## Abstract

In 2018, it is expected that there will be a major revision of the International System of Units (SI) which will result in all of the seven base units being defined by fixing the values of certain atomic or fundamental constants. As part of this revision, the kelvin, unit of thermodynamic temperature, will be redefined by assigning a value to the Boltzmann constant *k*. This explicit-constant definition will define the kelvin in terms of the SI derived unit of energy, the joule. It is sufficiently wide to encompass any form of thermometry. The planned redefinition has motivated the creation of an extended *mise en pratique* (‘practical realization’) of the definition of the kelvin (*MeP*-K), which describes how the new definition can be put into practice. The *MeP*-K incorporates both of the defined International Temperature Scales (ITS-90 and PLTS-2000) in current use and approved primary-thermometry methods for determining thermodynamic temperature values. The *MeP*-K is a guide that provides or makes reference to the information needed to perform measurements of temperature in accord with the SI at the highest level. In this article, the background and the content of the extended second version of the *MeP*-K are presented.

## 1. Introduction

In 2005, motivated by the need for a formal document to give definitive guidance for the practical realization of the kelvin, i.e. the measurement of temperature in kelvins in accordance with the International System of Units (SI), the Consultative Committee for Thermometry (CCT) recommended the creation of a *mise en pratique* for the definition of the kelvin (*MeP*-K) [1] (see also [2]). First of all it was needed to specify the isotopic composition for the triple points of water and hydrogen in such a document. In parallel, the International Committee for Weights and Measures (Comité International des Poids et Mesures, CIPM) foresaw that the adoption of the proposed redefinition of the kelvin, based on a fixed value for the Boltzmann constant, will require a *MeP*-K [3]. In accordance with the report of the 97th meeting of the CIPM in 2008, a *MeP* should include only top-level realization methods. To that end, the *MeP*-K provides the CCT with a flexible path for updating and expanding the range of recognized thermometric methods without changing the status or the text of the defined International Temperature Scales.

The *MeP*-K describes the connection of various documents to the SI definition of the kelvin and recommends briefly particular methods. The methods themselves are described in detail in separate documents or by citations to literature. Figure 1 shows the relationship between the *MeP*-K and other documents important for the realization of the kelvin. The International Bureau of Weights and Measures (Bureau International des Poids et Mesures, BIPM) issues ‘The International System of Units (SI)’ (commonly termed the SI brochure; http://www.bipm.org/en/publications/si-brochure/) to explain and disseminate the most recent version of the SI. The SI brochure discusses the definition of the kelvin and subsequent clarifications, briefly describes appropriate nomenclature for expressing temperature in the SI, and references the *MeP*-K and documents related to the International Temperature Scales. Although the main text of the SI brochure is only rarely updated, its Appendix 2, available on the Internet only, is updated regularly and contains the most recent version of the *MeP*-K, along with similar documents for other SI units. Figure 1 shows the general structure of the *MeP*-K as explained in §3. Section 4 presents the criteria for the approval of realization methods. Primary thermometry is discussed in §5, and the two defined International Temperature Scales ITS-90 [4] and PLTS-2000 [5,6] are described in §6.

The first version of the *MeP*-K was adopted by the CCT in April 2006. This version was an overall guideline for the two International Temperature Scales PLTS-2000 and ITS-90. Included were the brief text of the *MeP*-K itself, links to the official texts of the two scales, links to the Technical Annex for the ITS-90 and the supplementary information for the ITS-90, and links to guidelines on approximations to the ITS-90. The Technical Annex gives clear prescription on the isotopic abundances and correction methods specified for both hydrogen and water fixed points on the ITS-90. This was the main scientific progress connected with the first version of the *MeP*-K. An amendment of the *MeP*-K, called *MeP*-K-11 (http://www.bipm.org/utils/en/pdf/MeP.K.pdf), was prepared in 2011. This provides links to recommended differences between thermodynamic temperature *T* and temperature *T*_{90} on the ITS-90, *T*−*T*_{90}, together with their uncertainties, as published in [7], and to supplementary information for the PLTS-2000 [5,8]. Furthermore, the amended Technical Appendix contains an additional section on isotopic abundances and corrections for the triple point of neon. The content of the second version of the *MeP*-K, approved by the CCT in 2013, is described below. This version will come into force after the redefinition of the kelvin, which is planned for 2018 [9], and will be designated *MeP*-K-18.

## 2. Redefinition of the SI base unit kelvin

In 1954, the 10th General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, CGPM) defined the thermodynamic temperature scale by choosing the triple point of water (TPW) as the fundamental fixed point, and assigning to it the temperature 273.16 degrees kelvin, exactly [10]. The 13th CGPM in 1967 explicitly defined the kelvin as an SI unit: ‘The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the TPW’ [11]. At its 2005 meeting, the CIPM affirmed that ‘This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios that is called Vienna Standard Mean Ocean Water: 0.00015576 mole of ^{2}H per mole of ^{1}H, 0.0003799 mole of ^{17}O per mole of ^{16}O, and 0.0020052 mole of ^{18}O per mole of ^{16}O’ [12].

As part of the revision of the SI, it is planned that in 2018, the CGPM will adopt the following explicit-constant definition of the kelvin [9,13,14]:
The kelvin, symbol K, is the SI unit of thermodynamic temperature; its magnitude is set by fixing the numerical value of the Boltzmann constant to be equal to exactly 1.380 65X × 10

^{−23} when it is expressed in the SI units s^{−2} m^{2} kg K^{−1}, which is equal to J K^{−1}.

Thus one has the exact relation *k*=1.380 65X × 10^{−23} J K^{−1}, where X represents one or more additional digits to be fixed at the adoption of the definition. The new definition has its origin in statistical mechanics where thermodynamic temperature is a measure of the average thermal energy per degree of freedom in the system. The effect of the definition is that one kelvin will be equal to the change of thermodynamic temperature *T* that results in a change of thermal energy *kT* by 1.380 65X × 10^{−23} J. So the kelvin will now be defined in terms of the SI derived unit of energy, the joule. While, in principle, the natural unit of thermodynamic temperature in this relation is the joule and a separate base unit for temperature is not required, for historical and especially practical reasons the kelvin will continue to be a base unit of the SI. The explicit-constant definition is sufficiently wide to encompass any form of primary thermometry and leaves the *MeP*-K to provide guidance on the practical realization of the kelvin.

The CCT recommended that the numerical value of the Boltzmann constant is fixed when the following two conditions are met [15]:

(1) the relative standard uncertainty of the adjusted value of

*k*is less than 1×10^{−6}and(2) the determination of

*k*is based on at least two fundamentally different methods, of which at least one result for each shall have a relative standard uncertainty less than 3×10^{−6}.

These conditions will ensure that the best estimate of the TPW temperature *T*_{TPW} remains 273.16 K. One consequence of the new definition is that the former uncertainty in the determination of *k* is transferred to *T*_{TPW}. It will remain common practice to call the difference ‘*T*−273.15 K’ Celsius temperature, symbol *t*. The unit of Celsius temperature is the degree Celsius, symbol °C, which is, by definition, equal in magnitude to the kelvin.

The CCT is not aware of any thermometry technology likely to provide a significantly improved uncertainty of *T*_{TPW}. Consequently, there is unlikely to be any change in the value of *T*_{TPW} in the foreseeable future. On the other hand, the reproducibility of *T*_{TPW}, realized in water triple point cells with isotopic corrections applied, is better than 50 μK, i.e. 2 parts in 10^{7}. Experiments requiring the lowest practical uncertainties at or close to *T*_{TPW} will continue to rely on the reproducibility of the TPW. Although the value of *T*_{TPW} is not a fundamental constant, the TPW is an invariant of nature with the inherent long-term stability of fundamental constants.

Direct measurements of thermodynamic temperature require a primary thermometer based on a well-understood physical system whose temperature can be derived from measurements of other quantities, as described in the following sections. Unfortunately, primary thermometry is mostly complicated, time consuming and hence rarely used as a practical means of disseminating the kelvin. As a practical alternative, the defined International Temperature Scales provide internationally accepted procedures for both realizing and disseminating temperature in a straightforward and reproducible manner (see §6).

While the redefinition of the kelvin will have no impact on the status of the ITS-90 or PLTS-2000, there will be significant benefits, particularly for temperature measurements below approximately 20 K and above approximately 1300 K, where primary thermometers may offer a lower thermodynamic uncertainty than is currently available with the defined scales. In the future, as the primary methods evolve and achieve lower uncertainties, they will become more widely used and will gradually replace the defined scales as the basis of temperature measurement. However, the ITS-90 and PLTS-2000 will remain in use for the foreseeable future as precise, reproducible and convenient approximations to thermodynamic temperature. In particular, the most precise temperature measurements in the core temperature range from approximately 25 to 1235 K will, at least initially, continue to be traceable to standard platinum resistance thermometers calibrated according to the ITS-90.

Note that the fixed-point temperatures assigned in all of the defined scales are exact with respect to the respective scale temperature (there is no assigned uncertainty) and fixed (the value remains unchanged throughout the life of the scale). As a consequence, the redefinition of the kelvin in terms of the Boltzmann constant has no effect on the temperature values or realization uncertainties of the present two defined scales. In particular, the status of the TPW as a fixed point, with a defined temperature value on the ITS-90, will remain unchanged. Thus, the uncertainty of realization of the TPW on the ITS-90 will not acquire any additional uncertainty due to the change in definition.

## 3. Nomenclature (taxonomy of methods)

The endorsement of multiple methods for the realization of the kelvin in the *MeP*-K creates a risk of reported values of temperature being ambiguous: on which scale is the temperature reported? The *MeP*-K must provide clear recommendations on proper notation of temperature values and realization methods. It includes, therefore, the following nomenclature (or taxonomy), which clarifies what is meant by the terms (i) primary thermometry, (ii) defined temperature scales, and (iii) approximations to thermodynamic temperature. In the second version of the *MeP*-K, only (i) and (ii) are treated.

(i)

*Primary thermometry*is performed using a thermometer based on a well-understood physical system, for which the equation of state describing the relation between thermodynamic temperature*T*and other independent quantities, such as the ideal-gas law or Planck's equation, can be written down explicitly without unknown or significantly temperature-dependent constants. Thermodynamic temperature can be obtained by measuring the independent quantities. Accurate thermodynamic temperature values require not only accurate measurements of the independent quantities, but also sufficient understanding of the system to enable a quantitative assessment of departures from the ideal model in order to apply appropriate corrections. There are two classes of*primary thermometry*:—

*Absolute primary thermometry*measures thermodynamic temperature directly in terms of the definition of the base unit, the kelvin, i.e. from the defined numerical value of the Boltzmann constant, which determines the thermal energy*kT*. No reference is made to any temperature fixed point (*n*=0,*n*=number of points) and all other parameters specified in the equation of state are measured or otherwise determined.—

*Relative primary thermometry*measures thermodynamic temperature indirectly using a specified equation of state, with one or more key-parameter values determined from temperature fixed points (*n*>0), for which values for the thermodynamic temperature*T*and their uncertainties are known from previous absolute or relative primary thermometry. Tables containing data for*T*of fixed points are given in the*MeP*-K appendices. Compared with the thermodynamic uncertainty of the fixed-point values, the additional uncertainty of the relative methods is almost always smaller because they allow awkward influencing factors, such as dimensions of bulbs, spheres or aperture systems, to cancel or become more amenable to measurement.

(ii)

*Defined temperature scales*assign temperature values, which have been determined by primary thermometry, to a series of highly reproducible states of matter (e.g. freezing or triple points of pure substances), specify the interpolating or extrapolating instruments for a particular sub-range of temperature and define any necessary interpolating or extrapolating equations. For instance, at high temperatures, relative spectral radiation thermometry is used with reference to one defined fixed-point temperature (*n*=1), and from 3 to 25 K, interpolation between three fixed points (*n*=3) is performed with a constant-volume gas thermometer. The defined scales are highly prescriptive and define new temperature quantities*T*_{XX}(scale temperatures) that provide close approximations to the thermodynamic temperature*T*and have the same unit as*T*, i.e. the kelvin. Temperature values assigned to the fixed points of each scale are considered exact and do not change for the life of the scale, even if subsequent research reveals a bias of the values relative to true thermodynamic temperature. Currently, the only such defined temperature scales recommended by the CCT and approved by the CIPM are the International Temperature Scale of 1990 (ITS-90) from 0.65 K and above and the Provisional Low Temperature Scale from 0.9 mK to 1 K (PLTS-2000). The temperatures defined by ITS-90 and PLTS-2000 are denoted by*T*_{90}and*T*_{2000}, respectively. Non-prescriptive recommendations for the realization of the ITS-90 and the PLTS-2000 are given in the ‘Guide to the realization of the ITS-90’ (http://www.bipm.org/en/committees/cc/cct/guide-its90.html) and the ‘Guide to the realization of the PLTS-2000’ [5,8], respectively.The

*MeP*-K also includes a section entitled*approximations of defined scales*where fixed points, interpolating or extrapolating instruments, and interpolating or extrapolating equations are different from those specified in the defined scales, but any differences from a scale are sufficiently well understood. Such methods will be described in CCT guides being prepared.(iii)

*Approximations to thermodynamic temperature*do not explicitly use a specified equation of state but rather either some approximation to it or an empirical relation (e.g. virial expansions for gases with experimentally determined virial coefficients, approximations to Planck's law). Some of the parameters may be explicitly determined, or they may be arrived at through reference to temperature fixed points (e.g. fixed points of the defined scales together with data on the differences between thermodynamic temperature and the assigned temperature values), or through some mathematical process (e.g. interpolation or least squares approach). These methods are used, in the place of a defined scale or primary thermometry, when some advantage such as lower uncertainty or increased reliability in realization is achievable. For the*MeP*-K, only methods that can achieve uncertainties similar to the primary thermometry or defined scale approaches are included.

## 4. Criteria for the inclusion of a method in the *MeP*-K

Since a *MeP* should include only top-level (lowest uncertainty) realization methods, in 2012 the CCT adopted the following criteria for the inclusion of a method [16]:

— For primary-thermometry methods, a well-derived equation of state describing the relation between thermodynamic temperature and other independent quantities of the physical system used must exist that does not contain unknown or significantly temperature-dependent parameters. If the equation of state is based on an approximation of a complex theory, it must at least be possible to estimate the order of magnitude of the deviation from theory.

— Methods applied for the approximation of either thermodynamic temperature or defined temperature scales must be based on well-derived approximate formulae or empirical relations that allow a reliable interpolation or extrapolation after necessary parameters have been arrived at through reference to temperature fixed points.

— A complete uncertainty budget must be approved by the CCT.

— The uncertainty of the realization of the kelvin must not be more than one order of magnitude larger than the state-of-the-art uncertainty achieved with primary thermometry or defined temperature scales, or the uncertainty needed by the stakeholders.

— At least two independent realizations applying the method with the necessary uncertainty must exist. Ideally, the results have been compared directly.

— A comparison of the realizations with the results of already accepted methods must be performed; any significant, unresolved deviations should be addressed by the CCT prior to inclusion of the new method in the

*MeP*-K.— The methods should be applicable over temperature ranges that are acceptable for the stakeholders in metrology, science or industry.

— The experimental technique necessary for applying the methods should be documented in detail in the open literature so that experts in metrology can realize it independently.

## 5. Primary thermometry

In the second version of the *MeP*-K, approved by the CCT in 2013, two kinds of primary-thermometry methods are recommended: acoustic gas thermometry (AGT) [17] and spectral-band radiometric thermometry [18]. The brief descriptions given in this section are included in the text of the *MeP*-K. Detailed information is contained in the *MeP*-K appendices or review papers.

### (a) Thermodynamic temperature measurement by acoustic gas thermometry

#### (i) Principle of primary acoustic gas thermometry

Primary AGT exploits the relationship between the speed of sound, *u*, in an ideal gas in the limit of zero frequency and the thermodynamic temperature, *T*, of the gas,
where *k* is the Boltzmann constant, *m* is the mass of the gas particles and *γ* is the ratio of the heat capacity of the gas at constant pressure to its heat capacity at constant volume. For ideal monatomic gases, *γ*=5/3.

#### (ii) Absolute primary acoustic gas thermometry

The speed of sound is deduced from the resonance frequencies of a monatomic gas contained within an isothermal cavity. Accurate determinations of the resonance frequencies require the use of non-degenerate acoustic modes, and often the non-degenerate radially symmetrical modes of nearly spherical cavities are used. The average radius of the cavity is often determined using microwave resonances. The non-ideal properties of real gases are accommodated with the use of a virial expansion of the speed-of-sound relation and extrapolation to zero pressure.

Measurement of the acoustic resonance frequencies, pressures, cavity dimensions and molecular mass of the gas must be traceable to the metre, the kilogram and the second. Primary AGT has been conducted at the temperature of the TPW with relative uncertainties of the order of 10^{−6}. However, the low uncertainties claimed for AGT have only been confirmed by independent thermodynamic measurements at a level of a few parts in 10^{6}. Details are found in [17] and references therein.

#### (iii) Relative primary acoustic gas thermometry

Relative AGT determines the ratios of thermodynamic temperatures from measurements of the ratios of speeds of sound. Typically, a temperature is determined as a ratio with respect to the temperature of a fixed point for which the thermodynamic temperature is known. The fixed point is generally realized in the resonator, by proxy, through one or more calibrated platinum resistance thermometers. The measured temperature ratios are usually expressible in terms of measured ratios of lengths and frequencies. Relative AGT has been conducted over a wide temperature range from a few kelvins to above 550 K [19–22]. Independent realizations of relative AGT typically agree within 3×10^{−6} *T* in the sub-range 234–380 K. A table containing data for the thermodynamic temperature *T* of fixed points is given in the *MeP*-K appendix ‘Estimates of the differences *T*−*T*_{90}’ (see §6a).

### (b) Spectral-band radiometric thermometry

#### (i) Principle of primary radiometric thermometry

The basic equation for spectral-band radiometric thermometry is the Planck law, which gives the spectral radiance, *L*_{b,λ} (the subscript *λ* on *L*_{b,λ} in this case indicates that the value is per unit wavelength), of an ideal blackbody as a function of thermodynamic temperature, *T*,
where *k* is the Boltzmann constant, *h* is the Planck constant, *c* is the speed of light *in vacuo* and *λ* is the wavelength *in vacuo*. Spectral radiance is the power emitted per unit area per unit solid angle per unit wavelength and is often expressed with the units W m^{−2} sr^{−1} nm^{−1}.

#### (ii) Absolute primary radiometric thermometry

Absolute primary radiometric thermometry requires an accurate determination of the optical power, emitted over a known spectral band and known solid angle by an isothermal cavity of known emissivity. Measurement of the power requires a radiometer, comprising a detector and spectral filter, with known absolute spectral responsivity. The optical system typically includes two co-axial circular apertures separated by a known distance to define the solid angle, and may additionally include lenses or mirrors. The refractive index of the medium in which the measurement is made must also be known. All measurements of the quantities involved must be traceable to the corresponding units of the SI, in particular, the watt and the metre.

Lowest uncertainties of around 0.1 K (coverage factor *k*=1) at 2800 K are possible with primary radiometric thermometry. Practical guidelines for the realization, including typical uncertainty estimates, will be found in the *MeP*-K appendix ‘Absolute primary radiometric thermometry’ and references therein, see at present [23–27].

#### (iii) Relative primary radiometric thermometry

For relative primary radiometric thermometry, the absolute spectral responsivity of the radiometer is not required, nor is quantification of the geometric factors defining the solid angle. Instead, the optical power is measured relative to optical power measurements made of one or more fixed-point blackbodies, each with known thermodynamic temperature. There are three recognizable approaches to relative primary radiometric thermometry:

— extrapolation from one fixed point, which requires only knowledge of the relative spectral responsivity of the detector and filter;

— interpolation or extrapolation from two fixed points, which requires only the bandwidth of the responsivity; and

— interpolation or extrapolation from three or more fixed points, for which detailed measurements of responsivity are not required.

The interpolation and extrapolation are greatly simplified with the use of a well-understood parametric approximation of the integral expression of the optical power (e.g. by the Planck form of the Sakuma–Hattori equation [28]), which eliminates the need to iteratively solve the integral equation describing the measured optical power.

Relative primary radiometric thermometry gives uncertainties that are only slightly higher than absolute primary radiometric thermometry. Guidelines for the realization, including typical uncertainty estimates, will be found in the *MeP*-K appendix ‘Relative primary radiometric thermometry’ and references therein, see at present [18,23].

## 6. Defined temperature scales

The CIPM has adopted a series of International Temperature Scales; firstly in 1927, acting under the authority of the CGPM and, since 1937, on the advice of its CCT. Subsequent to the 1927 scale, new scales have been adopted in 1948, 1968, 1990 and 2000, with occasional minor revisions in intervening years.

Note that the fixed-point temperatures assigned in all of the defined scales are exact with respect to the respective scale (there is no assigned uncertainty) and fixed (the value remains unchanged throughout the life of the scale). As a consequence, the definition of the kelvin in terms of the Boltzmann constant has no effect on the temperature values or realization uncertainties of the defined scales.

The ITS-90 from 0.65 K upwards and the PLTS-2000 from 0.9 mK to 1 K will remain in use in the foreseeable future allowing precise, reproducible and practical approximations to thermodynamic temperature. In particular, the most precise temperature measurements in the temperature range from approximately −250°C to 960°C will continue in the near to medium term to be traceable to standard platinum resistance thermometers calibrated according to the ITS-90.

### (a) International Temperature Scale of 1990 for temperatures above 0.65 K

The ITS-90 [4,29] is the most recent descendant of the original International Temperature Scale of 1927 and replaced the International Practical Temperature Scale of 1968 (IPTS-68) and its extension, the 1976 Provisional 0.5–30 K Temperature Scale (EPT-76). The ITS-90 covers the temperature range from 0.65 K to the highest temperatures that can be determined practically by radiometric means. Guidance information is available for the realization of the ITS-90 (http://www.bipm.org/en/committees/cc/cct/guide-its90.html) and is being prepared for methods approximating the ITS-90.

Besides the text of the ITS-90, the Technical Annex of the *MeP*-K is mandatory for the realization of the ITS-90. This annex specifies the isotopic composition of the three fixed-point substances water, hydrogen and neon. Such a specification is not included in the scale definition itself. For the present definition of the base unit kelvin via the temperature of the TPW, the same isotopic composition as that given in the Technical Annex was specified by the CIPM at its 94th meeting in 2005 [12]. Furthermore, the Technical Annex contains equations, which facilitate corrections for the results obtained with fixed-point samples having other isotopic compositions.

Recommended estimates of the differences between thermodynamic temperature *T* and temperature *T*_{90} on the ITS-90, *T*−*T*_{90}, together with their uncertainties are given in the *MeP*-K appendix ‘Estimates of the differences *T*−*T*_{90}’, see also [7]. They allow corrections to be made to *T*_{90} values when accurate measurements of *T* are needed. Since the fixed-point temperatures assigned in the ITS-90 have no uncertainty, the differences *T*−*T*_{90} allow direct determination of *T* values for the fixed points and their uncertainties.

### (b) Provisional Low Temperature Scale from 0.9 mK to 1 K

Considerable research has been conducted on establishing a temperature scale extending to temperatures lower than 0.65 K [6]. The PLTS-2000 is the outcome, adopted in 2000 by the CIPM [5]. The PLTS-2000 is defined from 1 K down to 0.9 mK, in terms of a relation expressing *T*_{2000} as a function of the melting pressure of the light helium isotope ^{3}He. It is explicitly a provisional scale, recognizing that the datasets comprising the basis of the scale became increasingly inconsistent below 10 mK, disagreeing by around 6% at 0.9 mK. In the temperature range from 0.65 to 1 K, temperature may be measured on either the ITS-90 or the PLTS-2000. Either scale is acceptable; the choice of scale typically is dictated by convenience or the attainable uncertainty of realization. In those rare cases where use of either scale is convenient, *T*_{2000} is a better approximation of thermodynamic temperature than *T*_{90} in the region of overlap. For the range from 0.65 to 3.2 K, the application of the new ^{3}He vapour-pressure scale PTB-2006 [30], which is fully consistent with the PLTS-2000, has been recommended by the CCT Working Group dealing with ‘Thermodynamic temperature determinations and extension of the ITS-90 to lower temperatures’ [7,31].

In contrast to the ITS-90, for which the Technical Annex of the *MeP*-K contains important specifications, only the text of the scale is mandatory for the realization of temperatures *T*_{2000} on the PLTS-2000. A guide for the realization of the PLTS-2000 describes methods by which the PLTS-2000 can be realized successfully [5,8].

## 7. Conclusion and outlook

The *MeP*-K provides the CCT with a flexible path for updating and expanding the range of recognized thermometric methods, while at the same time supporting the defined International Temperature Scales. This document will grow substantially during the next few years dependent on the developments in thermometry. Besides the defined International Temperature Scales ITS-90 and PLTS-2000, the second version of the *MeP*-K, approved by the CCT in 2013, recommends two kinds of primary-thermometry methods, namely AGT [17] and spectral-band radiometric thermometry [18]. This version will come into force after the redefinition of the kelvin, expected in 2018 [9,14]. Future versions of the *MeP*-K are likely to include further primary-thermometry methods such as noise thermometry [32–35], dielectric-constant gas thermometry [36] and other kinds of thermometry.

## Authors' contributions

All authors meet the following criteria: (i) substantial contributions to conception and content of the *MeP*-K; (ii) drafting the article or revising it critically for important intellectual content; and (iii) final approval of the version to be published.

## Competing interests

We declare we have no competing interests.

## Funding

We received no funding for this study.

## Footnotes

One contribution of 16 to a Theo Murphy meeting isssue ‘Towards implementing the new kelvin’.

- Accepted July 17, 2015.

- © 2016 The Author(s)

Published by the Royal Society. All rights reserved.