Thermodynamic temperature, also known as absolute temperature, is a physical quantity that measures temperature starting from absolute zero, the point at which particles have minimal thermal motion.
Thermodynamic temperature is typically expressed using the Kelvin scale, on which the unit of measurement is the kelvin (unit symbol: K). This unit is the same interval as the degree Celsius, used on the Celsius scale but the scales are offset so that 0 K on the Kelvin scale corresponds to absolute zero. For comparison, a temperature of 295 K corresponds to 21.85 °C and 71.33 °F. Another absolute scale of temperature is the Rankine scale, which is based on the Fahrenheit degree interval.
Historically, thermodynamic temperature was defined by Lord Kelvin in terms of a relation between the macroscopic quantities thermodynamic work and heat transfer as defined in thermodynamics, but the kelvin was redefined by international agreement in 2019 in terms of phenomena that are now understood as manifestations of the kinetic energy of free motion of particles such as atoms, molecules, and electrons.
Overview Thermodynamic temperature can be defined in purely thermodynamic terms using the Carnot cycle. Thermodynamic temperature was rigorously defined historically long before particles such as atoms, molecules, and electrons were fully understood.
The International System of Units (SI) specifies the absolute scale for measuring temperature, and the unit of measure kelvin (symbol: K) for specific values along the scale. A temperature interval of one degree Celsius is the same as one kelvin. Since the 2019 revision of the SI, the kelvin has been defined in relation to the physical property underlying thermodynamic temperature: the kinetic energy of atomic free particle motion. The revision fixed the Boltzmann constant at exactly
The property that imbues material substances with a temperature can be readily understood by examining the ideal gas law, which relates, through the Boltzmann constant, how heat energy causes precisely defined changes in the pressure and temperature of certain gases. This is because monatomic gases like helium and argon behave kinetically like freely moving perfectly elastic and spherical billiard balls that move only in a specific subset of the possible motions that can occur in matter: that comprising the three translational degrees of freedom. The translational degrees of freedom are the familiar billiard ball-like movements along the -, -, and -axes of 3D space (see Fig. 1, below). This is why the noble gases all have the same heat capacity per atom and why that value is lowest of all the gases.
Molecules (two or more chemically bound atoms), however, have internal structure and therefore have additional internal degrees of freedom (see Fig. 3, below), which has the effect that molecules absorb more heat energy for any given rise in temperature than do the monatomic gases. Heat energy is born in all available degrees of freedom; this is in accordance with the equipartition theorem, so all available internal degrees of freedom have the same average energy as do their three external degrees of freedom. However, the property that gives all gases their pressure, which is the net force per unit area on a container arising from gas particles recoiling off it, is a function of the kinetic energy borne in the freely moving atoms' and molecules' three translational degrees of freedom.Georgia State University, HyperPhysics Project, "Equipartition of Energy"
Fixing the Boltzmann constant at a specific value had the effect of precisely establishing the magnitude of the kelvin in terms of the average kinetic behavior of the noble gases. Moreover, the starting point of the thermodynamic temperature scale, absolute zero, was reaffirmed as the point at which zero average kinetic energy remains in a sample; the only remaining particle motion being that comprising random vibrations due to zero-point energy.
Absolute zero of temperature
Temperature scales are numerical. The numerical zero of a temperature scale is not bound to the absolute zero of temperature. Nevertheless, some temperature scales have their numerical zero coincident with the absolute zero of temperature. Examples are the Kelvin temperature scale and the Rankine temperature scale. Other temperature scales have their numerical zero far from the absolute zero of temperature. Examples are the Celsius scale and the Fahrenheit scale.
At the zero point of thermodynamic temperature, absolute zero, the particle constituents of matter have minimal motion and can become no colder.Rankine, W. J. M., "A manual of the steam engine and other prime movers", Richard Griffin and Co., London (1859), p. 306–307.William Thomson, 1st Baron Kelvin, "Heat", Adam and Charles Black, Edinburgh (1880), p. 39. Absolute zero, which is a temperature of zero kelvins (0 K), precisely corresponds to −273.15 °C and −459.67 °F. Matter at absolute zero has no remaining transferable average kinetic energy and the only remaining particle motion is due to an ever-pervasive quantum mechanical phenomenon called ZPE (zero-point energy). While scientists are achieving temperatures ever closer to absolute zero, they can not fully achieve a state of zero temperature. However, even if scientists could remove all kinetic thermal energy from matter, quantum mechanical zero-point energy (ZPE) causes particle motion that can never be eliminated. Encyclopædia Britannica Online defines zero-point energy as the "vibrational energy that molecules retain even at the absolute zero of temperature". ZPE is the result of all-pervasive energy fields in the vacuum between the fundamental particles of nature; it is responsible for the Casimir effect and other phenomena. See Zero Point Energy and Zero Point Field. See also Solid Helium by the University of Alberta's Department of Physics to learn more about ZPE's effect on Bose–Einstein condensates of helium.
Although absolute zero () is not a state of zero molecular motion, it is the point of zero temperature and, in accordance with the Boltzmann constant, is also the point of zero particle kinetic energy and zero kinetic velocity. To understand how atoms can have zero kinetic velocity and simultaneously be vibrating due to ZPE, consider the following thought experiment: two helium atoms in zero gravity are carefully positioned and observed to have an average separation of between them (a gap of ten atomic diameters). It is an "average" separation because ZPE causes them to jostle about their fixed positions. Then one atom is given a kinetic kick of precisely 83 yoctokelvins (1 yK = ). This is done in a way that directs this atom's velocity vector at the other atom. With 83 yK of kinetic energy between them, the 620 pm gap through their common barycenter would close at a rate of 719 pm/s and they would collide after 0.862 second. This is the same speed as shown in the Fig. 1 animation above. Before being given the kinetic kick, both atoms had zero kinetic energy and zero kinetic velocity because they could persist indefinitely in that state and relative orientation even though both were being jostled by ZPE. At , no kinetic energy is available for transfer to other systems.
Note too that absolute zero serves as the baseline atop which thermodynamics and its equations are founded because they deal with the exchange of thermal energy between "systems" (a plurality of particles and fields modeled as an average). Accordingly, one may examine ZPE-induced particle motion within a system that is at absolute zero but there can never be a net outflow of thermal energy from such a system. Also, the peak emittance wavelength of black-body radiation shifts to infinity at absolute zero; indeed, a peak no longer exists and black-body photons can no longer escape. Because of ZPE, however, virtual photons are still emitted at . Such photons are called "virtual" because they can't be intercepted and observed. Furthermore, this zero-point radiation has a unique zero-point spectrum. However, even though a system emits zero-point radiation, no net heat flow Q out of such a system can occur because if the surrounding environment is at a temperature greater than , heat will flow inward, and if the surrounding environment is at ', there will be an equal flux of ZP radiation both inward and outward. A similar Q equilibrium exists at with the ZPE-induced spontaneous emission of photons (which is more properly called a stimulated emission in this context). The graph at upper right illustrates the relationship of absolute zero to zero-point energy. The graph also helps in the understanding of how zero-point energy got its name: it is the vibrational energy matter retains at the zero-kelvin point. Derivation of the classical electromagnetic zero-point radiation spectrum via a classical thermodynamic operation involving van der Waals forces, Daniel C. Cole, Physical Review A, 42 (1990) 1847. Though the atoms in, for instance, a container of liquid helium that was precisely at absolute zero would still jostle slightly due to zero-point energy, a theoretically perfect heat engine with such helium as one of its working fluids could never transfer any net kinetic energy (heat energy) to the other working fluid and no thermodynamic work could occur.
Temperature is generally expressed in absolute terms when scientifically examining temperature's interrelationships with certain other physical properties of matter such as its volume or pressure (see Gay-Lussac's law), or the wavelength of its emitted black-body radiation. Absolute temperature is also useful when calculating chemical reaction rates (see Arrhenius equation). Furthermore, absolute temperature is typically used in cryogenics and related phenomena like superconductivity, as per the following example usage: "Conveniently, tantalum's transition temperature (T) of 4.4924 kelvins is slightly above the 4.2221 K boiling point of helium."
Rankine scale
Though there have been many other temperature scales throughout history, there have been only two scales for measuring thermodynamic temperature which have absolute zero as their null point (0): The Kelvin scale and the Rankine scale.
Throughout the scientific world where modern measurements are nearly always made using the International System of Units, thermodynamic temperature is measured using the Kelvin scale. The Rankine scale is part of English engineering units and finds use in certain engineering fields, particularly in legacy reference works. The Rankine scale uses the degree Rankine (symbol: °R) as its unit, which is the same magnitude as the degree Fahrenheit (symbol: °F).
A unit increment of one kelvin is exactly 1.8 times one degree Rankine; thus, to convert a specific temperature on the Kelvin scale to the Rankine scale, , and to convert from a temperature on the Rankine scale to the Kelvin scale, . Consequently, absolute zero is "0" for both scales, but the melting point of water ice (0 °C and 273.15 K) is 491.67 °R.
To convert temperature intervals (a span or difference between two temperatures), the formulas from the preceding paragraph are applicable; for instance, an interval of 5 kelvins is precisely equal to an interval of 9 degrees Rankine.
Modern redefinition of the kelvin