How do you really know what the temperature is? Michael de Podesta
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1 How do you really know what the temperature is? Michael de Podesta Varenna 6 th July 2016 Talk#1
2 Michael de Podesta Age: 20,645 Earth rotations : More than 56 complete solar orbits Work Lecturer in Physics for 13 years Understanding the Properties of Matter NPL for 16 years. BIPM CCT TG-CTh (Old WG4) ISTI Most accurate thermometer in the world Not Work Married with two sons (17 & 19) Protons for Breakfast International Bureau of Weights and Measures Concerned with the minutiae of temperature measurement International Surface Temperature Initiative Open Source Databank of the more than 30,000 Meteorological Station Records
3 How do you really know what the temperature is? 1. What this talk is about 2. The International Temperature Scale of Primary Thermometry 4. Measuring the speed of sound really accurately 5. What next?
4 I measured the temperature of the antenna to be K Is that correct? On NPL-SAT-1 wasn t it 168 K in 2007? Image: NASA
5 Temperature Measurement Matters We need the temperature measurement system to be: Stable Enables comparability over time Consistent Enables comparability over distance and across boundaries Additionally the system should: Not be too complicated or expensive So that people actually use it Provide measurement uncertainty required Subject to the historical trend to always make things better! But does it need to tell us the right temperature?
6 Why are they measuring the temperature? Cooking Including most engineering and manufacturing Allows a particular thermal condition to be reproduced at different times and at different places Science Same as cooking, but also we require that the number describing the thermal condition be close to the thermodynamic temperature, T
7 Science Molecular Motion Rock Thermometer How do we relate the number produced by a thermometer (e.g. 20 C) to the basic physics describing the jiggling of molecules?
8 How do you really know what the temperature is? 1. What this talk is about 2. The International Temperature Scale of Primary Thermometry 4. Measuring the speed of sound really accurately 5. What next?
9 How do you know what the temperature is?
10 You use a thermometer Michael, Don t forget to put the heater on
11 And you get it calibrated! User 1 User 2 User 3 Calibration Lab NIM NIST NPL PTB LNE-CNAM International Bureau of Weights and Measures, BIPM
12 The International Temperature Scale of 1990 Temperature Fixed Points Interpolating Devices
13 Temperature Fixed Points of ITS90 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 Now Supplemented by Metal-Carbon Eutectic Fixed Points e.g. Freezing point 1 of indium Freezing point of tin Freezing point of zinc Pd-C 1492 C Freezing point of aluminum Pt-C 1737 C Freezing point of silver Ir-C 2290 C Freezing point of gold Freezing point of copper Re-C 2474 C
14 Tin Fixed-Point Cell
15 A Temperature Fixed-Point Cell Heat Furnace Insert Thermometer Melt Crucible of Pure Metal Allow it to cool slowly While the crucible freezes, the temperature is stable T Furnace Time
16 Demo! Analogue to Digital Converter Thermocouple Hot air gun Pot of Solder
17 Tin Fixed-Point Behaviour Temperature TIN Sn-A Freeze (24-25 August 2005) furnace C5 Set pt variac 22% Bridge ratio ºC ºC Time elapsed Elapsed Time (hours)
18 The International Temperature Scale of 1990 Temperature Fixed Points Interpolating Devices
19 ITS 90 Interpolating Instruments 0.65 K to 5.0 K vapour pressure 3 He (0.65 K to 3.2 K) and 4 He (1.25 K to 5.0 K) K to ºC: platinum resistance thermometers 3.0 K to K constant volume gas thermometer ºC to Planck radiation law
20 Interpolation: sprts Photographs Resistance typically ~25 Ω Uncertainty of Measurement Resistance: ~10 µω Temperature:~ few 10 s of µk
21 Interpolation: sprt Temperature ( C) Reference Function W dref for Platinum or Resistance Ratio ( T / ) ln ln( Wref ) = A0 + Ai i= Hg In Ga i Sn Zn W Al Ag ( t 481) = ref ( t90) = C0 + Ci i 1 In ITS-90, calibration involves Measuring at the triple point of Ar water 0.0 Measuring at another fixed point Finding out the differences Temperature (K) between actual the resistance ratio and that of an ideal thermometer i
22 How does NPL know its thermometers are correct? Fixed Points Interpolating Devices
23 International Temperature Scale of 1990 Cooking Including most engineering and manufacturing Allows a particular thermal condition to be reproduced at different times and at different places Science Same as cooking, but also we require that the number describing the thermal condition be close to the thermodynamic temperature, T Describes thermal condition with numbers called T 90 Answers the cooking requirements really well Practical, Precise, Reproducible Answers the science requirements modestly well T 90 is close to thermodynamic temperature T Based on best understanding in 1990
24 How big is the difference between T and T 90?
25 T T90
26 T T 90 showing only uncertainty in T Uncertainty in T 90
27 Implication#1: The size of the kelvin Just about every thermodynamic function measured in this range is wrong by ~1 part in Slope = 0.1 mk/k
28 Implication#2
29 How do you really know what the temperature is? 1. What this talk is about 2. The International Temperature Scale of Primary Thermometry 4. Measuring the speed of sound really accurately 5. What next?
30 Measurement is Quantitative Comparison Unknown Standard of an unknown quantity with a standard quantity The temperature of the triple-point of water is humanity s temperature standard
31 The International System of Units s second kelvin ampere A K m metre The kelvin, the unit of thermodynamic temperature, is the fraction 1/ of the thermodynamic temperature of the triple point of water kilogram kg mol Cd mole candela
32 A triple point of water cell Glass vessel K Liquid Water Water Vapour Solid Water 1. Fill with water 2. Remove the air 3. Seal 4. Water Vapour fills the space 5. Chill the middle 6. Leave to equilibrate All co-exist in equilibrium
33 Triple point of water Every temperature measurement is a quantitative comparison of the level of molecular jiggling in the target with the level of molecular jiggling in a triple-point cell
34 The reproducibility of TPW No temperature measurement can ever be more accurate than the uncertainty with which the triple point of water can be realised. u TPW (k = 1) is typically 0.05 mk u R (k = 1) ~ 0.2 parts in 10 6
35 Well that s great. But how do you measure the temperature of something that is not at K (0.01 C) Good Question. It turns out to be difficult! Why? You need a thermometer whose physics you understand completely. Such as?
36 Primary Thermometers 1. The electrical noise generated by a resistor. 2. The pressure of a known amount of gas in a known volume 3. The limiting low pressure speed of sound in a gas 4. The speed distribution of the molecules in a gas 5. The dielectric constant of a low pressure gas 6. The refractive index of a low pressure gas 7. The brightness of a hot surface 8. The Rayleigh Scattering of light from a gas
37 Example#1: Johnson Noise Thermometry Random thermal motion of electrons creates minute voltage fluctuations The fluctuations are small (typically microvolts) and hard to measure. But their magnitude is predicted exactly by the Nyquist formula V V RMS t Additionally one needs to know: The measurement bandwidth The resistance of the resistor The Boltzmann constant
38 Example#2: Constant Volume Gas Thermometry Low pressure gases are nearly ideal P V = n R T Molar Density Measure a known amount of gas into a bulb of known volume. Measure the resulting pressure in the limit of low density Main technique used as basis for ITS-90, but uncertainties were probably underestimated.
39 Example#3: Acoustic thermometry Exact in the limit of low density (Speed of Sound) 2 The Molar gas constant c 2 = 5 3 R T Measure the (speed of sound) 2... M Molar mass of the gas To work out the absolute temperature in kelvins in a pure gas of known molar mass
40 Acoustic thermometry Exact in the limit of a low-density monatomic gas (Speed of Sound) 2 The Boltzmann constant c 2 = 5 3 k B T Measure the (speed of sound) 2... m Mass of a molecule To work out the absolute temperature in kelvins in a pure gas of known molar mass
41 Primary Thermometers 1. The electrical noise generated by a resistor. 2. The pressure of a known amount of gas in a known volume 3. The limiting low pressure speed of sound in a gas 4. The speed distribution of the molecules in a gas 5. The dielectric constant of a low pressure gas 6. The refractive index of a low pressure gas 7. The brightness of a hot surface 8. The Rayleigh Scattering of light from a gas
42 Acoustic thermometry (Speed of Sound) 2 The Boltzmann constant c 2 = 5 3 k B T Exact in the limit of a low-density monatomic gas m Mass of a molecule If the same gas is used at both temperatures T 1 = c2 1 T 2 T TPW c2 2 TPW
43 How to work out an unknown temperature Speed of Sound squared (Speed 2) 2 (Speed 1) 2 Basic physics tells us Limiting low-pressure value of Absolute Zero Triple Point of Water Unknown Temperature Temperature K
44 How do you really know what the temperature is? 1. The problem 2. The International Temperature Scale of Primary Thermometry 4. Measuring the speed of sound really accurately 5. What next?
45 The NPL-Cranfield Acoustic Resonator
46 Measure the speed of sound in a spherical resonator ' (,* Signals / V Halfwidth Frequency / Hz Speed of Sound!"#$ % " "& " First three constants for spheres are 3.018, 1.880, 1.396
47 Demonstration!
48 Measure the speed of sound in a spherical resonator Microphone Loudspeaker Soundcard Scope ipad oscillator
49 Measure the speed of sound in a spherical resonator Peak./0120* Signals / V Frequency / Hz Frequency (Hz)
50 End of Demonstration.
51 To get very low uncertainty Measure the radius in situ at all pressures and temperatures Simultaneously measure microwave resonances Requires a tri-axially ellipsoidal resonator with a conducting inner surface Build resonator to be very perfectly the right shape The microwave and acoustic resonances occur at the frequencies expected from their calculated eigenvalues Self Check#1: Variability of radius inferred from different microwave resonances. Self Check#2: Check the variability of " 5 inferred from different acoustic resonances. Build resonator out of copper High thermal conductivity leads to low temperature gradients High electrical conductivity leads to sharp microwave resonances. Measure the half-widths of the resonances Check that nothing unexpected is happening.
52 Machining/metrology Make the resonator very set-up perfectly Hemisphere Turning tool Large single-crystal of diamond Optical Interferometer 52
53 One hemisphere
54 Measure it s shape
55 Comparative CMM Comparative CMM with a Coordinate Measuring Machine
56 Assemble it carefully
57 Wire it up Copper Resonator 124 mm inner diameter Argon Gas
58 Stabilise the temperature Resonator Placed inside a isothermal vessel Held inside a pressure vessel Dunked in bucket Liquid Stirred Observed T = 91 µk
59
60 Measure the speed of sound in a spherical resonator ' (,* Signals / V Halfwidth Frequency / Hz? Speed of Sound!"#$ % " "& " First three constants for spheres are 3.018, 1.880, 1.396
61 Measure the Average Radius using Microwaves 678 % " $ 9%8&!"#
62 Microwave Radius Estimates in Vacuum nanometres 10 (a (21.5 C) ), nm ±3.5 nm ±9 nm Mode (TM1n)
63 Measure the speed of sound versus pressure.
64 Other temperatures Estimated Speed of sound squared (m 2 s -2 ) K 253 K 118 K p /kpa K 253 K p /kpa K p /kpa p /kpa
65 How to work out an unknown temperature Speed of Sound squared (Speed 2) 2 (Speed 1) 2 Basic physics tells us Limiting low-pressure value of Absolute Zero Triple Point of Water Unknown Temperature Temperature K
66 NPL results
67 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
68 How do you really know what the temperature is? 1. What this talk is about 2. The International Temperature Scale of Primary Thermometry 4. Measuring the speed of sound really accurately 5. What next?
69 The Second Talk! 1. Triaxial Ellipsoids Or more details 2. Boltzmann Maths 3. More on Half-widths (How we know we are right!) 4. Why the gas doesn t matter 5. T T 90
70 Slides about triaxial ellipsoids
71 Microwave resonance in a perfect sphere TM11 Resonance F 0 is inversely proportional to the radius Signal Frequency (MHz)
72 Microwave resonance in a nearly perfect sphere TM11 Resonance F 0 is in error but not possible to say by how much! Signal Frequency (MHz)
73 Microwave resonance in a triaxial ellipsoid 100 TM11 Resonance Signal Measuring F 0, F 1 and F 2 Average radius Shape Uncertainty 62 mm mm deviation Frequency (MHz) Back
74 Heat Contact (Why the gas used in a primary thermometer doesn t matter)
75 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] Back
76 Boltzmann Maths
77 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 : ; < =? ; : AB Ar : ; < = 4 ; : AB : ; < = > ; : AB
78 The big idea Look up mass of an argon molecule Carry out experiment at T TPW A < IB = > ; J= ; 4 J= ; ; < = ; > J= ; 4 J= ;? A I< EF00G H' EH2*G? A B; DB C D EF00G H' EH2*G ; Back Measure the speed of sound
79 Half-widths
80 Central frequency changes with temperature Half-Width should be exactly what we expect Signals / V Frequency / Hz
81 Acoustic Data x x K K L 7 x x x x x x x K 253 K 118 K x x x (0,9) 253 K x x 10 5 (0,9) (0,2) x x p /kpa x 10 5 (0,9) 118 K x 10 5 (0,2) x (0,2) x 10 5 p /kpa p /kpa x x x p /kpa
82 Half-Width (Experiment Theory) Parts per million of resonance frequency x g/ f (0,n) (0,7) (0,5) (0,4) (0,8) (0,2) (0,3) (0,9) f 0 = Hz expected width = Hz measured width = Hz P / kpa
83 Half-Width Experiment Theory Experiment New Theory Parts per million of resonance frequency 10 6 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 Back
84 T T 90 in 2010
85 Differences Between ITS90 & T 2010 T T 90 (K) 0.15 Steur Edsinger & Schooley Guildner & Edsinger Astrov et al, revised Kemp et al Quinn et al Fox et al Stock et al T- T 90, K Taubert et al Noulkhow et al Goebel et al Yoon et al Fischer & Jung Moldover et al Ewing and Trusler Strouse et al Ripple et al Benedetto et al Pitre et al Edler et al Labenski et al various Temperature, K Temperature (K) (T68 - T90) ITS-90, +u (k = 1) ITS-90, -u (k = 1) mean smooth function
86 Differences Between ITS 90 & T T T 90 (K) Steur Astrov et al, revised Guildner & Edsinger Edsinger & Schooley Kemp Quinn et al Moldover et al T- T 90, K Strouse et al Ewing & Trusler Benedetto et al Pitre et al Ripple et al (T68 - T90) ITS-90, +u (k = 1) ITS-90, -u (k = 1) mean Temperature, K Temperature (K) smooth function smooth function above tpw mean
87 Acoustic data since 1990
88 Moldover 1999 Maraging Steel Resonator 180 mm inner diameter Argon Gas Estimated radius with microwaves at p = 0 Argon
89 Moldover et al 1999 t ( C) T- T (mk) T 90 (K)
90 Ewing and Trusler 2000 Aluminium Resonator 80 mm inner diameter Argon Gas Estimated radius with microwaves at p = 0 Argon
91 Ewing and Trusler t 90 ( C) T- T 90 (mk) T 90 (K)
92 Strouse et al 2003 t 90 ( C) T- T 90 (mk) T 90 (K)
93 Benedetto et al 2004 Stainless Steel Resonator 120 mm inner diameter Argon Gas Estimated radius with microwaves at p = 0 Argon
94 Benedetto et al 2004 t 90 ( C) T- T 90 (mk) T 90 (K)
95 Pitre et al 2006 Copper Resonator Quasi-spherical 120 mm inner diameter Argon AND Helium Gas Estimated radius with microwaves at all pressures. Argon & Helium
96 Pitre et al 2006 t 90 ( C) T- T 90 (mk) 0 Helium and Argon T 90 (K)
97 Ripple et al 2007 t 90 ( C) T- T 90 (mk) T 90 (K)
98 All Data 10 t 90 ( C) T- T 90 (mk) T 90 (K)
99 WG4 Recommendation t 90 ( C) T- T 90 (mk) T 90 (K) Back
100 Questions #Protons4B
101 Fixed Points For length or mass standards We can make standards with a convenient length or mass. We can create multiples and subdivisions of these units. Standard Standard Standard r Unknown
102 Fixed Points for temperature No possibility to create multiples or sub-divisions of units. Nature has given us only a few stable fixed temperatures. There is no simple relationship between fixed points. Fixed Point1 Fixed Point 2 Fixed Point 3 Unknown Temperature
103 The Kelvin: SI Unit of Temperature 1/ Chosen so that the magnitude of the kelvin would be close to the magnitude of the historical unit, the degree centigrade Length Mass Time Electrical Current Temperature Luminous Intensity Mole The kelvin, the unit of thermodynamic temperature, is the fraction 1/ of the thermodynamic temperature of the triple point of water
104 Speaking tube Microphone 1 Acoustic Thermometer Loudspeaker Microphone 2 Timer
105 How do we know we are right? Level of agreement between different acoustic modes Different acoustic modes agree on the " 5 within 1 part in 10 6 Simultaneously measure microwave resonances Different microwave modes agree on the 5 within 1 part in 10 7 Excess half-width Indistinguishable from zero. Results are reproducible over many years Largest uncertainty T - T 90 is now measurement of T 90
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