Absolute zero

Near absolute zero (0 K), matter exhibits strange properties. For example, below a temperature of 2.1768 K (the "lambda point"), helium is a superfluid that "creeps" along surfaces against the force of gravity and forms a film ("Rollin film"). Here, the Rollin film covers the interior of the larger, sealed container. After a short while, the levels of helium in the outer and inner containers will equalize.

Absolute zero is the lowest possible temperature, such that nothing could be colder and no heat energy remains in the material being examined. At this temperature, the molecules stop moving, with minimal or no vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion.

By international agreement, absolute zero is defined as precisely:

• 0 K on the Kelvin scale, which is a thermodynamic temperature (or absolute temperature) scale, and
• –273.15 °C on the Celsius scale.

In addition, absolute zero is precisely equivalent to:

• 0 R on the Rankine scale, a lesser-used thermodynamic temperature scale, and
• –459.67 °F on the Fahrenheit scale.

The ratios of two absolute temperatures, T₂/T₁, are the same in all scales.

Although scientists cannot fully achieve a state of “zero” heat energy in a substance, they have made great advances in achieving temperatures that draw ever closer to absolute zero, where matter exhibits odd quantum effects. In 1994, the National Institute of Standards and Technology (NIST) achieved a record cold temperature of 700 nK (nanokelvin, or 10^-9 K). In 2003, researchers at Massachusetts Institute of Technology (MIT) eclipsed this with a new record of 450 pK (picokelvin, or 10^-12 K).

Record cold temperatures approaching 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. To study such phenomena, scientists have worked to obtain ever lower temperatures.

• In September 2003, researchers at the Massachusetts Institute of Technology announced a record cold temperature of 450 picokelvin (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 1.15  K, 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 Low Temperature Lab of the Helsinki University of Technology. This, however, was the temperature of one particular type of motion—a quantum property called nuclear spin—not the overall average thermodynamic temperature for all possible degrees of freedom.

Thermodynamics near absolute zero

At 0 K, (nearly) all molecular motion ceases and $\Delta$S = 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 that 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 as 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)

Negative temperatures

Certain semi-isolated systems (for example a system of non-interacting spins in a magnetic field) can achieve "negative" temperatures. They, however, are not actually colder than absolute zero. They can be 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

• Celsius
• Fahrenheit
• Heat
• Kelvin
• Temperature

References

ISBN links support NWE through referral fees

• Shachtman, Tom (2000). Absolute Zero and the Conquest of Cold. First Mariner Books Edition. New York, NY: Houghton Mifflin Co. ISBN 0618082395 (ISBN-13: 978-0618082391).

• Enss, Christian, and Hunklinger, Siegfried (2005). Low-Temperature Physics. Berlin and Heidelberg (Germany); New York, NY: Springer-Verlag. ISBN 3540231641 (ISBN-13: 978-3540231646).

• Mendelssohn, Kurt (1977). The Quest for Absolute Zero: The Meaning of Low Temperature Physics. (2d ed edition). Hoboken, New Jersey: John Wiley & Sons. ISBN 0470991488 (ISBN-13: 978-0470991480).

• Kent, Anthony (1993). Experimental Low-Temperature Physics. New York, NY: American Institute of Physics. (First published in 1993, Hampshire and London, UK: The Macmillan Press.) ISBN 1563960303 (ISBN-13: 978-1563960307).

• Baierlein, Ralph (1999). Thermal Physics. Cambridge, UK: Cambridge University Press. ISBN 0521658381 (ISBN-13: 978-0521658386).

• Herbert B. Callen (1960). Thermodynamics, Chapter 10. John Wiley & Sons, Inc.. Library of Congress Catalog Card No. 60-5597.
• E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, 5th ed.. North Holland; John Wiley & Sons, Inc.. Library of Congress Catalog Card No. 60-20003.
• G. S. Rushbrooke (1949). Introduction to Statistical Mechanics. Oxford Univ. Press. 

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