Thermodynamic temperature
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. 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 specifies the absolute scale for measuring temperature, and the unit of measure kelvin 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. 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, however, have internal structure and therefore have additional internal degrees of freedom, 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.
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. Absolute zero, which is a temperature of zero kelvins, 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. 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 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, or the wavelength of its emitted black-body radiation. Absolute temperature is also useful when calculating chemical reaction rates. Furthermore, absolute temperature is typically used in cryogenics and related phenomena like superconductivity, as per the following example usage:
"Conveniently, tantalum's transition temperature 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 : 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 as its unit, which is the same magnitude as the degree Fahrenheit.
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 is 491.67 °R.
To convert temperature intervals, 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
For 65 years, between 1954 and the 2019 revision of the SI, a temperature interval of one kelvin was defined as of the temperature difference between the triple point of water and absolute zero. The 1954 resolution by the International Bureau of Weights and Measures, plus later resolutions and publications, defined the triple point of water as precisely 273.16 K and acknowledged that it was "common practice" to accept that due to previous conventions they defined absolute zero as precisely 0 K, and 2) they defined that the triple point of special isotopically controlled water called Vienna Standard Mean Ocean Water occurred at precisely 273.16 K and 0.01 °C. One effect of the aforementioned resolutions was that the melting point of water, while very close to 273.15 K and 0 °C, was not a defining value and was subject to refinement with more precise measurements.The 1954 BIPM standard did a good job of establishing—within the uncertainties due to isotopic variations between water samples—temperatures around the freezing and triple points of water, but required that intermediate values between the triple point and absolute zero, as well as extrapolated values from room temperature and beyond, to be experimentally determined via apparatus and procedures in individual labs. This shortcoming was addressed by the International Temperature Scale of 1990, or ITS90, which defined 13 additional points, from 13.8033 K, to 1,357.77 K. While definitional, ITS90 had—and still has—some challenges, partly because eight of its extrapolated values depend upon the melting or freezing points of metal samples, which must remain exceedingly pure lest their melting or freezing points be affected—usually depressed.
The 2019 revision of the SI was primarily for the purpose of decoupling much of the SI system's definitional underpinnings from the kilogram, which was the last physical artifact defining an SI base unit and which had highly questionable stability. The solution required that four physical constants, including the Boltzmann constant, be definitionally fixed.
Assigning the Boltzmann constant a precisely defined value had no practical effect on modern thermometry except for the most exquisitely precise measurements. Before the revision, the triple point of water was exactly 273.16 K and 0.01 °C and the Boltzmann constant was experimentally determined to be, where the "" denotes the uncertainty in the two least significant digits and equals a relative standard uncertainty of 0.37 ppm. Afterwards, by defining the Boltzmann constant as exactly, the 0.37 ppm uncertainty was transferred to the triple point of water, which became an experimentally determined value of . That the triple point of water ended up being exceedingly close to 273.16 K after the SI revision was no accident; the final value of the Boltzmann constant was determined, in part, through clever experiments with argon and helium that used the triple point of water for their key reference temperature.
Notwithstanding the 2019 revision, water triple-point cells continue to serve in modern thermometry as exceedingly precise calibration references at 273.16 K and 0.01 °C. Moreover, the triple point of water remains one of the 14 calibration points comprising ITS90, which spans from the triple point of hydrogen to the freezing point of copper, which is a nearly hundredfold range of thermodynamic temperature.