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Absolute zero

2007 Schools Wikipedia Selection. Related subjects: General Physics

   Absolute zero refers to the temperature of a system that is thermically
   inert. Such a (theoretical) system neither emits nor absorbs heat
   energy. The Absolute zero temperature is known to be 0 K (-273.15 C).
   While it is possible to cool any substance to near Absolute Zero, it
   can never actually be achieved.

   Absolute zero is the point at which particles have a minimum energy,
   determined by quantum mechanical effects, which is called the
   zero-point energy.

   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°C on the Celsius scale. Absolute zero is also
   precisely equivalent to 0 °R on the Rankine scale (also a thermodynamic
   temperature scale), and –459.67 °F on the Fahrenheit scale.

   Whilst scientists cannot fully achieve a state of “zero” heat energy in
   a substance, they have made great advancements in achieving
   temperatures ever closer to absolute zero (where matter exhibits odd
   quantum effects). In 1994, the NIST achieved a record cold temperature
   of 700  nK (billionths of a kelvin). In 2003, researchers at MIT
   eclipsed this with a new record of 450  pK (0.45 nK).

History

   To establish an instrument to measure a range of temperatures, in 1593
   Galileo Galilei invented a rudimentary water thermometer. One of the
   first to discuss the possibility of an “absolute cold” on such a scale
   was Robert Boyle who in his 1665 New Experiments and Observations
   touching Cold, stated the dispute which is the primum frigidum is very
   well known among naturalists, some contending for the earth, others for
   water, others for the air, and some of the moderns for nitre, but all
   seeming 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. 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 511, so that the zero of his scale was equivalent to about -240
   on the centigrade scale.

   This remarkably close approximation to the modern value of -273°C for
   the zero of the air-thermometer was further improved on by Johann
   Heinrich Lambert (Pyrometrie, 1779), 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. Laplace and Lavoisier, for
   instance, in their treatise on heat (1780), arrived at values ranging
   from 1500 to 3000 below the freezing-point of water, and thought that
   in any case it must be at least 600 below, while 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°, at almost precisely the same point as the zero of the
   air-thermometer.

Record temperatures near absolute zero

   It can be shown from the laws of thermodynamics that absolute zero can
   never be achieved artificially, though it is possible to reach
   temperatures arbitrarily close to it through the use of cryocoolers.
   This is the same principle that ensures no machine can be 100%
   efficient.

   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 September 2003, MIT announced a record cold temperature of 450
       pK, or 4.5 × 10^-10  K in a Bose-Einstein condensate of sodium
       atoms. This was performed by Wolfgang Ketterle and colleagues at
       MIT.

     * As of February 2003, the Boomerang Nebula, with a temperature of
       -272.15 Celsius; 1K, is the coldest place known outside a
       laboratory. The nebula is 5000 light-years from Earth and is in the
       constellation Centaurus.

     * As of 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 of freedom.

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  \rightarrow 0. Planck's strong form of the third law of
   thermodynamics states that the entropy of a perfect crystal vanishes at
   absolute zero. However, if the lowest energy state is degenerate (more
   than one microstate), this cannot be true. 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

   which implies 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 free energy, the
   enthalpy and the entropy is

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

   it follows that as T decreases, ΔG and ΔH approach each other (so long
   as ΔS is bounded). Experimentally, it is found that most chemical
   reactions are exothermic and release heat in the direction they are
   found to be going, toward equilbrium. That is, even at room temperature
   T is low enough so that the fact that (ΔG)[T,P] < 0 (usually) implies
   that ΔH < 0. (In the opposite direction, each such reaction would of
   course absorb heat.)

   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)

Absolute temperature scales

   As mentioned, absolute or thermodynamic temperature is conventionally
   measured in kelvins ( Celsius-size degrees), and increasingly rarely in
   the Rankine scale ( Fahrenheit-size degrees). Absolute temperature is
   uniquely determined up to a multiplicative constant which specifies the
   size of the "degree", so the ratios of two absolute temperatures,
   T[2]/T[1], 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.

Negative temperatures

   Certain semi-isolated systems (for example 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.

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