Zero, absolute

In theory there really is a coldest temperature possible in the universe, although in practice it is impossible to actually reach that temperature. To cool something down, an object has to be able to give offbeat to something else that is colder than it is. Since there is nothing colder than zero kelvin in the universe, there is nowhere left to which to transfer that last miniscule bit of heat. Scientists have reached temperatures on the order of one-millionth of a degree above absolute zero, but not absolute zero itself. For the sake of discussion, however, absolute zero corresponds to -273.15°C, or -459.67°F. 

If you were not famihar already with the units and vocabulary introduced in this chapter, don t worry. Since we will be referring to them repeatedly throughout this book, you should find that they eventually will become second nature to you. 

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Another important accomplislnnent of the free electron model concerns tire heat capacity of a metal. At low temperatures, the heat capacity of a metal goes linearly with the temperature and vanishes at absolute zero. This behaviour is in contrast with classical statistical mechanics. According to classical theories, the equipartition theory predicts that a free particle should have a heat capacity of where is the Boltzmann constant. An ideal gas has a heat capacity consistent with tliis value. The electrical conductivity of a metal suggests that the conduction electrons behave like free particles and might also have a heat capacity of 3/fg,... 

If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy, but at the absolute zero of temperature the entropy may become zero, and does so become in the case of perfect crystalline substances. 

In the Lewis and Gibson statement of the third law, the notion of a perfect crystalline substance , while understandable, strays far from the macroscopic logic of classical thennodynamics and some scientists have been reluctant to place this statement in the same category as the first and second laws of thennodynamics. Fowler and Guggenheim (1939), noting drat the first and second laws both state universal limitations on processes that are experunentally possible, have pointed out that the principle of the unattainability of absolute zero, first enunciated by Nemst (1912) expresses a similar universal limitation ... 

It is impossible by any procedure, no matter how idealized, to reduce the temperature of any. system, to the absolute zero of temperature in a finite number of operations. 

Figure A2.1.10. The impossibility of reaching absolute zero, a) Both states a and p in complete internal equilibrium. Reversible and irreversible paths (dashed) are shown, b) State P not m internal equilibrium and with residual entropy . The true equilibrium situation for p is shown dotted.

The principle of tire unattainability of absolute zero in no way limits one s ingenuity in trying to obtain lower and lower thennodynamic temperatures. The third law, in its statistical interpretation, essentially asserts that the ground quantum level of a system is ultimately non-degenerate, that some energy difference As must exist between states, so that at equilibrium at 0 K the system is certainly in that non-degenerate ground state with zero entropy. However, the As may be very small and temperatures of the order of As/Zr (where k is the Boltzmaim constant, the gas constant per molecule) may be obtainable. 

Helium has a small i and small foree between atoms. This results in a very large Ax. This implies that it is extremely diffieult for He atoms to "vibrate" with small displaeement as a solid even as absolute zero is approaehed. 

Liquid hydrogen is important in cryogenics and in the study of superconductivity, as its melting point is only 20 degrees above absolute zero. 

Helium has the lowest melting point of any element and is widely used in cryogenic research because its boiling point is close to absolute zero. Also, the element is vital in the study of super conductivity. 

It has other peculiar properties. Helium is the only liquid that cannot be solidified by lowering the temperature. It remains liquid down to absolute zero at ordinary pressures, but it can readily be solidified by increasing the pressure. Solid 3He and 4He are unusual in that both can be changed in volume by more than 30% by applying pressure. 

Zero energy is the energy which a species would have at absolute zero in the absence of zero-point vibrational energy. 

Radiometry. Radiometry is the measurement of radiant electromagnetic energy (17,18,134), considered herein to be the direct detection and spectroscopic analysis of ambient thermal emission, as distinguished from techniques in which the sample is actively probed. At any temperature above absolute zero, some molecules are in thermally populated excited levels, and transitions from these to the ground state radiate energy at characteristic frequencies. Erom Wien s displacement law, T = 2898 //m-K, the emission maximum at 300 K is near 10 fim in the mid-ir. This radiation occurs at just the energies of molecular rovibrational transitions, so thermal emission carries much the same information as an ir absorption spectmm. Detection of the emissions of remote thermal sources is the ultimate passive and noninvasive technique, requiring not even an optical probe of the sampled volume. 

Because the third law of thermodynamics requires S = 0 at absolute zero, the following equation is derived, which enables the determination of the absolute value of the Seebeck coefficient for a material without the added complication of a second conductor ... 

Oxirene is probably a true intermediate, but is separated from ketene by only a very low barrier. Since its instability results from unimolecular isomerization rather than from attack of other molecules, the only viable current technique for its direct observation seems to be generation and spectroscopic examination in an inert matrix at temperatures near absolute zero. 

Absolute zero is the theoretical temperature, at which the atoms and molecules of a substance have the least possible energy. This possibly is the lowest attainable temperature. 

A crystalline solid is never perfect in that all of tire lattice sites are occupied in a regular manner, except, possibly, at the absolute zero of temperature in a perfect crystal. Point defects occur at temperatures above zero, of which the principal two forms are a vacant lattice site, and an interstitial atom which... 

Figure 5.1 The parabolic distribution in energy, N(E), as function of energy, E, for free electrons. The Fermi surface represents the upper limit of electron energy at the absolute zero of temperature, but at higher temperatures a small fraction of the electrons can be excited to higher energy levels...

MPa. The temperature, normalised by the glass temperature T, is plotted linearly on the horizontal axis it runs from 0 (absolute zero) to 1.6 (below which the polymer decomposes). 

Temperatures Turboexpanders are routinely used to proeess gas streams ranging from 600°F down to a few degrees above absolute zero. Competent manufaeturers would be delighted to respond to inquiries about higher temperature applieations. 

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