Absolute zero

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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 zero kelvin. 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 degrees on the Celsius scale (International System of Units),^[1][2] which equals −459.67 degrees 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 at absolute zero is in its ground state, the point of lowest internal energy.

The

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

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 with no structural imperfections 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. 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:

${\displaystyle \lim _{T\to 0}\Delta S=0}$

The implication is that the entropy of a perfect crystal approaches a constant value. An adiabat is a state with constant entropy, typically represented on a graph as a curve in a manner similar to isotherms and isobars.

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 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

${\displaystyle \Delta G=\Delta H-T\Delta S\,}$

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

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

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

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,^{[citation needed]} 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 for the first time they had created a quantum gas made up of potassium atoms with a negative temperature in motional degrees of freedom.^[11]

History

One of the first to discuss the possibility of an absolute minimal temperature was

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 physicist Guillaume Amontons in 1703, 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 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.^[14] 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.^[15] Amontons held that the absolute zero cannot be reached, so never attempted to compute it explicitly.^[16] The value of −240 °C, or "431 divisions [in Fahrenheit's thermometer] below the cold of freezing water"^[17] 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.^[18]

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.

Charles's law

From 1787 to 1802, it was determined by Jacques Charles (unpublished), John Dalton,^[19] and Joseph Louis Gay-Lussac^[20] 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.

Lord Kelvin's work

After

With a better theoretical understanding of absolute zero, scientists were eager to reach this temperature in the lab.

The average temperature of the universe today is approximately 2.73 kelvins (−454.76 °F), or about −270.42 °C, based on measurements of

• 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.^[32][33]
• In February 2003, the Boomerang 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.^[34]
• 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 -400°F (-240°C),^[35] due to its extremely far orbit of 903 astronomical units.
• In May 2005, the
  femtokelvin temperatures.^[36]
• In May 2006, the Institute of Quantum Optics at the
  University of Hannover gave details of technologies and benefits of femtokelvin research in space.^[37]
• 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.^[38]
• 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.^[39]
• In June 2015, experimental physicists at
  MIT 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.^[40]
• In 2017,
  laws of physics.^[42][43]
• The current world record for effective temperatures was set in 2021 at 38 picokelvin (pK), or 0.000000000038 of a kelvin, through matter-wave lensing of rubidium Bose–Einstein condensates.^[44]

See also