Absolute zero is the theoretically coldest temperature, a state at which a system's internal energy, and in ideal cases entropy, reach their minimum values. The Kelvin scale is defined so that absolute zero is 0 K, equivalent to −273.15 °C on the Celsius scale, and −459.67 °F on the Fahrenheit scale. The Kelvin and Rankine temperature scales set their zero points at absolute zero by definition. This limit can be estimated by extrapolating the ideal gas law to the temperature at which the volume or pressure of a classical gas becomes zero.
Although absolute zero can be approached, it cannot be reached. Some isentropic processes, such as adiabatic expansion, can lower the system's temperature without relying on a colder medium. Nevertheless, the third law of thermodynamics implies that no physical process can reach absolute zero in a finite number of steps. As a system nears this limit, further reductions in temperature become increasingly difficult, regardless of the cooling method used. In 2018, scientists at the University of Bremen achieved temperatures as low as 38 picokelvin (pK), 38 trillionths of a degree above absolute zero. At these low temperatures, matter displays exotic quantum mechanical phenomena such as superconductivity, superfluidity, and Bose–Einstein condensation. The particles still exhibit zero-point energy motion, as mandated by the Heisenberg uncertainty principle and, for a system of fermions, the Pauli exclusion principle.
Ideal gas laws
For an ideal gas, the pressure at constant volume decreases linearly with temperature, and the volume at constant pressure also decreases linearly with temperature. When these relationships are expressed using the Celsius scale, both pressure and volume extrapolate to zero at approximately −273.15 °C. This implies the existence of a lower bound on temperature, beyond which the gas would have negative pressure or volume—an unphysical result.
To resolve this, the concept of absolute temperature is introduced, with 0 kelvins defined as the point at which pressure or volume would vanish in an ideal gas. This temperature corresponds to −273.15 °C, and is referred to as absolute zero. The ideal gas law is therefore formulated in terms of absolute temperature to remain consistent with observed gas behavior and physical limits.
Absolute temperature scales Absolute temperature is conventionally measured on the Kelvin scale (using Celsius-scaled increments) and, more rarely, on the Rankine scale (using Fahrenheit-scaled increments). 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.
Absolute temperature also emerges naturally in statistical mechanics. In the Maxwell–Boltzmann, Fermi–Dirac, and Bose–Einstein distributions, absolute temperature appears in the exponential factor that determines how particles populate energy states. Specifically, the relative number of particles at a given energy E depends exponentially on E/kT, where k is the Boltzmann constant and T is the absolute temperature.
Unattainability of absolute zero
The third law of thermodynamics concerns the behavior of entropy as temperature approaches absolute zero. It states that the entropy of a system approaches a constant minimum at 0 K. For a perfect crystal, this minimum is taken to be zero, since the system would be in a state of perfect order with only one microstate available. In some systems, there may be more than one microstate at minimum energy and there is some residual entropy at 0 K.
Several other formulations of the third law exist. Nernst heat theorem holds that the change in entropy for any constant-temperature process tends to zero as the temperature approaches zero. A key consequence is that absolute zero cannot be reached, since removing heat becomes increasingly inefficient and entropy changes vanish. This unattainability principle means no physical process can cool a system to absolute zero in a finite number of steps or finite time.
Thermal properties at low temperatures 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.
One model that estimates the properties of an electron gas at absolute zero in metals is the Fermi gas. The electrons, being fermions, must 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 the Boltzmann constant, and is on 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.
Gibbs free energy Since the relation between changes in Gibbs free energy (G), the enthalpy (H) and the entropy is
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 chemical reactions) 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 that evolves the greatest amount of heat, i.e., an actual process is the most exothermic one (Callen, pp. 186–187).
Zero-point energy
Even at absolute zero, a quantum system retains a minimum amount of energy due to the Heisenberg uncertainty principle, which prevents particles from having both perfectly defined position and momentum. This residual energy is known as zero-point energy. In the case of the quantum harmonic oscillator, a standard model for vibrations in atoms and molecules, the uncertainty in a particle's momentum implies it must retain some kinetic energy, while the uncertainty in its position contributes to potential energy. As a result, such a system has a nonzero energy at absolute zero.
Zero-point energy helps explain certain physical phenomena. For example, liquid helium does not solidify at normal pressure, even at temperatures near absolute zero. The large zero-point motion of helium atoms, caused by their low mass and weak interatomic forces, prevents them from settling into a solid structure. Only under high pressure does helium solidify, as the atoms are forced closer together and the interatomic forces grow stronger.
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 classical 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 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. Amontons described the relation between his new thermometer (which was based on the expansion and contraction of alcohol (esprit de vin)) and the old thermometer (which was based on air). From p. 52: " […] d'où il paroît que l'extrême froid de ce Thermométre seroit celui qui réduiroit l'air à ne soutenir aucune charge par son ressort, […] " ([…] whence it appears that the extreme cold of this [air] thermometer would be that which would reduce the air to supporting no load by its spring, […]) In other words, the lowest temperature which can be measured by a thermometer which is based on the expansion and contraction of air is that temperature at which the air's pressure ("spring") has decreased to zero. He used a scale that marked the boiling point of water at +73 and the melting point of ice at +, so that the zero was equivalent to about −240 on the Celsius scale. Amontons held that the absolute zero cannot be reached, so never attempted to compute it explicitly. The value of −240 °C, or "431 divisions [in Fahrenheit's thermometer] below the cold of freezing water" was published by George Martine in 1740.
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 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 −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,J. Dalton (1802), "Essay II. On the force of steam or vapour from water and various other liquids, both in vacuum and in air" and Essay IV. "On the expansion of elastic fluids by heat" , Memoirs of the Literary and Philosophical Society of Manchester, vol. 8, pt. 2, pp. 550–574, 595–602. and Joseph Louis Gay-Lussac. English translation (extract). 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