Absolute zero is the lower limit of the thermodynamic
temperature scale, a state at which the enthalpy
and entropy of a cooled ideal gas reaches
its minimum value, taken as 0. 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, which equates to −459.67°
on the Fahrenheit scale. 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 and enthalpy of fusion 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 laws of thermodynamics dictate that absolute
zero cannot be reached using only thermodynamic
means, as the temperature of the substance
being cooled approaches the temperature of
the cooling agent asymptotically. A system
at absolute zero still possesses quantum mechanical
zero-point energy, the energy of its ground
state. The kinetic energy of the ground state
cannot be removed.
Scientists have achieved temperatures extremely
close to absolute zero, where matter exhibits
quantum effects such as superconductivity
and superfluidity.
Thermodynamics near absolute zero
At temperatures near 0 K, nearly all molecular
motion ceases and ΔS = 0 for any adiabatic
process, where S is the entropy. In such a
circumstance, pure substances can 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. 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.
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.
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 axes.
Every lattice element of the structure is
in its proper place, whether it is a single
atom or a molecular grouping. For substances
which have two 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 materials,
simply get "frozen in" at low temperatures,
so transitions to more stable states do not
occur.
Using the Debye model, the specific heat and
entropy of a pure crystal are proportional
to T 3, while the enthalpy and chemical potential
are proportional to T 4. 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, the enthalpy and the entropy
is
thus, as T decreases, ΔG and ΔH approach
each other. Experimentally, it is found that
all spontaneous processes 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 which evolves
the greatest amount of heat, i.e. an actual
process is the most exothermic one.
One model that estimates the properties of
an electron gas at absolute zero in metals
is the Fermi gas. The electrons, being Fermions,
have to 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 condensates
A Bose–Einstein condensate 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.
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.
Einstein was impressed, translated the paper
himself 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 in two
other papers.
Seventy years later, the first gaseous condensate
was produced by Eric Cornell and Carl Wieman
in 1995 at the University of Colorado at Boulder
NIST-JILA lab, using a gas of rubidium atoms
cooled to 170 nanokelvin.
A record cold temperature of 450 ±80 pK
in a Bose–Einstein condensate of sodium
atoms was achieved in 2003 by researchers
at MIT. The associated black-body wavelength
of 6,400 kilometers is roughly the radius
of Earth.
Absolute temperature scales
Absolute, or thermodynamic, temperature is
conventionally measured in kelvins and in
the Rankine scale 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 and Bose–Einstein
statistics. All of these define the relative
numbers of particles in a system as decreasing
exponential functions of energy over kT, with
k representing the Boltzmann constant and
T representing the temperature observed at
the macroscopic level.
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 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 will flow from the negative-
to the positive-temperature system.
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. 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 this argument does not apply, and
negative effective temperatures are attainable.
On January 3, 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.
History
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. The concept was well
known among naturalists of the time. Some
contended an absolute minimum temperature
occurred within earth, 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."
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 addressed
by the French physicist Guillaume Amontons
in 1702, in connection with his improvements
in the air-thermometer. 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",
of which 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 close approximation to the modern value
of −273.15 °C for the zero of the air-thermometer
was further improved upon in 1779 by Johann
Heinrich Lambert, who observed that −270 °C
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 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 which was independent
of the properties of any particular substance
and was based on Carnot's theory of the Motive
Power of Heat. 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.
Very low temperatures
The average temperature of the universe today
is approximately 2.73 kelvins, based on measurements
of cosmic microwave background radiation.
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. 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, or 0.000 000 000 1 of a kelvin,
by cooling the nuclear spins in a piece of
rhodium metal.
In November 2000, nuclear spin temperatures
below 100 pK were reported for an experiment
at the Helsinki University of Technology's
Low Temperature Lab. However, this was the
temperature of one particular degree of freedom –
a quantum property called nuclear spin –
not the overall average thermodynamic temperature
for all possible degrees in freedom.
In February 2003, the Boomerang Nebula was
observed to have been releasing gases at a
speed of 500,000 km/h 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.
In May 2005, the European Space Agency proposed
research in space to achieve femto-kelvin
temperatures.
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.
See also
References
Further reading
Herbert B. Callen. "Chapter 10". Thermodynamics.
New York: John Wiley & Sons. ISBN 0-471-13035-4.
OCLC 535083. 
Herbert B. Callen. Thermodynamics and an Introduction
to Thermostatistics. New York: John Wiley
& Sons. ISBN 0-471-86256-8. 
E.A. Guggenheim. Thermodynamics: An Advanced
Treatment for Chemists and Physicists. Amsterdam:
North Holland Publishing. ISBN 0-444-86951-4.
OCLC 324553. 
George Stanley Rushbrooke. Introduction to
Statistical Mechanics. Oxford: Clarendon Press.
OCLC 531928. 
External links
"Absolute zero": a two part NOVA episode originally
aired January 2008
"What is absolute zero?" Lansing state journal
