Determination of the Boltzmann Constant and
new Definition of the Kelvin
Joachim Fischer
Physikalisch-Technische
Physikalisch
Technische Bundesanstalt
Berlin, Germany
1 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Determination of the Boltzmann Constant and
new Definition of the Kelvin
Contents
i l di
including
concerns off CCT/10-34
CCT/10 34
ƒ The Kelvin Definition
ƒ Impact
ƒ Implications of Changing the Definition
ƒ Determination of the Boltzmann Constant
ƒ Summary and Outlook
2 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Standards and Scales
the scale:
additional fixed points
and interpolating instruments
temperatures from
primary thermometers
0
H2 Ne
O2
triple
p point
p
of water
Ar
Hg
Ga
In
…
273.16 × the unit
intensive quantity
temperature
the unit
length
extensive quantity
the scale
3 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Definition of the Kelvin (1968)
and triple point of water
“The Kelvin : fraction
1/273 16 of the
1/273.16
thermodynamic
temperature of triple
point
i t off water”
t ”
(13. CGPM: Metrologia, 1968, 4, 43)
Ttpw = 273,16
273 16 K
definition = no uncertainty
ptpw = 611,66
611 66 Pa
William Thomson,
the later
Lord Kelvin of Largs
(1824-1907)
4 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Effects of D and 18O on TP temperature
0.02
D
0 04
0.04
Tempe
erqature diffference (K))
Temp
perature diffference (K))
0.05
10 mK
0.03
0.02
0.01
0
0.000
0.004
0.008
18
O
0.015
0.01
10 mK
0.005
0.012
Mole fraction
0
0.00
0.02
0.04
0.06
Mole fraction
Rod White,
MSL N.Z.
5 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Isotope effect, a material property
This substance is not available for filling of TPW cells
6 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
New definition based on Boltzmann constant k
system of “particles“
thermal energy E per degree
of freedom
thermodynamic temperature T
k = conversion factor
E = ½kT
CODATA value of Boltzmann constant 2006:
k = R/NA = 1.3806504 ((24)) ·10-23 J/K u = 1.7·10-6 *))
*) Rev. Mod. Phys. 80 2008, 633
7 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
The Boltzmann Constant k and the kelvin
Boltzmann: σ = ln P
entropy
1/τ = dσ / dU
measured in joule
thermodynamic temperature
measured in kelvin
Planck: S = k σ = k ln P
1/T = dS / dU
J
20
1 38 10-20
1.38x10
1.38x10-21
k = conversion factor
between energy and
temperature
fixing the value of k :
Boltzmann´s original
i
intention
i (concern
(
1)
8 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
1.38x10-22
1.38x10-23
1.38x10-24
1.38x10-25
1.38x10-26
P probability
U internal energy
Wording
1. Reliable determination of k with different methods
2 Fixing of the value of k
2.
3. New definition of the kelvin like:
Explicit-unit definition
Explicit-constant
p
definition
f
The kelvin is the change of
thermodynamic temperature T
The kelvin, unit of
that results in a change of thermal
thermodynamic temperature, is
energy kT by exactly
such
thejoule,
Boltzmann
1.380 65X
X ×that
10−23
where
constant is exactly
k is the Boltzmann constant
1.380 65X X × 10−23 joule per
kelvin.
9 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Ludwig
g Boltzmann
(1844 - 1906)
Determination of the Boltzmann Constant and
new Definition of the Kelvin
Contents
ƒ The Kelvin Definition
ƒ Impact
ƒ Implications of Changing the Definition
ƒ Determination of the Boltzmann Constant
ƒ Summary and Outlook
10 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Future uncertainties for high temperatures
0,35
Best uncertainty
0,30
ITS-90
0,25
At very low and very high temperatures there will
be in future no need to reference back to the triple
0,20
point of water
n=1 (ITS-90
thermodynamic
0,15
Main practical advantage of the new definition
0,10
0,05
0,00
0
00
1000
Bloembergen et al.
TMCSI 2003, 291-296
figure 2
ITS-XX
1500
2000
2500
Temperature
p
/K
11 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
3000
3500
The impact of a new definition of the kelvin
Short term:
• the kelvin definition is independent
of any material
• no favoured fixed point
• no favoured measurement method
• no error propagation from TPW
• thermodynamic measurements
and ITS-90 are coexisting
• <20 K and >1300 K
thermodynamics are superior
Long term:
• With improvement of primary
thermometry thermodynamic
y replace
p
ITS-90
measurements may
12 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Ludwig
g Boltzmann
(1844 - 1906)
Determination of the Boltzmann Constant and
new Definition of the Kelvin
Contents
ƒ The Kelvin Definition
ƒ Impact
ƒ Implications of Changing the Definition
ƒ Determination of the Boltzmann Constant
ƒ Summary and Outlook
13 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
CCT WG4 Task Group
p (TG-SI)
(
) members
Joachim Fischer ((PTB)) chairman
Anatoly Pokhodun (VNIIM)
Ken Hill (NRC)
G h
Graham
M
Machin
hi (NPL)
Mike Moldover (NIST)
Laurent Pitre (LNE/CNAM)
Andrea Merlone (INRIM)
Richard Davis ((BIPM)) Executive Secretaryy CCT
Osamu Tamura (NMIJ)
Hüseyin Ugur (CCT) President CCT
R d Whit
Rod
White (MSL)
Inseok Yang (KRISS)
Jintao Zhang (NIM)
14 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Status of ITS-90
For the foreseeable future :
Most temperature measurements in core temperature range
((~ - 200 ºC … 960 ºC ) with SPRTs calibrated accord. to ITS-90
ITS-90 will remain intact, with defined values of T90 for all of the
fixed points, including the TPW
Uncertainties in T90 will not change
Dominated byy uncertainties in the fixed-point
p
realizations,,
and the non-uniqueness of SPRTs, typically totalling < 1 mK
15 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Fixed points of ITS-90 ( table 1.2 red book )
T90
Cu (fp)
Au (fp)
Ag (fp)
Al (fp)
Zn (fp)
Sn (fp)
In (fp)
Ga (mp)
H2O (tp)
Hg (tp)
Ar (tp)
O2 (tp)
Ne (tp)
(t )
e-H2 (vp)
e-H2 (vp)
e-H
H2 (tp)
4
He (vp)
1357.77
1357
77 K
1337.33 K
1234.93 K
933 473 K
933.473
692.677 K
505.078 K
429 7485 K
429.7485
302.9146 K
273.16 K
234 3156 K
234.3156
83.8058 K
54.3584 K
24 5561 K
24.5561
≈20.3 K
≈17.0 K
13 8033 K
13.8033
4.2221 K
u(T90) / mK u(T) / mK
15
10
1
03
0.3
0.1
0.1
01
0.1
0.05
0.02
0 05
0.05
0.1
0.1
02
0.2
0.2
0.2
01
0.1
0.1
u(Tk fixed) / mK
60
no change
50
at all
40
25
13
5
3
1
0
15
1.5
1.5
1
05
0.5
0.5
0.5
05
0.5
0.3
16 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
60.1
60
1
50.1
40.1
25 1
25.1
13.1
5.10
3 11
3.11
1.15
0.49
1 55
1.55
1.50
1.00
0 50
0.50
0.50
0.50
0 50
0.50
0.30
Uncertainties in thermodynamic temperature
If 2002 CODATA recommended value of k were taken to be
exact and used to define the kelvin :
Uncertainty of k would be transferred to the value of TTPW
B t estimate
Best
ti t off the
th value
l off TTPW still
till 273
273.16
16 K
K,
but instead of being exact as result of definition of the kelvin :
Uncertainty associated with estimate would become :
ur(TTPW) = 1.8 × 10−6, corresponds to 0.49 mK
17 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Error propagation from TPW
All thermodynamic measurements currently defined
as ratios with respect to TPW :
The 0.49 mK uncertainty propagates to all historical
thermodynamic temperature measurements
3,0
Temperatue range of SPRTs
additio
onal
u (tt ) / mK
2,5
2,0
1,5
1,0
How well represents ITS-90
thermodynamic temperatures ?
0,5
0,0
-250
0
250
500
temperature / °C
18 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
750
1000
Fixed points of ITS-90 ( table 1.2 red book )
T90
Cu (fp)
(f )
Au (fp)
Ag (fp)
Al (fp)
(f )
Zn (fp)
Sn (fp)
I (fp)
In
Ga (mp)
H2O (tp)
H (tp)
Hg
Ar (tp)
O2 (tp)
N (tp)
Ne
e-H2 (vp)
e-H2 (vp)
e-H2 (tp)
4
He (vp)
1357.77
1357
77 K
1337.33 K
1234.93 K
933change
933.473
473
no
h K
692.677
at all K
505.078 K
429 7485 K
429.7485
302.9146 K
273.16 K
234 3156 K
234.3156
83.8058 K
54.3584 K
24 5561 K
24.5561
≈20.3 K
≈17.0 K
13.8033 K
4.2221 K
u(T90) / mK u(T) / mK
15
10
1
03
0.3
0.1
0.1
01
0.1
0.05
0.02
0 05
0.05
0.1
0.1
02
0.2
0.2
0.2
0.1
0.1
19 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
60
50
40
25
13
5
3
1
0
15
1.5
1.5
1
05
0.5
0.5
0.5
0.5
0.3
u(Tk fixed) / mK
60.1
60
1
50.1
40.1
25 1
25.1
13.1
5.10
3 11
3.11
1.15
0.49
1 55
1.55
1.50
1.00
0 50
0.50
0.50
0.50
0.50
0.30
change
> 0.1 mK
Uncertainties in thermodynamic temperature
⇒ TG-SI could not foresee any experiment where the slightly
increased uncertainties of u(Tk fixed) would present a problem
Anyy future changes
g in the temperature
p
scale much smaller than
tolerances associated with current documentary standards for
thermocouples and IPRTs :
⇒ No requirement is anticipated for any future change in
temperature scales to propagate to the documentary standards
Once k has been fixed in 2015 : TG-SI is not aware of any new
technology
gy for a p
primary
y thermometer p
providing
g a significantly
g
y
improved uncertainty u(TTPW)
⇒ no change of the assigned value of TTPW for the foreseeable
f
future
(
(concern
2)
20 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
The Roles of the Mise en Pratique for the
Definition of the Kelvin I
The mise en pratique (“practical realization”) for the definition of the kelvin
(MeP-K)
(MeP
K) was created by the Consultative Committee for Thermometry
(CCT) in 2006 to give practitioners of thermometry a guide to the
realization of the kelvin, i.e., measurement of temperature in kelvins, in
accord with the International System
y
of Units.
The International Committee for Weights and Measures also foresaw that
adoption
p
of the proposed
p p
new definition of the kelvin would require
q
a
MeP-K
MeP-K will describe three categories of measurements:
- primary methods for measuring thermodynamic temperature T
- formal approximations to T, in particular the International Temperature
S l off 1990 (ITS
Scale
(ITS-90)
90) and
d the
h Provisional
P
i i
l Low Temperature
T
Scale
S l from
f
0.9 mK to 1 K (PLTS-2000)
- indirect approximation methods that are neither primary nor defined on
a temperature
t
t
scale,
l yett capable
bl off exceptionally
ti
ll low
l
uncertainties
t i ti or
increased reliability.
21 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
The Roles of the Mise en Pratique for the
Definition of the Kelvin II ((concern 3))
By providing a framework for primary methods and indirect methods, the
MeP-K
MeP
K will foster development and application of new methods, such as
the use of absolute radiometry or high-temperature fixed points
MeP-K currently
y includes the text of the formal scales and a Technical Annex
of essential additional information
Next version will include recommended differences, T – T90, between the
thermodynamic temperature and the temperature on the ITS-90 along with
the associated uncertainty (ready for inclusion)
By documenting known ITS-90 biases, the MeP-K will support
thermodynamically accurate measurements without mandating
replacement of the ITS-90 in industry
In this way, the MeP-K provides the CCT with a mechanism to update and
expand the thermometric methods in common use, without imposing on
industry the high costs of changing the International Temperature Scale
22 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Schematic representation of relationship
between MeP-K and other documents
SI Definition
D fi i i
SI Brochure
MeP-K
Section 3
Primary Methods
Supplementary
Guides
Section 4
Formal Approximations
ITS-90 Text
PLTS-2000
Text
Section 5
Indirect Approximations
Supplementary
Guides
ITS-90 Technical
Annex
ITS-90
Supplementary
I f
Information
ti
PLTS-2000
Supplementary
I f
Information
ti
box with solid border: prescriptive document
box with dashed border: non-prescriptive guidance
23 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
M P K 2006
MeP-K
on CCT webpage
under preparation
Determination of the Boltzmann Constant and
new Definition of the Kelvin
Contents
ƒ The Kelvin Definition
ƒ Impact
ƒ Implications of Changing the Definition
ƒ Determination of the Boltzmann Constant
ƒ Summary and Outlook
24 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Determination of the Boltzmann constant for the redefinition
of the kelvin
Coordinator:
Physikalisch-Technische
Bundesanstalt
Partners:
at es
Danish Fundamental
Metrology
Collaborators:
Universidad de Valladolid
25 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Acoustic g
gas thermometry
y
u02 = γ kT / m
m atomic mass (40Ar)
γ ratio of heat capacities cp/ cV = 5/3 for gas of single atoms
u0 speed of sound
AGT
L. Pitre, C. Guianvarc'h, F. Sparasci,
A Guillou,
A.
Guillou D
D. Truong
Truong, Y
Y. Hermier
Hermier,
M. Himbert, C. R. Physique 10 (2009) 835-848
R.M. Gavioso,G.
, Benedetto,, P.A. Giuliano Albo,,
D. Madonna Ripa, A. Merlone, C. Guianvarc`h, receiver
F. Moro, and R. Cuccaro,
Metrologia
g 47 ((2010)) 387-409
Measured quantites:
¾ sound frequency ν at resonance
¾ dimension d of resonator
¾ yields
i ld speed
d off sound
d u0
26 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
transducer
d
Quasi-spherical cavity resonators
J.B. Mehl, M.R. Moldover,
L. Pitre Metrologia 41, 2004,
295 (QSCR)
E.F. May, L. Pitre, J.B. Mehl,
M.R. Moldover, J.W. Schmidt,
Re Sci
Rev.
Sci. Instr
Instrum.
m 75,
75 2004,
2004
3307 (QSCR)
J.W. Schmidt, R.M. Gavioso,
E F May,
E.F.
May and M
M.R.
R Moldover
Moldover,
PRL 98, 254504, 2007 (RIGT)
Refractive index gas thermometry
p = kT (n2 - 1) ε0 / α0
n refractive index
ε0 electric constant, defined
α0 atomic polarizability, known by theory
RIGT
QSCR enable
microwave measurement
to determine dimension
or RIGT: measurement of ε (p,T)
of helium and argon
27 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
QSCR
AGT preliminary results of spring 2010
Gavioso et al., Metrologia 47 387–409 (2010)
AGT
28 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Dielectric constant g
gas thermometry
y
p = k T ε0(εr - 1) / α0
ε0 electric constant, defined
εr ≈ C(p)/C(0)
α0 atomic
t i polarizability,
l i bilit
known by theory
Measured quantites:
¾ pressure p
¾ capacitance ratio C(p)/C(0)
DCGT
C. Gaiser, B. Fellmuth and N. Haft,
I t J.
Int.
J Thermophys.
Th
h
29 2008,
2008 18
29 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
DCGT: Critical parameters
pressure:
capacitance:
piston gauge:
¾ present uncertainty:
10 MPa Æ u (p)/p = 5 ppm
¾ main problem:
uncertainty of area determination
co-operation with
pressure lab
aim:
i 1 ppm
co-operation with electricity lab:
present uncertainty:
absolute: u (CN)
relative: u ((CX /CN)
aim:
30 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
u (ΔCX / CX)
20 ppb
3 pp
ppb
1 ppb
Doppler broadening thermometry
ΔνD = [2 kT /(mc02)]1/2⋅ν0
C. Daussy, M. Guinet, A. AmyKlein, K. Djerroud, Y. Hermier, S.
Bi d
Briaudeau,
Ch
Ch.J.
J B
Bordé,
dé and
dC
C.
Chardonnet, Phys. Rev. Lett. 98
2007, 250801
G Casa,
G.
Casa A.
A Castrillo,
Castrillo G.
G
Galzerano, R. Wehr, A. Merlone,
D. Di Serafino, P. Laporta and L.
Gianfrani Phys
Gianfrani,
Phys. Rev.
Rev Lett
Lett. 100
2008, 200801
J. Petersen, J. Hald, Danish
Fundamental Metrology
m atomic mass
p
of light
g
c0 speed
DBT
Δ νD
Measured quantites:
¾ doppler line width ΔνD
¾ centre wavelength ν0
31 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
ν0
University Paris North/LNE
Universities Naples
p
and Milan/INRiM
DBT
Paris: CO2 laser at 10 µm and ammonia cell
Naples: 1.4 µm diode laser and water-vapour cell
Problems in line fitting at 10-4 to 10-5 level
due to pressure effects
32 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Noise thermometry
<U2> = STΔf = 4 k T R Δf
Nyquist´s Formula
valid to order hf/2kT ~ 0.09 ppm at 1 MHz, 273 K
switched digital input correlator
bandwidth of detection system
mean square noise voltage
2
<U >
JNT
resistance
R
relative method
Zn fixed point : u = 2•10-5 (k=1)
33 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
absolute method
k/h from Noise Power Ratios
Spectral density of thermal noise power
Quantum-Hall Ohm
Spectral density of electrical noise power
AC Josephson Voltage
Jifeng Qu, S. P. Benz, H. Rogalla
and D
D. R
R. White
White, Metrologia 46
(2009) 512–524
XR ؆ 0.003874
0 003874 resistance in units of RK-90
T = 273.16 K temperature as realized in TPW cell
D2 = 1
1.47…×10
47 ×10-66/N2 dimensionless number from digital synthesis
fs= DAC sampling frequency, 10 GHz (f1= Δf = fs/M)
M = 24×106 bits,
bits pattern repetition length (memory)
N = number of Josephson junctions
34 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
JNT
Determination of the Boltzmann Constant and
new Definition of the Kelvin
Contents
ƒ The Kelvin Definition
ƒ Impact
ƒ Implications of Changing the Definition
ƒ Determination of the Boltzmann Constant
ƒ Summary and Outlook
35 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
36 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
Present state of k determination
confidence interval = 68.3 %
1,38075
23
-1
k x 10 ( J K )
1,38070
Review of methods in
F ll th Gaiser,
Fellmuth,
G i
Fischer,
Fi h
Meas. Sci. Technol. 17
2006, R145 - R159
AGT
NIST
CODATA 2006
1 38065
1,38065
35 ppm
RIGT
NIST
DCGT
PTB
1,38060
k =1
1,38055
1985
1995
DBT
UniNA
2005
Year
37 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
DBT
LPL
AGT
LNE
INRiM
NPL
2015
Development of the achieved and envisaged
relative standard uncertainties Δk/k
2nd WS 2006
4th WS 2009
2013 possibility
institute
> 20 ppm
3 ppm
1 ppm
CEM (UVa), INRiM, LNE/CNAM,
NPL, NIM
15 ppm
-
2 ppm
PTB
JNT
-
25 ppm
5 ppm
NIST, INRiM
DBT
200 ppm
37 ppm
only Type A
10 ppm
DFM, LNE/CNAM (LPL), INRiM
(UniNA2, PoliMI), UWA
Method
AGT
DCGT
38 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
2007 : Report to the CIPM on the implications of
changing
g g the definition of the base unit kelvin
…that
that within the next four years there exists the possibility of achieving a reliable
uncertainty of the value of k of order one part in 106 based on measurements
applying different methods of primary thermometry. Thus, an improved value of the
Boltzmann constant proposed for defining the kelvin would ideally have been
determined by at least the two fundamentally different methods AGT and DCGT
and be corroborated by other – preferably optical − measurements as TRT and
DBT with larger uncertainty
uncertainty.
The TG-SI appreciates the considerable progress of ongoing experiments to
determine the Boltzmann constant in order to corroborate the present value. It is
assumed that the experiments currently underway to measure R or k will achieve
consistent results by the end of 2010, so that the CODATA group can recommend in
its 2010 constants adjustment
j
a new value for k with a relative standard
uncertainty about a factor of two smaller than the current ur of approximately
2×10−6. With the new definition of the kelvin adopted, this would result in a value of
ur(TTPW) of about 1×10−6, corresponding to about 0.25 mK.
39 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
POSSIBLE CONSEQUENCES OF THE REDEFINION OF
KELVIN AND RECOMENDATION TO CCT AND CIPM
CCT/10-34 by A. Phokodun, VNIIM:
…In view of the above said, as a member of the CCT Task Group
investigating the consequences of a new definition of Kelvin based
on the Boltzmann constant, I would suggest the CCT not to be overhasty in adopting the new definition for the temperature unit of SI
and, by the example the last meeting of the CCM in March 2010,
to adopt a resolution stipulating that the redefinition of Kelvin
should be conditioned by a number of criteria removing the
above mentioned preoccupations.
40 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
2010 : RECOMMENDATION OF THE CCT
SUBMITTED TO THE CIPM
RECOMMENDATION T2 (2010)
Considerations for a new definition of the kelvin
The Consultative Committee for Thermometry (CCT)
recalling its previous Report to the CIPM in 2007, entitled “Report to the CIPM on the
implications of changing the definition of the base unit kelvin
kelvin”, TG-SI/docs05,
TG SI/docs05 and
considering
• further discussion at its 24th and 25th meetings held in 2008 and 2010,
• recent progress in experimental determinations of the Boltzmann constant,
constant k,
k as reported at
rd
th
the 3 and 4 International Workshops on Progress in Determining the Boltzmann Constant
held in 2008 and 2009 and
• other experimental progress allowing a mise en pratique for the new definition of the kelvin
y established and p
presently
y extended to cover direct measurement of thermodynamic
y
already
temperature,
noting
• that various experiments, such as acoustic gas thermometry, dielectric constant gas
thermometry, Johnson noise thermometry, total radiation thermometry and Doppler
broadening thermometry represent distinct routes to determining the Boltzmann constant,
• that the experiments currently underway to measure k need another two years before
CODATA can recommend a robust value for k with a relative standard uncertainty about a
f t off two
factor
t
smaller
ll than
th the
th currentt ur off approximately
i t l 2×10
2 10−66.
• That a relative standard uncertainty of 1×10−6 in k corresponds to a standard uncertainty of
about 0.25 mK in the temperature of the triple point of water after the redefinition,
41 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10
RECOMMENDATION OF THE CCT SUBMITTED
TO THE CIPM (continued)
(
)
appreciating the considerable progress of ongoing experiments to determine the Boltzmann constant in
order to improve confidence in the present value,
recommends
1. that before proceeding with the redefinition of the kelvin a relative standard uncertainty of
the value of k of order one part in 106 be obtained, based on measurements applying
different methods of primary thermometry,
2. that these measurements ideally include at least two fundamentally different methods such
as acoustic gas thermometry and dielectric constant gas thermometry and be corroborated
by other measurements such as Johnson noise thermometry, total radiation thermometry or
Doppler broadening thermometry,
3. that the CODATA recommended value be adopted for the Boltzmann constant.
42 50 years of efforts toward quantum SI, St. Petersburg, 6 Dec 10