand, have
In such cases, only experimental test data will provide resistivities much higher than those of their constituent
sufficiently reliable specific heat values. elements and resistance–temperature coefficients that are
In general, the specific heat of cryogenic liquids de- quite low. The electrical resistivity as a consequence is
creases in a manner similar to that noted for crystalline largely independent of temperature and may often be of
solids as the temperature is lowered. At low pressures, the same magnitude as the room-temperature value.
the specific heat decreases with a decrease in temperature. The insulating quality of solid electrical conductors
However, at high pressures in the neighborhood of the crit- usually improves as the temperature is lowered. In fact,
ical, humps in the specific-heat curve are also observed for all the common cryogenic fluids are good electrical
all normal cryogens. insulators.

2. Thermal Conductivity 2. Superconductivity
Adequate predictions of thermal conductivity for pure The phenomenon of superconductivity involving the si-
metals can be made by means of the Wiedemann–Franz multaneous disappearance of all electrical resistance and
law, which states that the ratio of the thermal conductivity the appearance of diamagnetism is undoubtedly the most
to the product of the electrical conductivity and the ab- distinguishing characteristic of cryogenics. The Bardeen–
solute temperature is a constant. High-purity aluminum Cooper–Schriefer (BCS) theory has been successful in
and copper exhibit peaks in thermal conductivity between accounting for most of the basic features observed of the
20 and 50 K, but these peaks are rapidly suppressed with superconducting state for low-temperature superconduc-
increased impurity levels and cold work of the metal. The tors (LTS) operating below 23 K. The advent of the ce-
aluminum alloys Inconel, Monel, and stainless steel show ramic high-temperature superconductors (HTS), operat-
a steady decrease in thermal conductivity with a decrease ing between 77 and 125 K, has called for modifications to
in temperature. This behavior makes these structural ma- existing theories that still have not been finalized. The list
terials useful in any cryogenic service that requires low of materials whose superconducting properties have been
thermal conductivity over an extended temperature range. measured extends into the thousands.
All cryogenic liquids except hydrogen and helium have Three important characteristics of the superconducting
thermal conductivities that increase as the temperature is state are the critical temperature, the critical magnetic