Zerokelvin (−273.15 °C) is defined as absolute zero.
Absolute zero is the lowest theoretically possibletemperature, a state at which a system'sinternal energy, and in ideal casesentropy, reach their minimum values. TheKelvin scale is defined so that absolute zero is 0 K, equivalent to −273.15 °C on theCelsius scale,[1][2] and −459.67 °F on theFahrenheit scale.[3] The Kelvin andRankine temperature scales set their zero points at absolute zero by definition. This limit can be estimated by extrapolating theideal gas law to the temperature at which the volume or pressure of a classical gas becomes zero.
Pressure–temperature plots for three different gas samples, measured at constant volume, all extrapolate to zero at the same point, the absolute zero.
For anideal gas, the pressure at constant volume decreases linearly with temperature, and the volume at constant pressure also decreases linearly with temperature. When these relationships are expressed using the Celsius scale, both pressure and volume extrapolate to zero at approximately −273.15 °C. This implies the existence of a lower bound on temperature, beyond which the gas would have negative pressure or volume—an unphysical result.[6][7]
To resolve this, the concept of absolute temperature is introduced, with 0 kelvins defined as the point at which pressure or volume would vanish in an ideal gas. This temperature corresponds to −273.15 °C, and is referred to as absolute zero. The ideal gas law is therefore formulated in terms of absolute temperature to remain consistent with observed gas behavior and physical limits.[8]
Absolute temperature is conventionally measured inKelvin scale (usingCelsius-scaled increments)[1] and, more rarely, inRankine scale (usingFahrenheit-scaled increments). Absolute temperature measurement is uniquely determined by a multiplicative constant which specifies the size of thedegree, so theratios of two absolute temperatures,T2/T1, are the same in all scales.
Absolute temperature also emerges naturally instatistical mechanics. In theMaxwell–Boltzmann,Fermi–Dirac, andBose–Einstein distributions, absolute temperature appears in the exponential factor that determines how particles populate energy states. Specifically, the relative number of particles at a given energyE depends exponentially onE/kT, wherek is theBoltzmann constant andT is the absolute temperature.[citation needed]
Left side: Absolute zero could be reached in a finite number of steps ifS(0,X1) ≠S(0,X2). Right: An infinite number of steps is needed sinceS(0,X1) =S(0,X2). Here,X is some controllable parameter of the system, such as its volume or pressure.
Thethird law of thermodynamics concerns the behavior ofentropy as temperature approaches absolute zero. It states that the entropy of a system approaches a constant minimum at 0 K. For a perfect crystal, this minimum is taken to be zero, since the system would be in a state of perfect order with only onemicrostate available. In some systems, there may be more than one microstate at minimum energy and there is some residual entropy at 0 K.[9]
Several other formulations of the third law exist.Nernst heat theorem holds that the change in entropy for any constant-temperature process tends to zero as the temperature approaches zero.[10] A key consequence is that absolute zero cannot be reached, since removing heat becomes increasingly inefficient and entropy changes vanish. This unattainability principle means no physical process can cool a system to absolute zero in a finite number of steps or finite time.[11]
Using theDebye model, thespecific heat and entropy of a pure crystal are proportional toT 3, while theenthalpy andchemical potential are proportional toT 4 (Guggenheim, p. 111). These quantities drop toward theirT = 0 limiting values and approach withzero 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 detailedEinstein 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 ofthermal expansion.Maxwell's relations show that various other quantities also vanish. These phenomena were unanticipated.
One model that estimates the properties of anelectron gas at absolute zero in metals is theFermi gas. The electrons, beingfermions, must be in different quantum states, which leads the electrons to get very high typicalvelocities, even at absolute zero. The maximum energy that electrons can have at absolute zero is called theFermi energy. The Fermi temperature is defined as this maximum energy divided by the Boltzmann constant, and is on 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 classicalequipartition theorem for metals that eluded classical physicists in the late 19th century.
Since the relation between changes inGibbs free energy (G), the enthalpy (H) and the entropy is
thus, asT decreases, ΔG and ΔH approach each other (so long as ΔS is bounded). Experimentally, it is found that all spontaneous processes (includingchemical reactions) result in a decrease inG as they proceed towardequilibrium. If ΔS and/orT are small, the condition ΔG < 0 may imply that ΔH < 0, which would indicate anexothermic reaction. However, this is not required;endothermic reactions can proceed spontaneously if theTΔS term is large enough.
Moreover, the slopes of thederivatives of ΔG and ΔH converge and are equal to zero atT = 0. This ensures that ΔG and ΔH are nearly the same over a considerable range of temperatures and justifies the approximateempirical Principle of Thomsen and Berthelot, which states thatthe equilibrium state to which a system proceeds is the one that evolves the greatest amount of heat, i.e., an actual process is themost exothermic one (Callen, pp. 186–187).
Probability densities and energies (indicated by an offset) of the four lowest energy eigenstates of aquantum harmonic oscillator. ZPE denotes the zero-point energy.
Even at absolute zero, a quantum system retains a minimum amount of energy due to theHeisenberg uncertainty principle, which prevents particles from having both perfectly defined position and momentum. This residual energy is known aszero-point energy. In the case of thequantum harmonic oscillator, a standard model for vibrations in atoms and molecules, the uncertainty in a particle's momentum implies it must retain somekinetic energy, while the uncertainty in its position contributes topotential energy. As a result, such a system has a nonzero energy at absolute zero.[12]
Zero-point energy helps explain certain physical phenomena. For example,liquid helium does not solidify at normal pressure, even at temperatures near absolute zero. The large zero-point motion of helium atoms, caused by their low mass and weak interatomic forces, prevents them from settling into a solid structure. Only under high pressure does helium solidify, as the atoms are forced closer together and the interatomic forces grow stronger.[12]
Robert Boyle, who pioneered the idea of an absolute zero.
One of the first to discuss the possibility of an absolute minimal temperature wasRobert Boyle. His 1665New Experiments and Observations touching Cold, articulated the dispute known as theprimum frigidum.[13] The concept was well known among naturalists of the time. Some contended an absolute minimum temperature occurred within earth (as one of the fourclassical elements), others within water, others air, and some more recently withinnitre. 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."[14]
The question of 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 physicistGuillaume Amontons in 1703, in connection with his improvements in theair thermometer. His instrument indicated temperatures by the height at which a certain mass of air sustained a column of mercury—the pressure, 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.[15] He used a scale that marked the boiling point of water at +73 and the melting point of ice at +51+1⁄2, so that the zero was equivalent to about −240 on the Celsius scale.[16] Amontons held that the absolute zero cannot be reached, so never attempted to compute it explicitly.[17] The value of −240 °C, or "431 divisions [in Fahrenheit's thermometer] below the cold of freezing water"[18] was published byGeorge 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 byJohann Heinrich Lambert, who observed that −270 °C (−454.00 °F; 3.15 K) might be regarded as absolute cold.[19]
Values of this order for the absolute zero were not, however, universally accepted about this period.Pierre-Simon Laplace andAntoine 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 hisChemical Philosophy gave ten calculations of this value, and finally adopted −3,000 °C as the natural zero of temperature.
From 1787 to 1802, it was determined byJacques Charles (unpublished),John Dalton,[20] andJoseph Louis Gay-Lussac[21] that, at constant pressure, ideal gases expanded or contracted their volume linearly (Charles's law) by about 1/273 parts per degree Celsius of temperature's change up or down, between 0° and 100° C. This suggested that the volume of a gas cooled at about −273 °C would reach zero.
AfterJames 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 onCarnot's theory of the Motive Power of Heat and data published byHenri Victor Regnault.[22] 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,[16] where the air volume would reach "nothing". 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 ofastronomical refraction, remained in use in the early 20th century.[23]
With a better theoretical understanding of absolute zero, scientists were eager to reach this temperature in the lab.[24] 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, andhydrogen, were permanent gases and could not be liquefied.[25] Decades later, in 1873 Dutch theoretical scientistJohannes 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 andRaoul Pictet in Switzerland succeeded in producing the first droplets ofliquid air at −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 professorsZygmunt Wróblewski andKarol Olszewski.
Scottish chemist and physicistJames Dewar and Dutch physicistHeike Kamerlingh Onnes took on the challenge to liquefy the remaining gases, hydrogen andhelium. In 1898, after 20 years of effort, Dewar was the first to liquefy hydrogen, reaching a new low-temperature record of −252 °C (−421.6 °F; 21.1 K). However, Kamerlingh Onnes, his rival, was the first to liquefy helium, in 1908, using several precooling stages and theHampson–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 thecoldest temperatures achieved on Earth at the time and his achievement earned him theNobel Prize in 1913.[26] Kamerlingh Onnes would continue to study the properties of materials at temperatures near absolute zero, describingsuperconductivity andsuperfluids for the first time.
Temperatures below zero on the Celsius or Fahrenheit scales are simply colder than the zero points of those scales. In contrast, certain isolated systems can achievenegative thermodynamic temperatures (in kelvins), which are not colder than absolute zero, but paradoxically hotter than any positive temperature. If a negative-temperature system and a positive-temperature system come in contact, heat flows from the negative to the positive-temperature system.[27][28]
Negative temperatures can only occur in systems that have an upper limit to the energy they can contain. In these cases, adding energy can decreaseentropy, reversing the usual relationship between energy and temperature. This leads to a negative thermodynamic temperature. However, such conditions only arise in specialized, quasi-equilibrium systems such as collections ofspins in a magnetic field. In contrast, ordinary systems with translational or vibrational motion have no upper energy limit, so their temperatures are always positive.[27][28]
The rapid expansion of gases leaving theBoomerang Nebula, a bi-polar, filamentary, likely proto-planetary nebula in Centaurus, has a temperature of 1 K, the lowest observed outside of a laboratory.Velocity-distribution data of a gas ofrubidium 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.
The average temperature of the universe today is approximately 2.73 K (−270.42 °C; −454.76 °F), based on measurements ofcosmic microwave background radiation.[29][30] Standard models of thefuture expansion of the universe predict that the average temperature of the universe is decreasing over time.[31] This temperature is calculated as the mean density of energy in space; it should not be confused with the meanelectron temperature (total energy divided by particle count) which has increased over time.[32]
In February 2003, theBoomerang Nebula was observed to have been releasing gases at a speed of 500,000 km/h (310,000 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.[37]
In November 2003,90377 Sedna was discovered and is one of the coldest known objects in the Solar System, with an average surface temperature of −240 °C (33 K; −400 °F),[38] due to its extremely far orbit of 903astronomical units.
In May 2006, the Institute of Quantum Optics at theUniversity of Hannover gave details of technologies and benefits of femtokelvin research in space.[40]
In January 2013, physicist Ulrich Schneider ofLMU 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.[41]
In September 2014, scientists in theCUORE collaboration at theLaboratori Nazionali del Gran Sasso in Italy cooled a copper vessel with a volume of one cubic meter to 0.006 K (−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.[42]
In June 2015, experimental physicists atMIT cooled molecules in a gas of sodium potassium to a temperature of 500 nanokelvin, and it is expected to exhibit an exotic state of matter by cooling these molecules somewhat further.[43]
In 2017,Cold Atom Laboratory (CAL), an experimental instrument was developed for launch to theInternational Space Station (ISS) in 2018.[44] The instrument has created extremely cold conditions in themicrogravity environment of the ISS leading to the formation ofBose–Einstein condensates. In this space-based laboratory, temperatures as low as1 picokelvin are projected to be achievable, and it could further the exploration of unknownquantum mechanical phenomena and test some of the most fundamentallaws of physics.[45][46]
The current world record for effective temperatures was set in 2021 at38 picokelvin through matter-wave lensing of rubidiumBose–Einstein condensates.[47]
^abc"SI Brochure: The International System of Units (SI) – 9th edition (updated in 2022in". BIPM. p. 133. Retrieved7 September 2022.[...], it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K, close to the ice point. This difference is called the Celsius temperature.
^Blundell, Stephen J.; Blundell, Katherine M. (2010).Concepts in Thermal Physics. Oxford: Oxford university press. pp. 193–198.ISBN978-0-19-956209-1.
^Atkins, Peter William; Paula, Julio De; Keeler, James (2018).Atkins' Physical Chemistry (11th ed.). Oxford, United Kingdom ; New York, NY: Oxford University Press. pp. 93–96.ISBN978-0-19-876986-6.
^Shell, M. Scott (16 April 2015).Thermodynamics and Statistical Mechanics. Cambridge: Cambridge University Press. pp. 312–315.ISBN978-1-107-01453-4.
^abTownsend, John (19 July 2012).A Modern Approach to Quantum Mechanics. Mill Valley, Calif: University Science Books. pp. 257–259.ISBN978-1-891389-78-8.
^Boyle, Robert (1665).New Experiments and Observations touching Cold.
^Amontons (18 April 1703)."Le thermomètre rèduit à une mesure fixe & certaine, & le moyen d'y rapporter les observations faites avec les anciens Thermométres" [The thermometer reduced to a fixed & certain measurement, & the means of relating to it observations made with old thermometers].Histoire de l'Académie Royale des Sciences, avec les Mémoires de Mathématique et de Physique pour la même Année (in French):50–56. Amontons described the relation between his new thermometer (which was based on the expansion and contraction of alcohol (esprit de vin)) and the old thermometer (which was based on air). From p. 52:" […] d'où il paroît que l'extrême froid de ce Thermométre seroit celui qui réduiroit l'air à ne soutenir aucune charge par son ressort, […] " ([…] whence it appears that the extreme cold of this [air] thermometer would be that which would reduce the air to supporting no load by its spring, […]) In other words, the lowest temperature which can be measured by a thermometer which is based on the expansion and contraction of air is that temperature at which the air's pressure ("spring") has decreased to zero.
^"Low Temperature World Record" (Press release). Low Temperature Laboratory, Teknillinen Korkeakoulu. 8 December 2000.Archived from the original on 18 February 2008. Retrieved11 February 2008.
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E.A. Guggenheim (1967).Thermodynamics: An Advanced Treatment for Chemists and Physicists (Fifth ed.). Amsterdam: North Holland Publishing.ISBN978-0-444-86951-7.OCLC324553.
