Difference between revisions of "Absolute zero" - New World Encyclopedia
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==Record cold temperatures approaching absolute zero== | ==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. | + | 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 [[superconductor|superconductivity]], [[superfluid]]ity, and [[Bose-Einstein condensate|Bose-Einstein condensation]]. | + | At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties including [[superconductor|superconductivity]], [[superfluid]]ity, and [[Bose-Einstein condensate|Bose-Einstein condensation]]. To study such [[phenomenon|phenomena]]*, [[scientist]]*s have worked to obtain ever lower temperatures. |
| − | *In September 2003, [[Massachusetts Institute of Technology | + | *In September 2003, researchers at the [[Massachusetts Institute of Technology]]* announced a record cold temperature of 450 [[1 E-12 K|pK]], or 4.5 × 10<sup>-10</sup>  K in a Bose-Einstein condensate of sodium atoms. This was performed by [[Wolfgang Ketterle]]* and colleagues at MIT.<ref>Leanhardt, A. ''et al.'' (2003) ''Science'' '''301''' 1513. [http://physicsweb.org/article/news/7/9/8 Physicsweb news report]</ref> |
| − | *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 [[1 E19 m|5000 light-years]] from [[Earth]] and is in the constellation [[Centaurus]].<ref>[http://www.smh.com.au/articles/2003/02/20/1045638427695.html Press report February 21 2003]</ref> | + | *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 [[1 E19 m|5000 light-years]]* from [[Earth]] and is in the constellation [[Centaurus]]*.<ref>[http://www.smh.com.au/articles/2003/02/20/1045638427695.html Press report February 21 2003]</ref> |
*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.<ref>The experimental methods and results are presented in detail in T.A. Knuuttila’s Ph.D. thesis, which can be accessed from [http://www.hut.fi/Yksikot/Kirjasto/Diss/2000/isbn9512252147/ this site]. The university’s press release on its achievement is [http://ltl.hut.fi/Low-Temp-Record.html here.]</ref> | *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.<ref>The experimental methods and results are presented in detail in T.A. Knuuttila’s Ph.D. thesis, which can be accessed from [http://www.hut.fi/Yksikot/Kirjasto/Diss/2000/isbn9512252147/ this site]. The university’s press release on its achievement is [http://ltl.hut.fi/Low-Temp-Record.html here.]</ref> | ||
==Thermodynamics near absolute zero== | ==Thermodynamics near absolute zero== | ||
| − | At 0 K, (nearly) all molecular motion ceases and <math>\Delta</math>''S'' = 0 for any [[adiabatic process]]. Pure substances can (ideally) form perfect [[crystal]]s as ''T'' <math>\rightarrow</math>0. [[Max Planck|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 energy level|degenerate]] (more than one [[microstate (statistical mechanics)|microstate]]), this cannot be true. The original [[Walther Nernst|Nernst]] ''heat theorem'' makes the weaker and less controversial claim that the entropy ''change'' for any isothermal process approaches zero as ''T'' → 0 | + | At 0 K, (nearly) all molecular motion ceases and <math>\Delta</math>''S'' = 0 for any [[adiabatic process]]*. Pure substances can (ideally) form perfect [[crystal]]s as ''T'' <math>\rightarrow</math>0. [[Max Planck|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 energy level|degenerate]]* (more than one [[microstate (statistical mechanics)|microstate]]*), this cannot be true. The original [[Walther Nernst|Nernst]]* ''heat theorem'' makes the weaker and less controversial claim that the entropy ''change'' for any isothermal process approaches zero as ''T'' → 0 |
:<math> \lim_{T \to 0} \Delta S = 0 </math> | :<math> \lim_{T \to 0} \Delta S = 0 </math> | ||
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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) | 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 (group)|lattice]] structure extends uninterrupted in all directions. The perfect order can be represented by translational [[symmetry]] along three (not usually [[orthogonality|orthogonal]]) [[Cartesian coordinate system|axes]]. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For [[chemical substance|substances]] | + | A perfect crystal is one in which the internal [[lattice (group)|lattice]]* structure extends uninterrupted in all directions. The perfect order can be represented by translational [[symmetry]]* along three (not usually [[orthogonality|orthogonal]]*) [[Cartesian coordinate system|axes]]*. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For [[chemical substance|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. | 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 [[Peter Debye|Debye]] model, the [[specific heat capacity|specific heat]] and entropy of a pure crystal are proportional to ''T''<sup> 3</sup>, while the [[enthalpy]] and [[chemical potential]] are proportional to ''T''<sup> 4</sup>. (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 [[Albert Einstein|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 relations|Maxwell's relations]] show that various other quantities also vanish. These [[phenomenon|phenomena]] were unanticipated. | + | Using the [[Peter Debye|Debye]]* model, the [[specific heat capacity|specific heat]]* and entropy of a pure crystal are proportional to ''T''<sup> 3</sup>, while the [[enthalpy]]* and [[chemical potential]]* are proportional to ''T''<sup> 4</sup>. (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 [[Albert Einstein|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 relations|Maxwell's relations]]* show that various other quantities also vanish. These [[phenomenon|phenomena]]* were unanticipated. |
| − | Since the relation between changes in the [[Gibbs free energy]], the enthalpy and the entropy is | + | Since the relation between changes in the [[Gibbs free energy]]*, the enthalpy and the entropy is |
:<math> \Delta G = \Delta H - T \Delta S \,</math> | :<math> \Delta G = \Delta H - T \Delta S \,</math> | ||
| − | it follows that as ''T'' decreases, Δ''G'' and Δ''H'' approach each other (so long as Δ''S'' is bounded). [[Experiment]]ally, it is found that most [[chemical reaction]]s are [[exothermic reaction|exothermic]] and release heat ''in the direction'' they are found to be going, toward [[thermodynamic equilibrium|equilbrium]]. That is, even at [[room temperature]] ''T'' is low enough so that the fact that (Δ''G'')<sub>''T,P''</sub> < 0 (usually) implies that Δ''H'' < 0. (In the opposite direction, each such reaction would of course absorb heat.) | + | it follows that as ''T'' decreases, Δ''G'' and Δ''H'' approach each other (so long as Δ''S'' is bounded). [[Experiment]]ally, it is found that most [[chemical reaction]]s are [[exothermic reaction|exothermic]]* and release heat ''in the direction'' they are found to be going, toward [[thermodynamic equilibrium|equilbrium]]*. That is, even at [[room temperature]]* ''T'' is low enough so that the fact that (Δ''G'')<sub>''T,P''</sub> < 0 (usually) implies that Δ''H'' < 0. (In the opposite direction, each such reaction would of course absorb heat.) |
| − | More than that, the ''slopes'' of the temperature derivatives of Δ''G'' and Δ''H'' converge and ''are equal to zero'' at ''T'' = 0, which ensures that Δ''G'' and Δ''H'' are nearly the same over a considerable range of temperatures, justifying the approximate [[empiricism|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) | + | More than that, the ''slopes'' of the temperature derivatives of Δ''G'' and Δ''H'' converge and ''are equal to zero'' at ''T'' = 0, which ensures that Δ''G'' and Δ''H'' are nearly the same over a considerable range of temperatures, justifying the approximate [[empiricism|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== | ==Absolute temperature scales== | ||
| − | As mentioned, absolute or [[thermodynamic temperature]] is conventionally measured in [[kelvin]]s (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''<sub>2</sub>/''T''<sub>1</sub>, 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 (physics)|spin]]*) and [[Bose-Einstein statistics]]* (particles of integer spin), all of which give the relative numbers of particles as (decreasing) [[exponential function]]*s of energy over ''kT''. On a [[macroscopic]]* level, a definition can be given in terms of the efficiencies of "reversible" [[heat engine]]s operating between hotter and colder thermal reservoirs. | + | As mentioned, absolute or [[thermodynamic temperature]]* is conventionally measured in [[kelvin]]s (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''<sub>2</sub>/''T''<sub>1</sub>, 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 (physics)|spin]]*) and [[Bose-Einstein statistics]]* (particles of integer spin), all of which give the relative numbers of particles as (decreasing) [[exponential function]]*s of energy over ''kT''. On a [[macroscopic]]* level, a definition can be given in terms of the efficiencies of "reversible" [[heat engine]]s operating between hotter and colder thermal reservoirs. |
==Negative temperatures== | ==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. | + | 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. |
== See also == | == See also == | ||
Revision as of 05:59, 31 December 2006
Absolute zero is the lowest possible temperature where nothing could be colder and no heat energy remains in a substance. Absolute zero is the point at which molecules stop and they have minimal movement vibrations or none, 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 (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.
While 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 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 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.[1]
- 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.[2]
- 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.[3]
Thermodynamics near absolute zero
At 0 K, (nearly) all molecular motion ceases and S = 0 for any adiabatic process. Pure substances can (ideally) form perfect crystals as T 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
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
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, 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.
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.
See also
Footnotes
- ↑ Leanhardt, A. et al. (2003) Science 301 1513. Physicsweb news report
- ↑ Press report February 21 2003
- ↑ The experimental methods and results are presented in detail in T.A. Knuuttila’s Ph.D. thesis, which can be accessed from this site. The university’s press release on its achievement is here.
ReferencesISBN 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-10: 0618082395; ISBN-13: 978-0618082391.
- Enss, Christian, and Hunklinger, Siegfried (2005). Low-Temperature Physics. Berlin and Heidelberg (Germany); New York, NY: Springer-Verlag. ISBN-10: 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-10: 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-10: 1563960303; ISBN-13: 978-1563960307.
- Baierlein, Ralph (1999). Thermal Physics. Cambridge, UK: Cambridge University Press. ISBN-10: 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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