Absolute zero is the coldest temperature
theoretically possible. It cannot be reached by artificial or
natural means, because it is impossible to decouple a system fully
from the rest of the universe. Technically, it is a temperature
marked by a 0
entropy configuration. When
defined in terms of entropy,
Temperature
is a quantity that determines the number of thermodynamically
possible states of a system within an energy range. Thus, absolute
zero possesses
quantum mechanical
zero-point energy. 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 molecular energy is minimal at
absolute zero.
By international agreement, absolute zero is defined as precisely 0
K on the
Kelvin scale, which is a
thermodynamic temperature scale,
and −273.15° on the
Celsius scale. Absolute
zero is also precisely equivalent to 0 R on the
Rankine scale (same as Kelvin but measured in
Fahrenheit intervals), and −459.67° on the
Fahrenheit scale.Though it is not theoretically
possible to cool any substance to 0 K, scientists have made
great advancements in achieving temperatures close to absolute
zero, where matter exhibits
quantum effects such as
superconductivity and
superfluidity.For the
kinematics of the molecules, on a larger scale,
which is easier to understand see
kinetic
energy.
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 (as
one of the four so-called '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."
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 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 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
J.P. 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 solely on
the fundamental
laws of
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.
Very Low Temperatures
In the vicinity of absolute zero, it is convenient to indicate
temperature using appropriate SI prefixes: microkelvin, nanokelvin,
and so forth.
Absolute zero cannot be achieved artificially, though it is
possible to reach temperatures close to it through the use of
cryocoolers.
Laser cooling is a technique used to take
temperatures to within a billionth of a degree of 0 K.
At very low temperatures in the vicinity of absolute zero, matter
exhibits many unusual properties including
superconductivity,
superfluidity, and
Bose-Einstein condensation. In
order to study such
phenomena, scientists
have worked to obtain ever lower temperatures.
At a temperature of 1 femtokelvin (fK), an
electron will have a
De Broglie wavelength of approximately
3.4 meters.
- In 1994, researchers at NIST achieved
a then-record cold temperature of 700 nK.
- May
2006 - Institute of Quantum Optics at the University of
Hanover gives details of technologies and benefits of
femto-kelvin research in space.
Thermodynamics near absolute zero
At temperatures near 0 K, nearly all molecular motion ceases
and Δ
S = 0 for any
adiabatic process. 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. 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:
- \lim_{T \to 0} \Delta S = 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)
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 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 which have 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 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}. (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 the
Gibbs energy, the enthalpy and the entropy
is
- \Delta G = \Delta H - T \Delta S \,
thus, as
T decreases, Δ
G and Δ
H approach
each other (so long as Δ
S is bounded).
Experimentally, it is found that all spontaneous
processes (including
chemical
reactions) result in a decrease in
G as they proceed
toward
equilbrium. If
Δ
S and/or
T are small, the condition
Δ
G <&NBSP;0 may="" imply="" that=""
Δ
H <&NBSP;0, which="" would="" indicate=""
an=""
exothermic
reaction that releases heat. However, this is not required;
endothermic reactions can proceed
spontaneously if the
TΔ
S term is large
enough.
More than that, the
slopes of the temperature derivatives
of Δ
G and Δ
H converge and
are equal to
zero at
T = 0, which ensures that
Δ
G and Δ
H are nearly the same over a considerable
range of temperatures, justifying the approximate
empirical 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)
One model that estimates the properties of an electron gas at the
absolute zero of temperature is the
fermi
gas. What is interesting is that the
fermi temperature of electrons, where the
lattice temperature is zero, is non-zero. In fact, the electrons
have very high velocities. For an isolated system, this is probably
a violation of conservation of momentum, since - if the electrons
are interacting with the lattice, and the total momentum is zero,
then the lattice cannot be at zero velocity. Also, if the lattice
were precisely at zero temperature, its nuclei would have infinite
de Broglie wavelength. (If the momementum goes to zero, the
wavelength becomes infinite).
Relation with Bose–Einstein condensates
A Bose-Einstein Condensate is an unusual state of matter that only
exists at extremely low temperatures, maybe a few billionths of a
degree above absolute zero.
Absolute temperature scales
Absolute or
thermodynamic
temperature is conventionally measured in
kelvins (
Celsius-scaled
increments), and increasingly rarely in the
Rankine scale (
Fahrenheit-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,
T_{2}/
T_{1}, 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
(particles of half-integer
spin) and
Bose-Einstein statistics
(particles of integer spin), all of which give the relative numbers
of particles as (decreasing)
exponential functions of energy over
kT. On a
macroscopic level, a
definition can be given in terms of the efficiencies of
"reversible"
heat engines operating
between hotter and colder thermal reservoirs.
Lowest observed temperatures
The average background temperature of the Universe today is 2.73
Kelvin, but it has spatial fluctuations. For example, the
Boomerang Nebula has been spraying out gas
at a speed of 500,000 km/h (over 300,000 mph) for the
last 1,500 years. That has cooled it down to 1 K, as deduced by
astronomical observation. This might be the lowest natural
temperature recorded.
Much lower temperatures, however, can be achieved in the
laboratory. The current (May 2009) world record was set in 1999 at
100 picokelvin by cooling a piece of
rhodium
metal.
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 = ∞", as energy will flow
from a negative temperature system to any other system with
positive temperature upon contact.
See also
Notes
References
External links