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Absolute zero is the temperature at which nothing could be colder as no heat energy remains in a substance. Absolute zero is the point at which the fundamental particles of nature have minimal vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. By international agreement, absolute zero is defined as precisely… While scientists can not fully achieve a state of “zero” heat energy in a substance, they have made great advancements in achieving temperatures ever closer to absolute zero (where matter exhibits odd quantum effects). In 1994, the NIST achieved a record cold temperature of 700 nK (billionths of a kelvin). In 2003, researchers at MIT eclipsed this with a new record of 450 pK (0.45 nK). History of absolute zero Kinetic theory and motion According to kinetic theory, there should be no movement of individual molecules at absolute zero, so any material at this temperature would be solid. In a monatomic gas, most of the energy is in the form of translational motion, and the temperature can be measured in terms of the distribution of this motion, with slower speeds corresponding to lower temperatures, perhaps even down to absolute zero. But this is contrary to experimental evidence, as helium will never solidify at normal pressures, regardless of temperature... Because of quantum-mechanical effects, the speed at absolute zero is larger than zero and depends, along with the energy, on the volume within which a particle is confined. At absolute zero, the molecules and atoms in a system are all in their ground state, the state of lowest possible energy, and a system has the least amount of kinetic energy allowed by the laws of physics. But the lowest possible zero-point energy for a confined particle in a box is not zero. Rather than being fixed and non-moving, the equation for the energy levels shows that no matter how low the temperature gets, even when the quantum number takes its minimum value of one, a particle still has some translational kinetic energy and motion. This is a reflection of Heisenberg's uncertainty principle, which states that the position and the momentum of a particle cannot both be known precisely at any given time. Similarly, using the harmonic approximation for the vibrations of a diatomic molecule, the quantum harmonic oscillator yields a positive zero-point energy even when the vibrational quantum number takes its minimum value of zero. For polyatomic molecules, and for bodies such as crystals, whose normal mode motions can not be assigned to individual atoms or chemical bonds, the lowest-energy state is that of the system as a whole. Classically, the absolute temperature T of a system of molecules at thermodynamic equilibrium assigns an average of ½ kT to each quadratic kinetic and/or potential energy term in each mechanical degree of freedom, where k is Boltzmann's constant. (See equipartition of energy and the role of the Boltzmann distribution in relating temperature to energy.) But quantum mechanics shows that this is obeyed only for temperatures such that kT > hν, where h is Planck's constant and ν is a characteristic frequency. As T decreases, the assumption that energy is continuously variable fails whenever hν exceeds kT. For vibrational modes in crystals, this happens at room temperature, which explains the deviation of the calculated specific heats of atomic crystals from the experimental Dulong-Petit law value of 3R /mole, a fact which puzzled late 19th century physicists and physical chemists. (Rushbrooke, p. 33) Record cold temperatures approaching absolute zero It can be shown from the laws of thermodynamics that absolute zero can never be achieved, though it is possible to reach temperatures arbitrarily close to it through the use of cryocoolers. This is the same principle that ensures no machine can be 100% efficient. 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. Thermodynamics near absolute zero At 0 K, (nearly) all molecular motion ceases and S = 0 for any adiabatic process. Pure substances can (ideally) form perfect crystals as T 0. Planck's strong form of the third law of thermodynamics states that the entropy of a perfect crystal vanishes at absolute zero. However, if the lowest energy state is degenerate (more than one microstate), this cannot be true. 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 which implies 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 as 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 free energy, the enthalpy and the entropy is it follows that as T decreases, ΔG and ΔH approach each other (so long as ΔS is bounded). Experimentally, it is found that most chemical reactions are exothermic and release heat in the direction they are found to be going, toward equilbrium. That is, even at room temperature T is low enough so that the fact that (ΔG)T,P < 0 (usually) implies that ΔH < 0. (In the opposite direction, each such reaction would of course absorb heat.) More than that, the slopes of the temperature derivatives of ΔG and ΔH converge and are equal to zero at T = 0, which ensures that ΔG and ΔH 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) Absolute temperature scales As mentioned, absolute or thermodynamic temperature is conventionally measured in kelvins (Celsius-size degrees), and increasingly rarely in the Rankine scale (Fahrenheit-size degrees). 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 (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. Negative temperatures Certain semi-isolated systems (for example 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 | |||||||
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