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Absolute zero is the coldest temperature theoretically possible. It cannot be reached by artificial or natural means, because it is impossible to decouple a system fully from the rest of the universe. Technically, it is a temperature marked by a 0 entropy configuration. When defined in terms of entropy, Temperature is a quantity that determines the number of thermodynamically possible states of a system within an energy range. Thus, absolute zero possesses quantum mechanical 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 molecular energy is minimal at absolute zero.

By international agreement, absolute zero is defined as precisely 0 K on the Kelvin scale, which is a thermodynamic temperature scale, and −273.15° on the Celsius scale. Absolute zero is also precisely equivalent to 0 R on the Rankine scale (same as Kelvin but measured in Fahrenheit intervals), and −459.67° 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.For the kinematics of the molecules, on a larger scale, which is easier to understand see kinetic energy.

History

One of the first to discuss the possibility of an absolute minimal temperature was Robert Boyle. His 1665 New Experiments and Observations touching Cold, articulated the dispute known as the primum frigidum. The concept was well known among naturalists of the time. Some contended an absolute minimum temperature occurred within earth (as one of the four so-called 'elements'), others within water, others air, and some more recently within nitre. But all of them seemed to agree that, "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."

Limit to the 'degree of cold'

The question whether there is a limit to the degree of cold possible, and, if so, where the zero must be placed, was first attacked by the French physicist Guillaume Amontons in 1702, in connection with his improvements in the air thermometer and in his instrument temperatures were indicated by the height at which a column of mercury was sustained by a certain mass of air, the volume or "spring" which of course varied with the heat to which it was exposed. Amontons therefore argued that the zero of his thermometer would be that temperature at which the spring of the air in it was reduced to nothing. On the scale he used, the boiling-point of water was marked at +73 and the melting-point of ice at 51, so that the zero of his scale was equivalent to about −240 on the Celsius scale.

This close approximation to the modern value of −273.15 °C for the zero of the air-thermometer was further improved upon in 1779 by Johann Heinrich Lambert, who observed that −270 °C 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 −3000 °C as the natural zero of temperature.

Lord Kelvin's work

After J.P. Joule had determined the mechanical equivalent of heat, Lord Kelvin approached the question from an entirely different point of view, and in 1848 devised a scale of absolute temperature which was independent of the properties of any particular substance and was based solely on the fundamental laws of thermodynamics. It followed from the principles on which this scale was constructed that its zero was placed at −273.15 °C, at almost precisely the same point as the zero of the air-thermometer.

Very Low Temperatures

In the vicinity of absolute zero, it is convenient to indicate temperature using appropriate SI prefixes: microkelvin, nanokelvin, and so forth.

Absolute zero cannot be achieved artificially, though it is possible to reach temperatures close to it through the use of cryocoolers. Laser cooling is a technique used to take temperatures to within a billionth of a degree of 0 K.

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.

At a temperature of 1 femtokelvin (fK), an electron will have a De Broglie wavelength of approximately 3.4 meters.

  • In 1994, researchers at NIST achieved a then-record cold temperature of 700 nK.








  • May 2006 - Institute of Quantum Optics at the University of Hanovermarker gives details of technologies and benefits of femto-kelvin research in space.


Thermodynamics near absolute zero

At temperatures near 0 K, nearly all molecular motion ceases and ΔS = 0 for any adiabatic process. Pure substances can (ideally) form perfect crystals as T → 0. Max Planck's strong form of the third law of thermodynamics states the entropy of a perfect crystal vanishes at absolute zero. The original Nernst heat theorem makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as T → 0:
\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 <&NBSP;0 may="" imply="" that="" ΔH <&NBSP;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)

One model that estimates the properties of an electron gas at the absolute zero of temperature is the fermi gas. What is interesting is that the fermi temperature of electrons, where the lattice temperature is zero, is non-zero. In fact, the electrons have very high velocities. For an isolated system, this is probably a violation of conservation of momentum, since - if the electrons are interacting with the lattice, and the total momentum is zero, then the lattice cannot be at zero velocity. Also, if the lattice were precisely at zero temperature, its nuclei would have infinite de Broglie wavelength. (If the momementum goes to zero, the wavelength becomes infinite).

Relation with Bose–Einstein condensates

A Bose-Einstein Condensate is an unusual state of matter that only exists at extremely low temperatures, maybe a few billionths of a degree above absolute zero.

Absolute temperature scales

Absolute or thermodynamic temperature is conventionally measured in kelvins (Celsius-scaled increments), and increasingly rarely in the Rankine scale (Fahrenheit-scaled increments). Absolute temperature is uniquely determined up to a multiplicative constant which specifies the size of the "degree", so the ratios of two absolute temperatures, T2/T1, are the same in all scales. The most transparent definition comes from the classical Maxwell-Boltzmann distribution over energies, or from the quantum analogs: Fermi-Dirac statistics (particles of half-integer spin) and Bose-Einstein statistics (particles of integer spin), all of which give the relative numbers of particles as (decreasing) exponential functions of energy over kT. On a macroscopic level, a definition can be given in terms of the efficiencies of "reversible" heat engines operating between hotter and colder thermal reservoirs.

Lowest observed temperatures

The average background temperature of the Universe today is 2.73 Kelvin, but it has spatial fluctuations. For example, the Boomerang Nebula has been spraying out gas at a speed of 500,000 km/h (over 300,000 mph) for the last 1,500 years. That has cooled it down to 1 K, as deduced by astronomical observation. This might be the lowest natural temperature recorded.

Much lower temperatures, however, can be achieved in the laboratory. The current (May 2009) world record was set in 1999 at 100 picokelvin by cooling a piece of rhodium metal.

Negative temperatures

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.

See also



Notes

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