Fundamental Temperature Measurement: Re-defining the Boltzmann Constant How do you really know what the temperature is? Michael de Podesta

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1 Fundamental Temperature Measurement: Re-defining the Boltzmann Constant How do you really know what the temperature is? Michael de Podesta NPL December 2014

2 Also my wonderful colleagues Gavin Sutton, Robin Underwood, Gordon Edwards, Graham Machin, Richard Rusby, David Flack, Andrew Lewis, Michael Perkin, Stuart Davidson, Kevin Douglas, Rob Ferguson, David Putland, Anthony Evenden, Louise Wright, Eric Bennett, Alan Turnbull, Gareth Hinds, Phil Cooling, Gergely Vargha, Martin Milton, Michael Parfitt, Peter Harris, Leigh Stanger and others

3 Measurement brings the world into focus

I measured the temperature of the antenna to be 148.

4 I measured the temperature of the antenna to be K Is that correct? On NPL-SAT-1 wasn t it K in 2007? Image: NASA

5 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time: one last thing

6 Measurement is Quantitative Comparison Unknown Standard of an unknown quantity with a standard quantity

7 The Challenge Molecular Motion A thermometer How do we relate the number produced by a thermometer (e.g. 20 º C) to the basic physics describing the jiggling of molecules?

8 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time:one last thing

9 The International System of Units s Sèvres: We have a problem K m A The definition of the kelvin is not connected to the units which define energy! kg The kelvin, the unit of thermodynamic temperature, is the fraction mol 1/ of the thermodynamic temperature of the triple point of water Cd

10 Triple point of water Every temperature measurement is a quantitative comparison of T TPW the level of molecular jiggling in the target with the level of molecular jiggling at this point in a triple-point cell

11 The NEW International System of Units ν 133 Cs Energy (joule) e s A c m kg h K cd Cd k B K N A mol

12 The NEW International System ν of Units 133 Cs k B s c K m e A The definition of the kelvin is now connected to the units which define energy! kg h mol Cd N A K cd

$The NEW International System ν of Units k B The kelvin, the 133 unit Cs of thermodynamic temperature, is the fraction 1/273.$

13 The NEW International System ν of Units k B The kelvin, the 133 unit Cs of thermodynamic temperature, is the fraction 1/ of s the thermodynamic temperature c of the triple point of water K m e A The kelvin, the unit of thermodynamic temperature, is such that the Boltzmann constant has the exact kg value h k B = XX joules per kelvin mol Cd N A K cd

14 From 2018 T TPW will still be a useful reproducible temperature But it will not define what we mean by one degree Every temperature measurement will be a quantitative comparison of the energy of molecular jiggling in the target with one joule of energy

15 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time:one last thing

16 Changing from old to new We want the size of the kelvin to stay the same: T TPW will still be K How many joules of energy does a molecule possess at T TPW? Value of the Boltzmann constant k B is fixed in the new SI. What is value of the Boltzmann constant k B in the current SI? New kelvin Absolute Zero Old kelvin

17 How can we estimate the Boltzmann Constant?

18 Heat Hot Object Cold Object When materials touch, fast atoms slow down, slow atoms speed up until Average energy per molecule is equal. [Actually what equalises is the average energy per accessible degree of freedom]

19 Warning! Next two slides contain equations!

20 We measure in argon gas Molecular motions are simple in a gas We can approach ideal gas conditions at low pressure In an ideal gas the internal energy is just the kinetic energy of the molecules 1 2 m v z 2 = 1 2 k BT Ar 1 2 m v y 2 = 1 2 k BT 1 2 m v x 2 = 1 2 k BT

21 The big idea Look up mass of an argon molecule Carry out experiment at T TPW 1 k B = m 3T v x 2 + v 2 y + v2 2 m v x 2 + v 2 y + v2 z = 3 k 2 k B = 3m z B T 2 speed of sound 5T 9 5 speed of sound 2 Measure the speed of sound

22 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time:one last thing

23 Speaking tube Microphone 1 Acoustic Thermometer Loudspeaker Microphone 2 Timer

24 The NPL-Cranfield Acoustic Thermometer Measures the speed of sound in a spherical resonator

25 All required to u 1 ppm. a, radius of sphere To be measured Resonant Frequency To be measured c 2 z a n, l f n, l Eigenvalues Calculable for known shapes 25

26 Machining/metrology Ultra-Precision Manufacture set-up Hemisphere Turning tool Interferometer 26

27 Comparative CMM

28 Comparative CMM Comparative CMM CMM Position 1 CMM Position 2

29 All required to u 1 ppm. a, radius of sphere To be measured Resonant Frequency To be measured c 2 z a n, l f n, l Eigenvalues Calculable for known shapes 29

31 Resonator Placed inside a isothermal vessel Held inside a pressure vessel Dunked in bucket Liquid Stirred

32 Temperature Observed ΔT = 91 μk µk

33 Thermometer Reading ( C) Temperature bottom L&N bottom equator16 elapsed hours top L&N top

34 Amplitude (V) Acoustic Spectrum Argon T = 30 C (0,3) (0,2) (2,1) (1,1) Frequency / Hz

35 Acoustic Resonance

36 Acoustic Resonance Signals / V Centre Frequency Hz ± Hz Temperature C ± C Frequency / Hz

37 All required to u 1 ppm. a, radius of sphere To be measured Resonant Frequency To be measured c 2 z a n, l f n, l Eigenvalues Calculable for known shapes 37

38 Microwave Resonance

39 Microwave Radius Estimates in Vacuum (a (21.5 C) ), nm nanometres 10 0 ±3.5 nm ±9 nm Mode (TM1n)

40 All required to u 1 ppm. a, radius of sphere To be measured Resonant Frequency To be measured c 2 z a n, l f n, l Eigenvalues Calculable for known shapes 40

41 Speed of Sound Squared c 2 (m 2 s -2 ) Amplitude (V) Data for c 2 c2 EXP 95,000 94, Argon T = 30 C (0,2) (2,1) (1,1) (0,3) , Frequency / Hz c ,850 94,800 (0,2) (0,3) (0,4) (0,5) (0,7) k B is inferred from (0,8) this intercept (0,9) 94, Pressure (kpa)

42 k B - NPL (parts in 10 6 ) k B - CODATA (parts in 10 6 ) Result 1 u(k =1) = This Work NIST 1988 LNE

43 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time:one last thing

44 We don t know we are right!

45 Data for c 2 Speed of Sound Squared c 2 (m 2 s -2 ) c2 EXP 95,000 94,950 94,900 c ,850 94,800 (0,2) (0,3) (0,4) A factor 3 lower than (0,5) anyone else! (0,7) Spread of estimates (0,8) is just 0.18 parts per (0,9) million 94, Pressure (kpa)

46 Signals / V Central frequency changes with temperature Half-Width should be exactly what we expect When f 0 = Hz expected width = Hz measured width = Hz 0 Frequency / Hz

47 Half-Width (Experiment Theory) Parts per million of resonance frequency 10 8 (0,7) 10 8 (0,7) 10 6 x g/ f (0,n) (0,5) (0,4) (0,8) (0,2) (0,3) (0,9) 10 6 x g/f (0,n) (0,5) (0,4) (0,8) (0,2) (0,3) (0,9) P / kpa f 0 = Hz expected width = Hz measured width = Hz Pressure (kpa)

48 Half-Width Parts per million of resonance frequency Experiment Theory Experiment New Theory x g/ f (0,n) (0,2) (0,3) (0,4) (0,5) (0,7) (0,8) (0,9) P / kpa 10 6 x g/f (0,n) (0,2) (0,3) (0,4) (0,5) (0,7) (0,8) (0,9) Pressure (kpa) f 0 = Hz expected width = Hz measured width = Hz

49 How do you really know what the temperature is? 1. Measurement 2. The International System of Units (The SI) 3. The change to the New SI 4. Measuring the speed of sound really accurately 5. How do we know we are right? 6. If we have time:one last thing

50 How do you know your thermometer is correct?

51 User 1 User 2 User 3 Calibration Lab NIM NIST NPL PTB LNE-CNAM International Bureau of Weights and Measures, BIPM

52 The International Temperature Scale of 1990 Temperature Fixed Points Interpolating Devices

53 Temperature Fixed Points of ITS90 How do we know that? T(K) T (ºC) Triple point of hydrogen Triple point of neon Triple point of oxygen Triple point of argon Triple point of mercury Triple point of water Melting point 1 of gallium Freezing point 1 of indium Freezing point of tin Freezing point of zinc Freezing point of aluminum Freezing point of silver Freezing point of gold Freezing point of copper

54 How to work out the Freezing point of Tin K Speed of Sound squared (Speed 2) 2 (Speed 1) 2 Basic physics tells us Speed of Sound 2 Temperature Absolute Triple Point Freezing Point Temperature Zero of Water of Tin

55 T- T 90 (mk) How wrong is ITS 90? 10 5 NPL Preliminary PRELIMINARY DATA t 90 ( C)

56 How do you really know what the temperature is? Inter-comparisons and calibrations according to ITS-90 Make sure everyone agrees Fundamental Measurements Measure the errors in ITS-90

57 The Challenge? Molecular Motion Primary Thermometer A thermometer How do we relate the number produced by a thermometer (e.g. 20 º C) to the basic physics describing the jiggling of molecules?

58 How do you really know what the temperature is? 1. Measurement The definition of the units of temperature (the kelvin and the degree Celsius) 2. The International is about System to change. of Units (The SI) 3. The From change 2018, to temperature the New SI measurements will be fundamentally linked to the units of energy. 4. Measuring the speed of sound really accurately Every temperature measurement you make 5. How is do linked we know to our we fundamental are right? understanding of the thermal properties of matter 6. If we have time:one last thing

How do you really know what the temperature is? Michael de Podesta

How do you really know what the temperature is? Michael de Podesta TECO: Madrid September 2016 GOLDEN RULE OF TALKS One talk: one thing This Talk: TWO THINGS! Thing 1: The definitions of the SI units of