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absolute zero, the zero point of the ideal gas temperature scale, denoted by 0 degrees on the Kelvin and Rankine temperature scales, which is equivalent to -273.15°C; and -459.67°F;. For most gases there is a linear relationship between temperature and pressure (see gas laws), i.e., gases contract indefinitely as the temperature is decreased. Theoretically, at absolute zero the volume of an ideal gas would be zero and all molecular motion would cease. In actuality, all gases condense to solids or liquids well above this point. Although absolute zero cannot be reached, temperatures within a few billionths of a degree above absolute zero have been achieved in the laboratory. At such low temperatures, gases assume nontraditional states, the Bose-Einstein and fermionic condensates. See also low-temperature physics; temperature.

The Columbia Electronic Encyclopedia Copyright © 2004.

Licensed from Columbia University Press

Licensed from Columbia University Press

Absolute zero is the point at which molecules do not move (relative to the rest of the body) more than they are required to by a quantum mechanical effect called zero-point energy. Having a limited temperature has several thermodynamic consequences; for example, at absolute zero all molecular motion does not cease but does not have enough energy for transference to other systems, it is therefore correct to say that at 0 kelvin molecular energy is minimal

By international agreement, absolute zero is defined as precisely 0 K on the Kelvin scale, which is a thermodynamic (absolute) temperature scale, and −273.15° on the Celsius (centigrade) scale. Absolute zero is also precisely equivalent to 0 °R on the Rankine scale (also a thermodynamic temperature scale), and −459.67 degrees on the Fahrenheit scale. Though it is not theoretically possible to cool any substance to 0 K, scientists have made great advancements in achieving temperatures close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity. In 2000 the Helsinki University of Technology reported reaching temperatures of 100 pK (0.1K).

There is some body or other that is of its own nature supremely cold and by participation of which all other bodies obtain that quality.

This remarkably close approximation to the modern value of −273.15 °C for the zero of the air-thermometer was further improved on by Johann Heinrich Lambert, who gave the value −270 °C and observed that this temperature might be regarded as absolute cold.

Values of this order for the absolute zero were not, however, universally accepted about this period. Pierre-Simon Laplace and Antoine Lavoisier, in their 1780 treatise on heat, arrived at values ranging from 1,500 to 3,000 below the freezing-point of water, and thought that in any case it must be at least 600 below. John Dalton in his Chemical Philosophy gave ten calculations of this value, and finally adopted −3,000 °C as the natural zero of temperature.

At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties including superconductivity, superfluidity, and Bose-Einstein condensation. In order to study such phenomena, scientists have worked to obtain ever lower temperatures.

- In 1994, researchers at NIST achieved a then-record cold temperature of 700 nK (billionths of a kelvin).
- In November 2000, nuclear spin temperatures below 100 pK were reported for an experiment at the Helsinki University of Technology's Low Temperature Lab. However, this was the temperature of one particular degree of freedom—a quantum property called nuclear spin—not the overall average thermodynamic temperature for all possible degrees in freedom.
- In February 2003, the Boomerang Nebula, was found to be −272.15 °C; 1 K, the coldest place known outside a laboratory. The nebula is 5,000 light-years from Earth and is in the constellation Centaurus.

- $lim\_\{T\; to\; 0\}\; Delta\; S\; =\; 0$

The implication is that the entropy of a perfect crystal simply approaches a constant value.

The Nernst postulate identifies the isotherm T = 0 as coincident with the adiabat S = 0, although other isotherms and adiabats are distinct. As no two adiabats intersect, no other adiabat can intersect the T = 0 isotherm. Consequently no adiabatic process initiated at nonzero temperature can lead to zero temperature. (≈ Callen, pp. 189-190)

An even stronger assertion is that It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations. (≈ Guggenheim, p. 157)

A perfect crystal is one in which the internal lattice structure extends uninterrupted in all directions. The perfect order can be represented by translational symmetry along three (not usually orthogonal) axes. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For substances which have two (or more) stable crystalline forms, such as diamond and graphite for carbon, there is a kind of "chemical degeneracy". The question remains whether both can have zero entropy at T = 0 even though each is perfectly ordered.

Perfect crystals never occur in practice; imperfections, and even entire amorphous materials, simply get "frozen in" at low temperatures, so transitions to more stable states do not occur.

Using the Debye model, the specific heat and entropy of a pure crystal are proportional to T^{ 3}, while the enthalpy and chemical potential are proportional to T^{ 4}. (Guggenheim, p. 111) These quantities drop toward their T = 0 limiting values and approach with zero slopes. For the specific heats at least, the limiting value itself is definitely zero, as borne out by experiments to below 10 K. Even the less detailed Einstein model shows this curious drop in specific heats. In fact, all specific heats vanish at absolute zero, not just those of crystals. Likewise for the coefficient of thermal expansion. Maxwell's relations show that various other quantities also vanish. These phenomena were unanticipated.

Since the relation between changes in the Gibbs energy, the enthalpy and the entropy is

- $Delta\; G\; =\; Delta\; H\; -\; T\; Delta\; S\; ,$

thus, as T decreases, ΔG and ΔH approach each other (so long as ΔS is bounded). Experimentally, it is found that all spontaneous processes (including chemical reactions) result in a decrease in G as they proceed toward equilbrium. If ΔS and/or T are small, the condition ΔG < 0 may imply that ΔH < 0, which would indicate an exothermic reaction that releases heat. However, this is not required; endothermic reactions can proceed spontaneously if the TΔS term is large enough.

More than that, the slopes of the temperature derivatives of ΔG and ΔH converge and are equal to zero at T = 0, which ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures, justifying the approximate empirical Principle of Thomsen and Berthelot, which says that the equilibrium state to which a system proceeds is the one which evolves the greatest amount of heat, i.e., an actual process is the most exothermic one. (Callen, pp. 186-187)

A Bose-Einstein Condensate is a substance that behaves very unusually but only at extremely low temperatures, maybe a few billionths of a degree above absolute zero. It is at this point the laws of thermodynamics become very important.

Certain semi-isolated systems, such as a system of non-interacting spins in a magnetic field, can achieve negative temperatures; however, they are not actually colder than absolute zero. They can be however thought of as "hotter than T = ∞", as energy will flow from a negative temperature system to any other system with positive temperature upon contact.

- Celsius
- Cosmic microwave background radiation (this spacetime currently has a background temperature of roughly 2.7 K)
- Delisle scale
- Fahrenheit
- Heat
- ITS-90
- Kelvin
- Orders of magnitude (temperature)
- Planck temperature
- Rankine scale
- Thermodynamic (absolute) temperature
- Triple point

- Herbert B. Callen (1960).
*Thermodynamics*. New York: John Wiley & Sons, Inc. - Herbert B. Callen (1985).
*Thermodynamics and an Introduction to Thermostatistics*. Second Edition, New York: John Wiley & Sons, Inc. - E.A. Guggenheim (1967).
*Thermodynamics: An Advanced Treatment for Chemists and Physicists*. Fifth Edition, Amsterdam: North Holland Publishing. - George Stanley Rushbrooke (1949).
*Introduction to Statistical Mechanics*. Oxford: Clarendon Press.

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Last updated on Thursday October 09, 2008 at 14:54:31 PDT (GMT -0700)

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