Absolute zero

Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as 0. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15° on the Celsius scale (International System of Units),[1][2] which equals −459.67° on the Fahrenheit scale (United States customary units or Imperial units).[3] The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.

It is commonly thought of as the lowest temperature possible, but it is not the lowest enthalpy state possible, because all real substances begin to depart from the ideal gas when cooled as they approach the change of state to liquid, and then to solid; and the sum of the enthalpy of vaporization (gas to liquid) and enthalpy of fusion (liquid to solid) exceeds the ideal gas's change in enthalpy to absolute zero. In the quantum-mechanical description, matter (solid) at absolute zero is in its ground state, the point of lowest internal energy.

The laws of thermodynamics indicate that absolute zero cannot be reached using only thermodynamic means, because the temperature of the substance being cooled approaches the temperature of the cooling agent asymptotically,[4] and a system at absolute zero still possesses quantum mechanical zero-point energy, the energy of its ground state at absolute zero. The kinetic energy of the ground state cannot be removed.

Scientists and technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity.

Zero kelvin (−273.15 °C) is defined as absolute zero.

Thermodynamics near absolute zero

At temperatures near 0 K (−273.15 °C; −459.67 °F), nearly all molecular motion ceases and ΔS = 0 for any adiabatic process, where S is the entropy. In such a circumstance, 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 in which a perfect crystal is gone. 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:

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)

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 exist in 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 material inclusions, can and do 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 Gibbs free energy (G), the enthalpy (H) and the entropy is

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 equilibrium. If ΔS and/or T are small, the condition ΔG < 0 may imply that ΔH < 0, which would indicate an exothermic reaction. However, this is not required; endothermic reactions can proceed spontaneously if the TΔS term is large enough.

Moreover, the slopes of the derivatives of ΔG and ΔH converge and are equal to zero at T = 0. This ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures and justifies the approximate empirical Principle of Thomsen and Berthelot, which states that the equilibrium state to which a system proceeds is the one that 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 absolute zero in metals is the Fermi gas. The electrons, being Fermions, must be in different quantum states, which leads the electrons to get very high typical velocities, even at absolute zero. The maximum energy that electrons can have at absolute zero is called the Fermi energy. The Fermi temperature is defined as this maximum energy divided by Boltzmann's constant, and is of the order of 80,000 K for typical electron densities found in metals. For temperatures significantly below the Fermi temperature, the electrons behave in almost the same way as at absolute zero. This explains the failure of the classical equipartition theorem for metals that eluded classical physicists in the late 19th century.

Relation with Bose–Einstein condensate

Bose Einstein condensate
Velocity-distribution data of a gas of rubidium atoms at a temperature within a few billionths of a degree above absolute zero. Left: just before the appearance of a Bose–Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate.

A Bose–Einstein condensate (BEC) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near absolute zero. Under such conditions, a large fraction of the bosons occupy the lowest quantum state of the external potential, at which point quantum effects become apparent on a macroscopic scale.[5]

This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924–25. Bose first sent a paper to Einstein on the quantum statistics of light quanta (now called photons). Einstein was impressed, translated the paper from English to German and submitted it for Bose to the Zeitschrift für Physik, which published it. Einstein then extended Bose's ideas to material particles (or matter) in two other papers.[6]

Seventy years later, in 1995, the first gaseous condensate was produced by Eric Cornell and Carl Wieman at the University of Colorado at Boulder NIST-JILA lab, using a gas of rubidium atoms cooled to 170 nanokelvins (nK)[7] (1.7×10−7 K).[8]

A record cold temperature of 450 ±80 picokelvins (pK) (4.5×10−10 K) in a Bose–Einstein condensate (BEC) of sodium atoms was achieved in 2003 by researchers at MIT.[9] The associated black-body (peak emittance) wavelength of 6,400 kilometers is roughly the radius of Earth.

Absolute temperature scales

Absolute, or thermodynamic, temperature is conventionally measured in kelvins (Celsius-scaled increments) and in the Rankine scale (Fahrenheit-scaled increments) with increasing rarity. Absolute temperature measurement is uniquely determined by 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 of this standard comes from the Maxwell–Boltzmann distribution. It can also be found in Fermi–Dirac statistics (for particles of half-integer spin) and Bose–Einstein statistics (for particles of integer spin). All of these define the relative numbers of particles in a system as decreasing exponential functions of energy (at the particle level) over kT, with k representing the Boltzmann constant and T representing the temperature observed at the macroscopic level.[1]

Negative temperatures

Temperatures that are expressed as negative numbers on the familiar Celsius or Fahrenheit scales are simply colder than the zero points of those scales. Certain systems can achieve truly negative temperatures; that is, their thermodynamic temperature (expressed in kelvins) can be of a negative quantity. A system with a truly negative temperature is not colder than absolute zero. Rather, a system with a negative temperature is hotter than any system with a positive temperature, in the sense that if a negative-temperature system and a positive-temperature system come in contact, heat flows from the negative to the positive-temperature system.[10]

Most familiar systems cannot achieve negative temperatures because adding energy always increases their entropy. However, some systems have a maximum amount of energy that they can hold, and as they approach that maximum energy their entropy actually begins to decrease. Because temperature is defined by the relationship between energy and entropy, such a system's temperature becomes negative, even though energy is being added.[10] As a result, the Boltzmann factor for states of systems at negative temperature increases rather than decreases with increasing state energy. Therefore, no complete system, i.e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures. However, for quasi-equilibrium systems (e.g. spins out of equilibrium with the electromagnetic field) this argument does not apply, and negative effective temperatures are attainable.

On 3 January 2013, physicists announced that they had created a quantum gas made up of potassium atoms with a negative temperature in motional degrees of freedom for the first time.[11]


Robert Boyle 0001
Robert Boyle pioneered the idea of an absolute zero.

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.[12] The concept was well known among naturalists of the time. Some contended an absolute minimum temperature occurred within earth (as one of the four classical 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."[13]

Limit to the "degree of cold"

The question whether there is a limit to the degree of coldness possible, and, if so, where the zero must be placed, was first addressed by the French physicist Guillaume Amontons in 1702, in connection with his improvements in the air-thermometer. His instrument indicated temperatures by the height at which a certain mass of air sustained a column of mercury—the volume, or "spring" of the air varying with temperature. Amontons therefore argued that the zero of his thermometer would be that temperature at which the spring of the air was reduced to nothing. He used a scale that marked the boiling-point of water at +73 and the melting-point of ice at +​51 12, so that the zero was equivalent to about −240 on the Celsius scale.[14] Amontons held that the absolute zero cannot be reached, so never attempted to compute it explicitly. [15] The value of −240 °C, or "431 divisions [in Fahrenheit's thermometer] below the cold of freezing water"[16] was published by George Martine in 1740.

This close approximation to the modern value of −273.15 °C[1] for the zero of the air-thermometer was further improved upon in 1779 by Johann Heinrich Lambert, who observed that −270 °C (−454.00 °F; 3.15 K) might be regarded as absolute cold.[17]

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 James Prescott 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 that was independent of the properties of any particular substance and was based on Carnot's theory of the Motive Power of Heat and data published by Henri Victor Regnault.[18] It followed from the principles on which this scale was constructed that its zero was placed at −273 °C, at almost precisely the same point as the zero of the air-thermometer.[14] This value was not immediately accepted; values ranging from −271.1 °C (−455.98 °F) to −274.5 °C (−462.10 °F), derived from laboratory measurements and observations of astronomical refraction, remained in use in the early 20th century.[19]

The race to absolute zero

Commemorative plaque in Leiden

With a better theoretical understanding of absolute zero, scientists were eager to reach this temperature in the lab.[20] By 1845, Michael Faraday had managed to liquefy most gases then known to exist, and reached a new record for lowest temperatures by reaching −130 °C (−202 °F; 143 K). Faraday believed that certain gases, such as oxygen, nitrogen, and hydrogen, were permanent gases and could not be liquefied.[21] Decades later, in 1873 Dutch theoretical scientist Johannes Diderik van der Waals demonstrated that these gases could be liquefied, but only under conditions of very high pressure and very low temperatures. In 1877, Louis Paul Cailletet in France and Raoul Pictet in Switzerland succeeded in producing the first droplets of liquid air −195 °C (−319.0 °F; 78.1 K). This was followed in 1883 by the production of liquid oxygen −218 °C (−360.4 °F; 55.1 K) by the Polish professors Zygmunt Wróblewski and Karol Olszewski.

Scottish chemist and physicist James Dewar and the Dutch physicist Heike Kamerlingh Onnes took on the challenge to liquefy the remaining gases hydrogen and helium. In 1898, after 20 years of effort, Dewar was first to liquefy hydrogen, reaching a new low temperature record of −252 °C (−421.6 °F; 21.1 K). However Onnes, his rival, was the first to liquefy helium, in 1908, using several precooling stages and the Hampson–Linde cycle. He lowered the temperature to the boiling point of helium −269 °C (−452.20 °F; 4.15 K). By reducing the pressure of the liquid helium he achieved an even lower temperature, near 1.5 K. These were the coldest temperatures achieved on earth at the time and his achievement earned him the Nobel Prize in 1913.[22] Onnes would continue to study the properties of materials at temperatures near absolute zero, describing superconductivity and superfluids for the first time.

Very low temperatures

Boomerang nebula
The rapid expansion of gases leaving the Boomerang Nebula, a bi-polar, filamentary, likely proto-planetary nebula in Centaurus, causes the lowest observed temperature outside a laboratory: 1 K

The average temperature of the universe today is approximately 2.73 kelvins (−270.42 °C; −454.76 °F), based on measurements of cosmic microwave background radiation.[23][24]

Absolute zero cannot be achieved, although it is possible to reach temperatures close to it through the use of cryocoolers, dilution refrigerators, and nuclear adiabatic demagnetization. The use of laser cooling has produced temperatures less than a billionth of a kelvin.[25] 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 even lower temperatures.

  • The current world record was set in 1999 at 100 picokelvins (pK), or 0.000 000 000 1 of a kelvin, by cooling the nuclear spins in a piece of rhodium metal.[26]
  • In November 2000, nuclear spin temperatures below 100 pK were reported for an experiment at the Helsinki University of Technology's Low Temperature Lab in Espoo, Finland. 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 in freedom.[27][28]
  • In February 2003, the Boomerang Nebula was observed to have been releasing gases at a speed of 500,000 km/h (over 300,000 mph) for the last 1,500 years. This has cooled it down to approximately 1 K, as deduced by astronomical observation, which is the lowest natural temperature ever recorded.[29]
  • In May 2005, the European Space Agency proposed research in space to achieve femto-kelvin temperatures.[30]
  • In May 2006, the Institute of Quantum Optics at the University of Hannover gave details of technologies and benefits of femto-kelvin research in space.[31]
  • In January 2013, physicist Ulrich Schneider of the University of Munich in Germany reported to have achieved temperatures formally below absolute zero ("negative temperature") in gases. The gas is artificially forced out of equilibrium into a high potential energy state, which is however cold. When it then emits radiation it approaches the equilibrium, and can continue emitting despite reaching formal absolute zero; thus, the temperature is formally negative.[32]
  • In September 2014, scientists in the CUORE collaboration at the Laboratori Nazionali del Gran Sasso in Italy cooled a copper vessel with a volume of one cubic meter to 0.006 kelvins (−273.144 °C; −459.659 °F) for 15 days, setting a record for the lowest temperature in the known universe over such a large contiguous volume.[33]
  • In June 2015, experimental physicists at Massachusetts Institute of Technology (MIT) successfully cooled molecules in a gas of sodium potassium to a temperature of 500 nanokelvins, and it is expected to exhibit an exotic state of matter by cooling these molecules a bit further.[34]

See also


  1. ^ a b c "Unit of thermodynamic temperature (kelvin)". SI Brochure, 8th edition. Bureau International des Poids et Mesures. 13 March 2010 [1967]. Section Archived from the original on 7 October 2014. Retrieved 20 June 2017. Note: The triple point of water is 0.01 °C, not 0 °C; thus 0 K is −273.15 °C, not −273.16 °C.
  2. ^ Arora, C. P. (2001). Thermodynamics. Tata McGraw-Hill. Table 2.4 page 43. ISBN 978-0-07-462014-4.
  3. ^ Zielinski, Sarah (1 January 2008). "Absolute Zero". Smithsonian Institution. Retrieved 2012-01-26.
  4. ^ Masanes, Lluís; Oppenheim, Jonathan (14 March 2017), "A general derivation and quantification of the third law of thermodynamics", Nature Communications, 8 (14538): 14538, doi:10.1038/ncomms14538, PMC 5355879, PMID 28290452
  5. ^ Donley, Elizabeth A.; Claussen, Neil R.; Cornish, Simon L.; Roberts, Jacob L.; Cornell, Eric A.; Wieman, Carl E. (2001). "Dynamics of collapsing and exploding Bose–Einstein condensates". Nature. 412 (6844): 295–299. arXiv:cond-mat/0105019. Bibcode:2001Natur.412..295D. doi:10.1038/35085500. PMID 11460153.
  6. ^ Clark, Ronald W. "Einstein: The Life and Times" (Avon Books, 1971) pp. 408–9 ISBN 0-380-01159-X
  7. ^ "New State of Matter Seen Near Absolute Zero". NIST. Archived from the original on 1 June 2010.
  8. ^ Levi, Barbara Goss (2001). "Cornell, Ketterle, and Wieman Share Nobel Prize for Bose–Einstein Condensates". Search & Discovery. Physics Today online. Archived from the original on 2007-10-24. Retrieved 2008-01-26.
  9. ^ Leanhardt, A. E.; Pasquini, TA; Saba, M; Schirotzek, A; Shin, Y; Kielpinski, D; Pritchard, DE; Ketterle, W (2003). "Cooling Bose–Einstein Condensates Below 500 Picokelvin" (PDF). Science. 301 (5639): 1513–1515. Bibcode:2003Sci...301.1513L. doi:10.1126/science.1088827. PMID 12970559.
  10. ^ a b Chase, Scott. "Below Absolute Zero -What Does Negative Temperature Mean?". The Physics and Relativity FAQ. Retrieved 2010-07-02.
  11. ^ Merali, Zeeya (2013). "Quantum gas goes below absolute zero". Nature. doi:10.1038/nature.2013.12146.
  12. ^ Stanford, John Frederick (1892). The Stanford Dictionary of Anglicised Words and Phrases.
  13. ^ Boyle, Robert (1665). New Experiments and Observations touching Cold.
  14. ^ a b Wikisource Chisholm, Hugh, ed. (1911). "Cold" . Encyclopædia Britannica (11th ed.). Cambridge University Press.
  15. ^ Talbot, G.R.; Pacey, A.C. (1972). "Antecedents of thermodynamics in the work of Guillaume Amontons". Centaurus. 16 (1): 20–40. doi:10.1111/j.1600-0498.1972.tb00163.x.
  16. ^ Essays Medical and Philosophical, p. PA291, at Google Books
  17. ^ Lambert, Johann Heinrich (1779). Pyrometrie. Berlin. OCLC 165756016.
  18. ^ Thomson, William (1848). "On an Absolute Thermometric Scale founded on Carnot's Theory of the Motive Power of Heat, and calculated from Regnault's observations". Proceedings of the Cambridge Philosophical Society. 1: 66–71.
  19. ^ Newcomb, Simon (1906), A Compendium of Spherical Astronomy, New York: The Macmillan Company, p. 175, OCLC 64423127
  20. ^ "ABSOLUTE ZERO - PBS NOVA DOCUMENTARY (full length)". YouTube. Retrieved November 23, 2016.
  21. ^ Cryogenics. Scienceclarified.com. Retrieved on 2012-07-22.
  22. ^ "The Nobel Prize in Physics 1913: Heike Kamerlingh Onnes". Nobel Media AB. Retrieved 24 April 2012.
  23. ^ Kruszelnicki, Karl S. (25 September 2003). "Coldest Place in the Universe 1". Australian Broadcasting Corporation. Retrieved 2012-09-24.
  24. ^ "What's the temperature of space?". The Straight Dope. 3 August 2004. Retrieved 2012-09-24.
  25. ^ Catchpole, Heather (2008-09-04). "Cosmos Online – Verging on absolute zero". Archived from the original on 22 November 2008.
  26. ^ "World record in low temperatures". Archived from the original on 2009-06-18. Retrieved 2009-05-05.
  27. ^ Knuuttila, Tauno (2000). Nuclear Magnetism and Superconductivity in Rhodium. Espoo, Finland: Helsinki University of Technology. ISBN 978-951-22-5208-4. Archived from the original on 28 April 2001. Retrieved 2008-02-11.
  28. ^ "Low Temperature World Record" (Press release). Low Temperature Laboratory, Teknillinen Korkeakoulu. 8 December 2000. Archived from the original on 2008-02-18. Retrieved 2008-02-11.
  29. ^ Sahai, Raghvendra; Nyman, Lars-Åke (1997). "The Boomerang Nebula: The Coldest Region of the Universe?". The Astrophysical Journal. 487 (2): L155–L159. Bibcode:1997ApJ...487L.155S. doi:10.1086/310897. hdl:2014/22450.
  30. ^ "Scientific Perspectives for ESA's Future Programme in Life and Physical sciences in Space" (PDF). esf.org.
  31. ^ "Atomic Quantum Sensors in Space" (PDF). University of California, Los Angeles.
  32. ^ "Atoms Reach Record Temperature, Colder than Absolute Zero". livescience.com.
  33. ^ "CUORE: The Coldest Heart in the Known Universe". INFN Press Release. Retrieved 21 October 2014.
  34. ^ "MIT team creates ultracold molecules". Massachusetts Institute of Technology, Massachusetts, Cambridge.

Further reading

  • Herbert B. Callen (1960). "Chapter 10". Thermodynamics. New York: John Wiley & Sons. ISBN 978-0-471-13035-2. OCLC 535083.
  • Herbert B. Callen (1985). Thermodynamics and an Introduction to Thermostatistics (Second ed.). New York: John Wiley & Sons. ISBN 978-0-471-86256-7.
  • E.A. Guggenheim (1967). Thermodynamics: An Advanced Treatment for Chemists and Physicists (Fifth ed.). Amsterdam: North Holland Publishing. ISBN 978-0-444-86951-7. OCLC 324553.
  • George Stanley Rushbrooke (1949). Introduction to Statistical Mechanics. Oxford: Clarendon Press. OCLC 531928.

External links


The Celsius scale, also known as the centigrade scale, is a temperature scale used by the International System of Units (SI). As an SI derived unit, it is used by all countries except the United States, the Bahamas, Belize, the Cayman Islands and Liberia. It is named after the Swedish astronomer Anders Celsius (1701–1744), who developed a similar temperature scale. The degree Celsius (°C) can refer to a specific temperature on the Celsius scale or a unit to indicate a difference between two temperatures or an uncertainty. Before being renamed to honor Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps.

From 1743, the Celsius scale is based on 0 °C for the freezing point of water and 100 °C for the boiling point of water at 1 atm pressure. Prior to 1743, the scale was also based on the boiling and melting points of water, but the values were reversed (i.e. the boiling point was at 0 degrees and the melting point was at 100 degrees). The 1743 scale reversal was proposed by Jean-Pierre Christin.

By international agreement, since 1954 the unit degree Celsius and the Celsius scale are defined by absolute zero and the triple point of Vienna Standard Mean Ocean Water (VSMOW), a specially purified water. This definition also precisely relates the Celsius scale to the Kelvin scale, which defines the SI base unit of thermodynamic temperature with symbol K. Absolute zero, the lowest temperature possible, is defined as being exactly 0 K and −273.15 °C. The temperature of the triple point of water is defined as exactly 273.16 K (0.01 °C). This means that a temperature difference of one degree Celsius and that of one kelvin are exactly the same.On 20 May 2019, the kelvin, and along with it the degree Celsius, will be redefined so that its value will be determined by definition of the Boltzmann constant.

Charles's law

Charles' law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is:

This directly proportional relationship can be written as:



V is the volume of the gas,
T is the temperature of the gas (measured in kelvins),
k is a constant.

This law describes how a gas expands as the temperature increases; conversely, a decrease in temperature will lead to a decrease in volume. For comparing the same substance under two different sets of conditions, the law can be written as:

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.


Cold is the presence of low temperature, especially in the atmosphere. In common usage, cold is often a subjective perception. A lower bound to temperature is absolute zero, defined as 0.00 K on the Kelvin scale, an absolute thermodynamic temperature scale. This corresponds to −273.15 °C on the Celsius scale, −459.67 °F on the Fahrenheit scale, and 0.00 °R on the Rankine scale.

Since temperature relates to the thermal energy held by an object or a sample of matter, which is the kinetic energy of the random motion of the particle constituents of matter, an object will have less thermal energy when it is colder and more when it is hotter. If it were possible to cool a system to absolute zero, all motion of the particles in a sample of matter would cease and they would be at complete rest in this classical sense. The object would be described as having zero thermal energy. Microscopically in the description of quantum mechanics, however, matter still has zero-point energy even at absolute zero, because of the uncertainty principle.

Fermi energy

The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.

In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band.

Confusingly, the term "Fermi energy" is often used to refer to a different yet closely related concept, the Fermi level (also called electrochemical potential).

There are a few key differences between the Fermi level and Fermi energy, at least as they are used in this article:

The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature.

The Fermi energy is an energy difference (usually corresponding to a kinetic energy), whereas the Fermi level is a total energy level including kinetic energy and potential energy.

The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi level (the electrochemical potential of an electron) remains well defined even in complex interacting systems, at thermodynamic equilibrium.Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state,

then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature.

Gone Sovereign/Absolute Zero

"Gone Sovereign/Absolute Zero", is a double-single from American rock band Stone Sour, released as the first single from their fourth album House of Gold & Bones – Part 1.

"Absolute Zero"'s reprise is featured on the track "The House of Gold & Bones", from the part two of the album.

Ground state

The ground state of a quantum-mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In the quantum field theory, the ground state is usually called the vacuum state or the vacuum.

If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system.

According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temperature for systems that exhibit negative temperature.


The Kelvin scale is an absolute thermodynamic temperature scale using as its null point absolute zero, the temperature at which all thermal motion ceases in the classical description of thermodynamics. The kelvin (symbol: K) is the base unit of temperature in the International System of Units (SI).

Until 2018, the kelvin was defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C or 32.018 °F). In other words, it was defined such that the triple point of water is exactly 273.16 K.

On 16 November 2018, a new definition was adopted, in terms of a fixed value of the Boltzmann constant. For legal metrology purposes, the new definition will officially come into force on 20 May 2019 (the 130th anniversary of the Metre Convention).The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Thomson, 1st Baron Kelvin (1824–1907), who wrote of the need for an "absolute thermometric scale". Unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or written as a degree. The kelvin is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the degree Celsius, which has the same magnitude. The definition implies that absolute zero (0 K) is equivalent to −273.15 °C (−459.67 °F).

Laws of thermodynamics

The four laws of thermodynamics define fundamental physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems at thermal equilibrium. The laws describe how these quantities behave under various circumstances, and preclude the possibility of certain phenomena (such as perpetual motion).

The four laws of thermodynamics are:

Zeroth law of thermodynamics: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law helps define the concept of temperature.

First law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible.

Second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.

Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero.There have been suggestions of additional laws, but none of them achieve the generality of the four accepted laws, and they are not mentioned in standard textbooks.The laws of thermodynamics are important fundamental laws in physics and they are applicable in other natural sciences.

Planck temperature

Planck temperature, denoted by TP, is the unit of temperature in the system of natural units known as Planck units.

It serves as the defining unit of the Planck temperature scale. In this scale the magnitude of the Planck temperature is equal to 1, while that of absolute zero is 0.

Other temperatures can be converted to Planck temperature units. For example, 0 °C = 273.15 K = 1.9279×10−30 TP.

In SI units, the Planck temperature is about 1.417×1032 kelvin (equivalently, degrees Celsius, since the difference is trivially small at this scale), or 2.55×1032 degrees Fahrenheit or Rankine.


Temperature is a physical quantity expressing hot and cold. It is measured with a thermometer calibrated in one or more temperature scales. The most commonly used scales are the Celsius scale (formerly called centigrade) (denoted °C), Fahrenheit scale (denoted °F), and Kelvin scale (denoted K). The kelvin (the word is spelled with a lower-case k) is the unit of temperature in the International System of Units (SI), in which temperature is one of the seven fundamental base quantities. The Kelvin scale is widely used in science and technology.

Theoretically, the coldest a system can be is when its temperature is absolute zero, at which point the thermal motion in matter would be zero. However, an actual physical system or object can never attain a temperature of absolute zero. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale.

For an ideal gas, temperature is proportional to the average kinetic energy of the random microscopic motions of the constituent microscopic particles.

Temperature is important in all fields of natural science, including physics, chemistry, Earth science, medicine, and biology, as well as most aspects of daily life.

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter's particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a "degree of freedom". At equilibrium, each degree of freedom will have on average the same energy: where is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

Third law of thermodynamics

The third law of thermodynamics is sometimes stated as follows, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value as its temperature approaches absolute zero.

This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic field. At absolute zero (zero kelvin) the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, and there is typically one unique state (called the ground state) with minimum energy. In such a case, the entropy at absolute zero will be exactly zero. If the system does not have a well-defined order (if its order is glassy, for example), then there may remain some finite entropy as the system is brought to very low temperatures, either because the system becomes locked into a configuration with non-minimal energy or because the minimum energy state is non-unique. The constant value is called the residual entropy of the system. The entropy is essentially a state-function meaning the inherent value of different atoms, molecules, and other configurations of particles including subatomic or atomic material is defined by entropy, which can be discovered near 0 K.

The Nernst–Simon statement of the third law of thermodynamics concerns thermodynamic processes at a fixed, low temperature: The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K.

Here a condensed system refers to liquids and solids.

A classical formulation by Nernst (actually a consequence of the Third Law) is: It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.

There also exists a formulation of the Third Law which approaches the subject by postulating a specific energy behavior: If the composite of two thermodynamic systems constitutes an isolated system, then any energy exchange in any form between those two systems is bounded.

William Giauque

William Francis Giauque (; May 12, 1895 – March 28, 1982) was an American chemist and Nobel laureate recognized in 1949 for his studies in the properties of matter at temperatures close to absolute zero. He spent virtually all of his educational and professional career at the University of California, Berkeley.

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