Absolute zero

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Absolute zero

Absolute zero is a temperature marked by a 0 entropy

Entropy

In many branches of science, entropy is a measure of the disorder of a system. The concept of entropy is particularly notable as it is applied across physics, information theory and mathematics....
configuration. It is the coldest temperature theoretically possible, and cannot be reached, by artificial or natural means. Temperature is an entropically defined quantity that effectively determines the number of thermodynamically accessible states of a system within an energy range. Absolute zero physically possesses quantum mechanical

Quantum mechanics

Quantum mechanics is a set of principles underlying the most fundamental known description of all physical systems at the microscopic scale . Notable amongst these principles are both a dual wave-like and particle-like behavior of matter and radiation, and prediction of probabilities in situations where classical physics predicts certaintie...
zero-point energy

Zero-point energy

In physics, the zero-point energy is the lowest possible energy that a quantum mechanical physical system may have and is the energy of the ground state....
. Having a limited temperature has several thermodynamic consequences; for example, at absolute zero all molecular motion does not cease but does not have enough energy for transference to other systems, it is therefore correct to say that at 0 kelvin molecular energy is minimal.

By international agreement, absolute zero is defined as precisely 0 K on the Kelvin

Kelvin

The kelvin is a Units of measurement of temperature and is one of the seven SI base units. The Kelvin scale is a Thermodynamic temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero ....
scale, which is a thermodynamic (absolute) temperature

Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is an ?absolute? scale because it is the measure of the fundamental property underlying temperature: its null or zero point, absolute zero, is the temperature at which the particle constitue...
scale, and -273.15° on the Celsius

Celsius

Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death....
scale.

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History

One of the first to discuss the possibility of an "Absolute Cold" on such a scale was Robert Boyle

Robert Boyle

Robert Boyle was an Irish People theologian, natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry....
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

Niter

Niter or nitre is the mineral form of potassium nitrate, KNO3, also known as saltpeter or saltpetre . Historically, the term "nitre" ? cognate with "natrium", an old word for sodium ? has been very vaguely defined, and it has been applied to a variety of other minerals and chemical compounds, including sodium n...
, but all seeming to agree that:

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

Guillaume Amontons

Guillaume Amontons was a France scientific instrument inventor and physicist. He was one of the pioneers in tribology, apart from Leonardo da Vinci, John Theophilius Desanguliers, Leonard Euler and Charles-Augustin de Coulomb....
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.

This remarkably close approximation to the modern value of -273.16 °C for the zero of the air-thermometer was further improved on by Johann Heinrich Lambert

Johann Heinrich Lambert

Johann Heinrich Lambert , was a Switzerland mathematician, physicist and astronomer.He was born in M?lhausen . His father was a poor tailor, so Johann had to struggle to gain an education....
, who gave the value -270 °C and observed that this temperature might be regarded as absolute cold.

Values of this order for the absolute zero were not, however, universally accepted about this period. Pierre-Simon Laplace

Pierre-Simon Laplace

Pierre-Simon, marquis de Laplace was a France mathematician and astronomer whose work was pivotal to the development of astronomy and statistics....
and Antoine Lavoisier

Antoine Lavoisier

Antoine-Laurent de Lavoisier , the Fathers_of_scientific_fields#Chemistry, was a French people noble prominent in the histories of chemistry and biology....
, 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

John Dalton

John Dalton Fellow of the Royal Society was an England chemist, meteorologist and physicist. He is best known for his pioneering work in the development of modern atomic theory, and his research into Color blindness ....
in his Chemical Philosophy gave ten calculations of this value, and finally adopted -3,000 °C as the natural zero of temperature.

Lord Kelvin's work

After J.P. Joule

James Prescott Joule

James Prescott Joule Fellow of the Royal Society was an English physicist and brewing , born in Salford, Lancashire. Joule studied the nature of heat, and discovered its relationship to mechanical work ....
had determined the mechanical equivalent of heat, Lord Kelvin

William Thomson, 1st Baron Kelvin

William Thomson, 1st Baron Kelvin , Order of Merit , Royal Victorian Order, Privy Council of the United Kingdom, Presidents of the Royal Society, Royal Society of Edinburgh, was an Ireland-born United Kingdom of Great Britain and Ireland Mathematical physics and engineer....
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

Laws of thermodynamics

The laws of thermodynamics, in principle, describe the specifics for the transport of heat and Work in thermodynamic processes. Since their inception, however, these Physical laws have become some of the most important in all of physics and other branches of science connected to 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.

Additional Information

It can be shown from the laws of thermodynamics

Thermodynamics

In physics, thermodynamics is the study of the conversion of heat energy into different forms of energy ; different energy conversions into heat energy; and its relation to macroscopic variables such as temperature, pressure, and volume....
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

Machine

A machine is any device that uses energy to perform some activity. In common usage, the meaning is that of a device having parts that perform or assist in performing any type of work....
can be 100% efficient. Laser cooling

Laser cooling

Laser cooling is a technique that uses light to cool atoms to a very low temperature.It was simultaneously proposed by Wineland and Dehmelt and by Theodor W....
is another technique used to take temperatures to within a billionth of a degree of 0K.

At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties including superconductivity, superfluid

Superfluid

Phenomenon

A phenomenon is any observation occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In physics, a phenomenon may be a feature of matter, energy, or spacetime....
, scientists have worked to obtain ever lower temperatures.

In 1994, researchers at NIST
National Institute of Standards and Technology

The National Institute of Standards and Technology , known between 1901 and 1988 as the National Bureau of Standards , is a measurement standards laboratory which is a non-regulatory agency of the United States Department of Commerce....
achieved a then-record cold temperature of 700 nK
Kelvin

The kelvin is a Units of measurement of temperature and is one of the seven SI base units. The Kelvin scale is a Thermodynamic temperature scale where absolute zero, the theoretical absence of all thermal energy, is zero ....
(billionths of a Kelvin).

In November 2000, nuclear spin temperatures below 100 pK were reported for an experiment at the Helsinki University of Technology
Helsinki University of Technology

Helsinki University of Technology is the premier technical university in Finland. It is located in Otaniemi, Espoo in the area of Greater Helsinki....
'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 in freedom.

In February 2003, the Boomerang Nebula
Boomerang Nebula

The Boomerang Nebula is a protoplanetary nebula located 5,000 light-years away from Earth in the Centaurus. The nebula is measured at , the coldest place known in the universe....
was found to be -272.15 °C; 1 K, the coldest place known outside a laboratory. The nebula
Nebula

A nebula is an interstellar cloud of cosmic dust, hydrogen gas and Plasma . Originally nebula was a general name for any extended astronomy astronomical object, including galaxy beyond the Milky Way ....
is 5,000 light-years from Earth
Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
and is in the constellation Centaurus
Centaurus

Centaurus is a bright constellation in the celestial sphere. list of constellations by area constellations in the sky, Centaurus was included among the 48 constellations listed by of 1st century astronomer Ptolemy, and it remains one of the 88 modern constellations....
.

Thermodynamics near absolute zero

At temperatures near 0 K, nearly all molecular motion ceases and S = 0 for any adiabatic process

Adiabatic process

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....
. Pure substances can (ideally) form perfect crystal

Crystal

A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions....
s as T0. Max Planck

Max Planck

Karl Ernst Ludwig Marx Planck, better known as Max Planck was a Germany physicist. He is considered to be the founder of the Quantum mechanics, and one of the most important physicists of the twentieth century....
's strong form of the third law of thermodynamics

Third law of thermodynamics

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature....
states the entropy

Entropy

Walther Nernst

Walther Hermann Nernst was a Germany physical chemist 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....
heat theorem

Nernst heat theorem

The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics....
makes the weaker and less controversial claim that the entropy change for any isothermal process approaches zero as T0

The implication is that the entropy of a perfect crystal simply approaches a constant value.

The Nernst postulate
Third law of thermodynamics

The third law of thermodynamics is a statistical law of nature regarding entropy and the impossibility of reaching absolute zero of temperature....
identifies the isotherm
Isotherm

An isotherm may refer to:*A type of contour line or surface connecting points of equal temperature*An isothermal process in a thermodynamic cycle....
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
Line-line intersection

In Euclidean geometry, the intersection of a line and a line can be the empty set,a point , ora line. Distinguishing these cases, and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection....
the T = 0 isotherm. Consequently no adiabatic process initiated at nonzero temperature can lead to zero temperature. (˜ Callen, pp. 189-190)

An even stronger assertion is that It is impossible by any procedure to reduce the temperature of a system to zero in a finite number of operations. (˜ Guggenheim, p. 157)

A perfect crystal is one in which the internal lattice

Lattice (group)

In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which linear span the real number vector space Rn....
structure extends uninterrupted in all directions. The perfect order can be represented by translational symmetry

Symmetry

Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance; such that it reflects beauty or perfection....
along three (not usually orthogonal

Orthogonality

In mathematics, two vectors are orthogonal if they are perpendicular, i.e., they form a right angle. The word comes from the Greek language ' , meaning "straight", and ' , meaning "angle"....
) axes

Cartesian coordinate system

In mathematics, the Cartesian coordinate system is used to determine each Point uniquely in a Plane through two numbers, usually called the x-coordinate or abscissa and the y-coordinate or ordinate of the point....
. Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For substances

Chemical substance

A chemical substance is a material with a specific Empirical formula. It is a concept that became firmly established in the late eighteenth century after work by the chemist Joseph Proust on the composition of some pure chemical compounds such as basic copper carbonate....
which have two (or more) stable crystalline forms, such as diamond

Diamond

In mineralogy, diamond is the Allotropes of carbon where the carbon atoms are arranged in an isometric-hexoctahedral crystal lattice. After graphite, diamond is the second most stable form of carbon....
and graphite

Graphite

The mineral graphite is one of the allotropes of carbon. It was named by Abraham Gottlob Werner in 1789 from the Greek language ??afe?? : "to draw/write", for its use in pencils, where it is commonly called lead, as distinguished from the actual metallic element lead....
for carbon

Carbon

Carbon is a chemical element with chemical symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalence?making four electrons available to form covalent bond chemical bonds....
, there is a kind of "chemical degeneracy". The question remains whether both can have zero entropy at T = 0 even though each is perfectly ordered.

Perfect crystals never occur in practice; imperfections, and even entire amorphous materials, simply get "frozen in" at low temperatures, so transitions to more stable states do not occur.

Using the Debye

Peter Debye

Peter Joseph William Debye was a Netherlands physics and physical chemistry, and Nobel laureate....
model, the specific heat

Specific heat capacity

Specific heat capacity, also known simply as specific heat, is the measure of the energy required to increase the temperature of a of a substance by a certain Celsius#Temperatures_and_intervals....
and entropy of a pure crystal are proportional to T³, while the enthalpy

Enthalpy

In thermodynamics and chemistry, the enthalpy is a quotient or description of thermodynamic potential of a system, which can be used to calculate the heat transfer during a quasistatic process taking place in a closed system thermodynamic system under constant pressure....
and chemical potential

Chemical potential

In thermodynamics, physics and chemistry, chemical potential, symbolized by ?, is a term introduced by the American engineer, chemist and mathematical physicist Willard Gibbs, which he defined as follows:...
are proportional to T⁴. (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

Albert Einstein

Albert Einstein was a Germany-born theoretical physics. He is best known for his theory of relativity and specifically mass?energy equivalence, expressed by the equation E = mc2....
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

Thermal expansion

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature. When a substance is heated, its constituent particles move around more vigorously and by doing so generally maintain a greater average separation....
. Maxwell's relations

Maxwell relations

Maxwell's relations are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials. The Maxwell relations are statements of equality among the second derivatives of the thermodynamic potentials....
show that various other quantities also vanish. These phenomena

Phenomenon

A phenomenon is any observation occurrence. In popular usage, a phenomenon often refers to an extraordinary event. In physics, a phenomenon may be a feature of matter, energy, or spacetime....
were unanticipated.

Since the relation between changes in the Gibbs energy

Gibbs free energy

In thermodynamics, the Gibbs free energy is a thermodynamic potential that measures the "useful" or process-initiating Work obtainable from an isothermal, Isobaric process thermodynamic system....
, the enthalpy and the entropy is

thus, as T decreases, ?G and ?H approach each other (so long as ?S is bounded). Experiment

Experiment

In scientific inquiry, an experiment is a method of investigating causal relationships among variables. An experiment is a cornerstone of the empiricism approach to acquiring data about the world and is used in both natural sciences and social sciences....
ally, it is found that all spontaneous processes (including chemical reaction

Chemical reaction

A chemical reaction is a process that always results in the interconversion of chemical substances. The substance or substances initially involved in a chemical reaction are called reactants....
s) result in a decrease in G as they proceed toward equilbrium

Thermodynamic equilibrium

In thermodynamics, a thermodynamics#Thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium....
. If ?S and/or T are small, the condition ?G < 0 may imply that ?H < 0, which would indicate an exothermic

Exothermic

File:Explosion1.JPG In thermodynamics, the term exothermic describes a process or reaction that releases energy usually in the form of heat, but also in form of light , electricity , or sound....
reaction that releases heat. However, this is not required; endothermic

Endothermic

In thermodynamics, the word endothermic "within-heating" describes a process or reaction that absorbs energy in the form of heat. Its etymology stems from the Greek prefix endo-, meaning ?inside? and the Greek suffix ?thermic, meaning ?to heat?....
reactions can proceed spontaneously if the T?S term is large enough.

More than that, the slopes of the temperature derivatives of ?G and ?H converge and are equal to zero at T = 0, which ensures that ?G and ?H are nearly the same over a considerable range of temperatures, justifying the approximate empirical

Empiricism

In philosophy, empiricism is a theory of knowledge which asserts that knowledge arises from experience. Empiricism is one of several competing views about how we know "things," part of the branch of philosophy called epistemology, or "theory of knowledge"....
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)

Relation with Bose Einstein Condensates

A Bose-Einstein Condensate is a substance that behaves very unusually but only at extremely low temperatures, maybe a few billionths of a degree above absolute zero.

Absolute temperature scales

Absolute or thermodynamic temperature

Thermodynamic temperature

Kelvin

Celsius

Celsius is a temperature scale that is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death....
-scaled increments), and increasingly rarely in the Rankine scale (Fahrenheit

Fahrenheit

Fahrenheit is a temperature scale named after the physicist Daniel Gabriel Fahrenheit , who proposed it in 1724. Today, the scale has largely been replaced by the Celsius scale; it is still in use for non-scientific purposes in the United States and a few other countries such as Belize....
-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

Fermi-Dirac statistics

Fermi-Dirac statistics is a part of the science of physics, that applies to a system comprised of many particles that obey the Pauli Exclusion Principle....
(particles of half-integer spin

Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
) and Bose-Einstein statistics (particles of integer spin), all of which give the relative numbers of particles as (decreasing) exponential function

Exponential function

The exponential function is a function in mathematics. The application of this function to a value x is written as exp. Equivalently, this can be written in the form ex, where e is the mathematical constant that is the base of the natural logarithm and that is also known as Euler's number....
s of energy over kT. On a macroscopic

Macroscopic

Macroscopic is a word commonly used to describe physics objects that are measurement and observation by the naked eye. When applied to phenomena and abstract objects, it describes existence in the world as we perceive it....
level, a definition can be given in terms of the efficiencies of "reversible" heat engine

Heat engine

A heat engine is a physical or theoretical device that converts thermal energy to mechanical output. The mechanical output is called Mechanical work, and the thermal energy input is called heat....
s operating between hotter and colder thermal reservoirs.

Negative temperatures

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 = 8", as energy will flow from a negative temperature system to any other system with positive temperature upon contact.

The notion of a negative temperature is quite misleading. As mentioned previously, temperature is an entropically defined quantity. Temperature is effectively a measure of the number of thermally accessible states of a system at equilibrium. If the system is not in an equilibrium configuration, it will have a negative temperature.

Absolute zero

History

Limit to the 'degree of cold'

Lord Kelvin's work

Additional Information

Thermodynamics near absolute zero

Relation with Bose Einstein Condensates

Absolute temperature scales

Negative temperatures

See also

External links