The International Temperature Scale and the new Definition of the Kelvin Joachim Fischer Fundamental Constants Meeting 2015 Eltville 4th February 2015 The International Temperature Scale and the new Definition of the Kelvin Contents: ° Introduction ° International Temperature Scale ° Consequences of the new definition ° Determination of the Boltzmann constant ° New definition of the kelvin Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 2 of 47 Why do we need a temperature scale ? Temperature not additive Two systems with T do not yield 2T (in contrast to mass or length) 2 kg 1 kg 1 kg + = + T1 T1 = T1 T1 Temperature scale based on temperature fixed points realized by phase transitions of pure elements Temperatures of fixed points determined by primary thermometers Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 3 of 47 Standards and Scales the scale: additional fixed points and interpolating instruments temperatures from primary triple point thermometers of water H2 Ne O Ar In 2 Hg Ga 0 … 273.16 × the unit temperature intensive quantity the unit length extensive quantity the scale Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 4 of 47 The Meter Convention of 1875 Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 5 of 47 Units and Fundamental Constants 10 -12 10 -8 Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 6 of 47 New definitions of SI base units Prospected SI Base unit Definition Uncertainty Related FC FC kilogram 1889 10 −8 h ampere 1948 10 −7 e second 1967 10 −15 133 Cs kelvin 1967 10 −7 k −7 mole 1971 10 NA candela 1979 10 −4 −12 metre 1983 10 c0 Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 7 of 47 Annalen der Physik, 1, 69-122, 1900 Planck´s natural units −1 2 λ = 2hc hc − Ls ( ,T) exp 1 λ5 λkT Max Planck (Nobel price 1918) Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 8 of 47 New definition based on Boltzmann constant k ideal system of “particles“ thermal energy E per degree of freedom thermodynamic temperature T k conversion factor E = ½kT 2010 CODATA value of Boltzmann constant : Rev. Mod. Phys. 84 2012, 1527 × -23 -1 × -7 k = R/N A = 1.3806488 10 JK u r = 9.1 10 Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 9 of 47 The International Temperature Scale and the new Definition of the Kelvin Contents: ° Introduction ° International Temperature Scale ° Consequences of the new definition ° Determination of the Boltzmann constant ° New definition of the kelvin Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 10 of 47 Temperature scales ITS-90 and PLTS-2000 PLTS-2000 ITS-90 T 1 mK 1 K 1000 K 10 6 K 3He melting pressure thermometer He vapor pressure thermometer He gas thermometer Pt resistance thermometer radiation thermometer contact methods optical methods Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 11 of 47 The International Temperature Scale ITS-90 fixed points Figure 1. Schematic representation of the ranges, sub- ranges and interpolation instruments of ITS-90. The temperatures shown are approximate only. interpolation Gas thermometer 3He 4He II 4He I 0.65 K 1.25 K 2.18 K 3 K 3.2 K 5 K He vapour pressure Gas thermometer Platinum resistance thermometer 0.65 K 3 K 5 K 14 K 25 K 54 K 84 K 273.16 K 234 K 17 K 20 K Platinum resistance thermometer Radiation thermometer -39°C 157 °C 232 °C 420 °C 660 °C 962 °C 1064 °C 1085 °C 0 °C 30 °C Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 12 of 47 Definition of the Kelvin (1968) and triple point of water “The Kelvin : fraction 1/273.16 of the thermodynamic temperature of triple point of water” (13. CGPM: Metrologia, 1968, 4, 43) Ttpw = 273.16 K definition = no uncertainty William Thomson, ptpw = 611.66 Pa the later Lord Kelvin of Largs (1824-1907) Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 13 of 47 Phase diagram Gibb´s rule : f = N1 – P3 + 2 1 component 3 phases Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 14 of 47 Undercooling Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 15 of 47 The measurement Melting of fixed point before measurement metal is to be melted temperature Melting temperature time Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 17 of 47 Freezing of fixed point only freezing plateau used for calibration of thermometer temperature Freezing temperature undercooling time Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 18 of 47 The International Temperature Scale and the new Definition of the Kelvin Contents: ° Introduction ° International Temperature Scale ° Consequences of the new definition ° Determination of the Boltzmann constant ° New definition of the kelvin Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 19 of 47 Status of ITS-90 For the foreseeable future : Most temperature measurements in core temperature range (~ - 200 °C … 960 °C ) 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 by uncertainties in the fixed-point realizations , and the non-uniqueness of SPRTs , typically totalling < 1 mK Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 20 of 47 Fixed points of ITS-90 (table 1 ITS guide) 10,00 1,00 u(T) 1990 Uncertainty Uncertainty Uncertainty / mK / mK 0,10 u(T) 2014 u(ITS-90) 1990 u(ITS-90) 2014 0,01 0 200 400 600 800 1000 1200 1400 TPW Temperature / K Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 21 of 47 Uncertainties in thermodynamic temperature If 2010 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 Best estimate of the value of TTPW still 273.16 K, but instead of being exact as result of definition of the kelvin : Uncertainty associated with estimate would become today : −7 ur(T TPW ) = 9.1 × 10 , corresponds to 0.25 mK Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 22 of 47 Error propagation from TPW All thermodynamic measurements currently defined as ratios with respect to TPW : The 0.25 mK uncertainty propagates to all historical thermodynamic temperature measurements 1,60 Temperature range of SPRTs 1,40 1,20 1,00 0,80 ) / mK / ) t ( 0,60 u 0,40 How well represents ITS-90 0,20 thermodynamic temperatures ? 0,00 -250 0 250 500 750 1000 additional temperature / °C Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 23 of 47 Uncertainties in thermodynamic temperature ⇒ TG-SI could not foresee any experiment where the slightly increased uncertainties of u(Tk fixed ) would present a problem Any future changes in the temperature 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 2018 : TG-SI is not aware of any new technology for a primary thermometer providing a significantly improved uncertainty u(TTPW ) ⇒ no change of the assigned value of TTPW for the foreseeable future Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 24 of 47 The International Temperature Scale and the new Definition of the Kelvin Contents: ° Introduction ° International Temperature Scale ° Consequences of the new definition ° Determination of the Boltzmann constant ° New definition of the kelvin Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 25 of 47 Measurement of temperatures Gas molecules: Equation of state for ideal gas Dielectric constant of gas Speed of sound in gas Speed of molecules: Doppler broadening Electrons: Thermal noise Light quanta: Radiation of blackbody Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 26 of 47 Determination of k p Iin Iout + _ _ + ∆ν = [2 kT /( mc 2)] 1/2 ⋅ν + _ _ _ D 0 0 + + + _ _ C(p) _ + + DBT + + _ _ _ + DCGT AGT p =kT ε (ε - 1)/ α 0 r 0 JNT 2 γ u0 = kT / m γ 2 ∆ν = cp/cV <U > = 4 kT R Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 27 of 47 Principle of AGT method standing waves in a resonator to be measured: ν frequency a dimensions via ν microwaves m or pyknometry, CMM M.R. Moldover et al. Quasi-spheres J. Res. NBS 93(2), 85-144 and microwaves: (1988) 2 ν 2006 recommended = M 2 a ( p) k c0 lim γ p→0 ν CODATA value of k 0 TTPW NA m ( p) × -6 ur = 1.7 10 (k= 1) Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 28 of 47 2013 AGT at NPL: lowest uncertainty Uncertainty contributions molar mass temperature speed of sound radius 62 mm, filled with Argon Explanation of discrepancy between NPL 2013 and LNE 2011 requires error of ≈ 85 nm on radius compared with NPL uncertainty estimate of 12 nm M. de Podesta, R. Underwood, G. Sutton, P. Morantz, P. Harris, D.F. Mark, F.M. Stuart, G. Vargha, G. Machin Metrologia 50 354-376 (2013) ∆k = 2.8 ppm ± 1.4 ppm Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 29 of 47 LNE AGT results: 2011 Argon 2015 Helium Uncertainty contributions radius 50 mm Scatter among modes L. Pitre, F. Sparasci, D. Truong, A. Guillou, L. Risegari, M. E. Himbert Int. J. Thermophys. 32 1825-86 (2011) u (k )/ k = 1.24 ppm L. Pitre, L. Risegari, F. Sparasci, M.D. Plimmer, M. E. Himbert Metrologia 52 (2015) u (k )/ k = 1.02 ppm Fundamental ConstantsMeeting Eltville4 Feb 2015 Page 30 of 47 Molar mass measurement The KRISS equipment and reference gas were used for the redetermination of the isotopic abundance of the atmospheric argon (J.-Y. Lee et al . Geochimica et Cosmochimica Acta, 2006) Lee was reference for NPL Boltzmann measurement • Largest single uncertainty in acoustic values of k with Ar originates in determination of relative