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Encyclopedia > Absolute zero

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 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. Absolute Zero may refer to: Absolute Zero, the lowest possible temperature, occurring when no heat energy remains in a substance. ... For other uses, see Temperature (disambiguation). ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may possess and is the energy of the ground state of the system. ...


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.[1] 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 possible to cool any substance to 0 K,[2] 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 has reported reaching temperatures of 100 pK (0.1×10−9K) and in 2003, researchers at MIT achieved 500 pK (0.5×10−9 K).[3] For other uses, see Kelvin (disambiguation). ... Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. ... For other uses, see Celsius (disambiguation). ... For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. ... For other uses, see Fahrenheit (disambiguation). ... A Bose–Einstein condensate (BEC) is a state of matter formed by a system of bosons confined in an external potential and cooled to temperatures very near to absolute zero (0 kelvin or −273. ... A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. ... Helium II will creep along surfaces in order to find its own level - after a short while, the levels in the two containers will equalize. ... Helsinki University of Technology (TKK) (Finnish: Teknillinen korkeakoulu; Swedish: Tekniska högskolan) is the premier technical university in Finland and the largest in the Nordic Countries with over 15000 students. ... For other uses, see Kelvin (disambiguation). ... “MIT” redirects here. ...

Contents

History

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: Robert Boyle (Irish: Robaird Ó Bhaoill) (25 January 1627 – 30 December 1691) was an Irish natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry. ... Niter or nitre is the mineral form of potassium nitrate, KNO3, also known as saltpeter. ...

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. Guillaume Amontons (August 31, 1663 - October 11, 1705) was a French instrument inventor and physicist. ...


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.[4] Johann Heinrich Lambert Johann Heinrich Lambert (August 26, 1728 – September 25, 1777), was a mathematician, physicist and astronomer. ...


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. Pierre-Simon, marquis de Laplace (March 23, 1749 - March 5, 1827) was a French mathematician and astronomer whose work was pivotal to the development of mathematical astronomy. ... Lavoisier redirects here. ... John Dalton John Dalton (September 6, 1766 – July 27, 1844) was an English chemist and physicist, born at Eaglesfield, near Cockermouth in Cumberland. ...


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.[5] James Prescott Joule, FRS (IPA: ; December 24, 1818 – October 11, 1889) was an English physicist (and brewer), born in Salford, Lancashire. ... For other persons named William Thomson, see William Thomson (disambiguation). ... The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. ...


Additional Information

It can be shown from the laws of thermodynamics that absolute zero can never be achieved artificially, though it is possible to reach temperatures close to it through the use of cryocoolers. This is the same principle that ensures no machine can be 100% efficient. Thermodynamics (from the Greek θερμη, therme, meaning heat and δυναμις, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Cryocoolers are refrigerators used to reach cryogenic temperatures. ... This article is about devices that perform tasks. ...


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. Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ... Helium II will creep along surfaces in order to find its own level - after a short while, the levels in the two containers will equalize. ... A Bose–Einstein condensate is a phase of matter formed by bosons cooled to temperatures very near to absolute zero (0 kelvins or -273. ... For other uses, see Phenomena (disambiguation). ... A scientist, in the broadest sense, refers to any person that engages in a systematic activity to acquire knowledge or an individual that engages in such practices and traditions that are linked to schools of thought or philosophy. ...

  • 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 of freedom.[6][7]
  • 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.[8]
  • In 2000 the Helsinki University of Technology has reported reaching record low temperatures of 100 pK (0.1×10−9K) .[9][10]

NIST logo The National Institute of Standards and Technology (NIST, formerly known as The National Bureau of Standards) is a non-regulatory agency of the United States Department of Commerce’s Technology Administration. ... For other uses, see Kelvin (disambiguation). ... Helsinki University of Technology (TKK) (Finnish: Teknillinen korkeakoulu; Swedish: Tekniska högskolan) is the premier technical university in Finland and the largest in the Nordic Countries with over 15000 students. ... The Boomerang Nebula. ... The Triangulum Emission Nebula NGC 604 The Pillars of Creation from the Eagle Nebula For other uses, see Nebula (disambiguation). ... This article is about Earth as a planet. ... Centaurus (Latin for centaur) was one of the 48 constellations listed by Ptolemy, and counts also among the 88 modern constellations. ...

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 Tto0. Max Planck's strong form of the third law of thermodynamics states the entropy of a perfect crystal vanishes at absolute zero. However, this cannot be true if the lowest energy state is degenerate, or more than one microstate. The original Nernst heat theorem makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as Tto0 In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which no heat is transferred to or from the working fluid. ... For other uses, see Crystal (disambiguation). ... Planck redirects here. ... The third law of thermodynamics (hereinafter Third Law) states that as a system approaches the zero absolute temperature (hereinafter ZAT), all processes cease and the entropy of the system approaches a minimum value. ... For other uses, see: information entropy (in information theory) and entropy (disambiguation). ... The energy levels of two or more physical states are said to be degenerate when they have the same value. ... In statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system, that the system visits in the course of its thermal fluctuations. ... Walther Hermann Nernst (June 25, 1864 – November 18, 1941) was a German physicist who is known for his theories behind the calculation of chemical affinity as embodied in the third law of thermodynamics, for which he won the 1920 Nobel Prize in chemistry. ...

 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) The third law of thermodynamics (hereinafter Third Law) states that as a system approaches the zero absolute temperature (hereinafter ZAT), all processes cease and the entropy of the system approaches a minimum value. ... An isotherm is a line of equal or constant temperature on a graph, plot, or map; an isopleth of temperature. ... Adiabatic may refer to: Adiabatic process, in thermodynamics Adiabatic process (quantum mechanics) Adiabatic theorem, in quantum mechanics. ... Intersecting airplane trails. ...


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. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. ... Sphere symmetry group o. ... In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. ... Fig. ... Water and steam are two different forms of the same chemical substance A chemical substance is a material with a definite chemical composition. ... This article is about the mineral. ... For other uses, see Graphite (disambiguation). ... For other uses, see Carbon (disambiguation). ...


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. Petrus Josephus Wilhelmus Debije (March 24, 1884 – November 2, 1966) was a Dutch physical chemist. ... Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the temperature of a unit quantity of a substance by a certain temperature interval. ... t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... In thermodynamics and chemistry, chemical potential, symbolized by μ, is a term introduced in 1876 by the American mathematical physicist Willard Gibbs, which he defined as follows: Gibbs noted also that for the purposes of this definition, any chemical element or combination of elements in given proportions may be considered a... “Einstein” redirects here. ... In physics, thermal expansion is the tendency of matter to change in volume in response to a change in temperature. ... Maxwells relations are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials. ... For other uses, see Phenomena (disambiguation). ...


Since the relation between changes in the Gibbs energy, the enthalpy and the entropy is In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure. ...

 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. In the scientific method, an experiment (Latin: ex- periri, of (or from) trying) is a set of observations performed in the context of solving a particular problem or question, to retain or falsify a hypothesis or research concerning phenomena. ... For other uses, see Chemical reaction (disambiguation). ... In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ... In thermodynamics, the word exothermic outside heating describes a process or reaction that releases energy usually in the form of heat, but it can also release energy in form of light (e. ... This article is about the physical effect. ...


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) In philosophy generally, empiricism is a theory of knowledge emphasizing the role of experience, especially sensory perception, in the formation of ideas, while discounting the notion of innate ideas. ...


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. Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. ... For other uses, see Kelvin (disambiguation). ... For other uses, see Celsius (disambiguation). ... For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. ... For other uses, see Fahrenheit (disambiguation). ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Fermi-Dirac distribution as a function of ε/μ plotted for 4 different temperatures. ... In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is the motion of its center of mass about an external point. ... In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. ... The exponential function is one of the most important functions in mathematics. ... Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ... A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. ...


Negative temperatures

Main article: Negative temperature

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. In physics, certain systems can achieve negative temperatures; that is, their thermodynamic temperature can be a negative quantity. ...


See also

For other uses, see Celsius (disambiguation). ... CMB redirects here. ... For other uses of this term, see Spacetime (disambiguation). ... The Delisle scale (°D) is a temperature scale invented in 1732 by the French astronomer Joseph-Nicolas Delisle (1688–1768). ... For other uses, see Fahrenheit (disambiguation). ... For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ... The International Temperature Scale of 1990 (ITS-90) is an equipment calibration standard for making measurements on the kelvin and Celsius temperature scales. ... For other uses, see Kelvin (disambiguation). ... Circumstances where water naturally occurs in liquid form are shown in light grey. ... The Planck temperature, named after German physicist Max Planck, is the natural unit of temperature, denoted by TP. The Planck units, in general, represent limits of quantum mechanics. ... For the idealized thermodynamic cycle for a steam engine, see Rankine cycle. ... Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. ... In physics, the triple point of a substance is the temperature and pressure at which three phases (gas, liquid, and solid) of that substance may coexist in thermodynamic equilibrium. ...

Notes

  1. ^ Unit of thermodynamic temperature (kelvin). SI Brochure, 8th edition Section 2.1.1.5. Bureau International des Poids et Mesures (1967). Retrieved on 2008-02-11.
  2. ^ Davies, Jeremy Dunning (1996). Concise Thermodynamics. Horwood Publishing, 43. ISBN 1898563152. 
  3. ^ MIT News Office. "MIT Team Achieves Coldest Temperature Ever", Massachusetts Institute of Technology, 11 September 2003. Retrieved on 2008-02-11. 
  4. ^ Lambert, Johann Heinrich (1779). Pyrometrie. OCLC 165756016. 
  5. ^ "Cold". Encyclopædia Britannica (Eleventh Edition). (1911). The LoveToKnow Wiki. Retrieved on 2008-02-11. 
  6. ^ Knuuttila, Tauno (2000). Nuclear Magnetism and Superconductivity in Rhodium. Espoo, Finland: Helsinki University of Technology. ISBN 9512252082. Retrieved on 2008-02-11. 
  7. ^ Low Temperature Laboratory, Teknillinen Korkeakoulu (8 December 2000). "Low Temperature World Record". Press release. Retrieved on 2008-02-11.
  8. ^ Stephen Cauchi. "Coolest Bow Tie in the Universe", The Sydney Morning Herald, 21 February 2003. Retrieved on 2008-02-11. Archived from the original on 2006-09-01. 
  9. ^ Leanhardt, A. E.; et al. (2000). "Cooling Bose-Einstein Condensates Below 100 Picokelvin". Science 301 (5639): 1513-1515. doi:10.1126/science.1088827. 
  10. ^ Belle Dumé. "Bose-Einstein Condensates Break Temperature Record", PhysicsWeb, 12 September 2003. Retrieved on 2008-02-11. 

Year 1967 (MCMLXVII) was a common year starting on Sunday (link will display full calendar) of the 1967 Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... The Online Computer Library Center (OCLC) was founded in 1967 and originally named the Ohio College Library Center. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... For information on Wikipedia press releases, see Wikipedia:Press releases. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 244th day of the year (245th in leap years) in the Gregorian calendar. ... Science is the academic journal of the American Association for the Advancement of Science and is considered one of the worlds most prestigious scientific journals. ... A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ... 2008 (MMVIII) is the current year, a leap year that started on Tuesday of the Anno Domini (or common era), in accordance to the Gregorian calendar. ... is the 42nd day of the year in the Gregorian calendar. ...

References

  • Herbert B. Callen (1960). "Chapter 10", Thermodynamics. New York: John Wiley & Sons, Inc. OCLC 535083. 
  • Herbert B. Callen (1985). Thermodynamics and an Introduction to Thermostatistics, Second Edition, New York: John Wiley & Sons, Inc. ISBN 0-471-86256-8. 
  • E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists, Fifth Edition, Amsterdam: North Holland Publishing. OCLC 324553. 
  • George Stanley Rushbrooke (1949). Introduction to Statistical Mechanics. Oxford: Clarendon Press. OCLC 531928. 

The Online Computer Library Center (OCLC) was founded in 1967 and originally named the Ohio College Library Center. ... The Online Computer Library Center (OCLC) was founded in 1967 and originally named the Ohio College Library Center. ... The Online Computer Library Center (OCLC) was founded in 1967 and originally named the Ohio College Library Center. ...

External links


  Results from FactBites:
 
Absolute zero - Wikipedia, the free encyclopedia (1806 words)
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 the fundamental particles of nature have minimal vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion.
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 zero: Definition and Much More from Answers.com (2722 words)
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.
Absolute zero is the point on the thermodynamic (absolute) temperature scale where the heat energy is at a minimum, that is, no more heat can be removed from the system.
At absolute zero, the molecules and atoms in a system are all in their ground state, the state of lowest possible energy, and a system has the least amount of kinetic energy allowed by the laws of physics.
  More results at FactBites »

 
 

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