Temperature Measurements
According to the International
Temperature Scale of 1990 and
Associated Uncertainties
PB
Steffen Rudtsch
7.42
230th PTB Seminar Conductivity and Salinity
Content

Thermodynamic temperatures and temperature scales
Definition of the unit kelvin
ITS-90 and fixed points
Resistance thermometry
Error sources and uncertainty budget
Steffen Rudtsch
Physikalisch-Technische Bundesanstalt
Definition of a Temperature Scale
Physikalisch-Technische
Bundesanstalt
Problem: Temperature is an intensive
thermodynamic property (value does not depend
on the amount of the substance).
How can we define a universal temperature scale
whose properties does not depend on specific
substances or thermometers?
W. Thomson (later Lord Kelvin, 1848)
 Absolute zero and a second fixed
point
 Efficiency of reversible Carnot-cycle
T1=T2(1-η)
Measurement of Thermodynamic Temperatures
Physikalisch-Technische
Bundesanstalt
Gas thermometer: equation of state of an ideal gas
T
pV
k = 1,38065·10-23 J/K
p V = N k T bzw.
=
Ttpw ptpwVtpw
(Boltzmann constant)
V=const., p→0
N: Number of atoms
Dielectric constant gas thermometer (DCGT)
N
ε = ε0+α0
V
ε − ε0
p= kT
α0
α0- atomic polarisibility
T
p ε tpw − ε 0
=
⋅
Ttpw ptpw ε − ε 0
Measurement of the change in capacitance of a gas-filled
capacitor after evacuation
Thermodynamic Temperatures
Basis: Fundamental Physical Laws
Gas Properties:
- Equation of state of an ideal gas
- Dielectric constant
- Speed of sound
- Spectral-line Doppler broadening
Electron Gas:
- Thermal noise
Photons:
- Total radiation of a blackbody
- Spectral emission of a blackbody
Physikalisch-Technische
Bundesanstalt
International Temperature Scale of 1990
 Definition of the unit kelvin
 Fixed points of the ITS-90
 Interpolation instruments
 Interpolation equations
Physikalisch-Technische
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Definition of the Kelvin and Triple Point of Water
Physikalisch-Technische
Bundesanstalt
The kelvin, unit of thermodynamic temperature,
is the fraction 1/273.16 of the thermodynamic
temperature of the triple point of water.
13. CGPM (1967): Metrologia, 4 (1968), 147
Ttpw = 273,16 K (Definition)
ptpw = 611,66 Pa
Fixed Points of the ITS-90
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)
e-H2 (vp)
e-H2 (vp)
e-H2 (tp)
4
He (vp)
1084,62 °C
1064,62 °C
961,78 °C
660,323 °C
419,527 °C
231,928 °C
156,5985 °C
29,7646 °C
273,16 K
234,3156 K
83,8058 K
54,3584 K
24,5561 K
≈ 20,3 K
≈ 17,0 K
13,8033 K
4,2221 K
∆ Tth.dyn /mK ∆ TITS-90 /mK
60
50
40
25
13
5
3
1
0
1,5
1,5
1
0,5
0,5
0,5
0,5
0,3
15
10
3
2
1
1
1
0,25
0,1
0,25
0,3
0,4
0,4
0,4
0,4
0,4
0,1
Fixed-Point Measurement
Physikalisch-Technische
Bundesanstalt
ITS-90: Interpolation Instruments and Equations
0,65 K to 5,0 K:
Vapour pressure 3He und 4He
3,0 K to 24,5561 K:
Gasthermometer (He)
T90 / K = A0 +
9
∑
i= 1
Physikalisch-Technische
Bundesanstalt
 ln( p ) / Pa - B 
Ai 

C


i
a + bp + cp 2
T90 =
1 + Bx ( T90 ) N / V
 T90 / K - 754,15 
13,8033 K bis 961,78 °C:
Wr ( T90 ) = C0 + ∑ Ci 

481

Standard Platinum Resistance Thermometer i = 1 
9
above 961,78 °C:
Radiation Thermometer
(
)
Lλ ( T90 )
exp c2 [ λ T90 ( X ) ] − 1
=
−1
Lλ [T90 ( X ) ]
exp c2 [ λ T90 ] − 1
−1
(
)
X: Ag, Au, Cu; c2=0,014388 m·K
i
Standard Platinum Resistance Thermometer
Physikalisch-Technische
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Platinum wire of highest purity
 Induction free winding,

Free of mechanical stress
Specific gas filling in order to control oxidation
Special heat treatment....
Resistance Thermometers
IPRT
Physikalisch-Technische
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SPRT
Reference Function for Resistance Thermometers
Physikalisch-Technische
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[
Callendar-van Dusen: R( t ) = R (0 ° C) ⋅ 1 + At + Bt 2 + C (t − 100)t 3
ITS-90 (SPRT calibration)
Determination of
resistance ratio W is required.
- extrapolated to I = 0 mA
Reference Function
0 °C to 961.78 °C:
]
RSPRT ( Fixed Point ) R
W =
=
RSPRT (TPW)
R0
 T90 / K - 754,15 
Wr ( T90 ) = C0 + ∑ Ci 

481


i= 1
9
i
 Wr (T90 ) − 2,64 
T90 / K = 273,15 + D0 + ∑ Di 

1,64


i=1
9
i
Calibration of Platinum Resistance Thermometers
Purity of the Platinum:
Physikalisch-Technische
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W(29,7646 °C) ≥ 1,1807
W(-38,8344 °C) ≤ 0,844235
Calibration Certificate for SPRTs:
Deviation Function (deviation from reference function)
W (T90 ) − Wr (T90 ) = a (W − 1) + b(W − 1) +
2
5
∑ c [ ln(W )]
i= 1
i
2+ i
SPRT-Calibration: Uncertainty Budget
Physikalisch-Technische
Bundesanstalt
Quantity
u(TGa)
mK
u(TIn)
mK
u(TSn)
mK
u(TZn)
mK
u(TAl)
mK
u(TAg)
mK
Impurities
0,06
0,25
0,31
0,40
0,65
Hydrost. Pressure
0,01
0,02
0,02
0,54
0,54
0,02
0,02
0,08
Gas Pressure
0,01
0,10
0,08
0,12
0,30
0,30
Standard Resistor
0,01
0,01
0,01
0,01
0,01
0,01
Bridge
0,02
0,11
0,12
0,16
0,20
0,25
TPW
0,08
0,09
0,11
0,15
0,20
0,28
Self-heating
0,05
0,15
0,20
0,20
0,20
0,20
Immersion
0,01
0,20
0,10
0,10
0,10
0,10
Fixed Point Value
0,03
0,06
0,06
0,06
0,20
0,20
Type B (combined)
0,12
0,40
0,43
0,64
0,65
0,87
Type A
0,05
0,20
0,15
0,15
0,30
0,30
Standard Uncertainty
0,13
0,45
0,45
0,66
0,66
0,71
0,92
PTB-Budget
Resistance Measurement
Physikalisch-Technische
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Resistance Thermometer
typically between 25 Ω and 10 kΩ
1. Digital Multimeter (8 ½ digits)
U(T) ≈5 mK
Problems:
- Stability reference resistor
- Self-heating
- Offset thermovoltages
2. Potentiometric Method
U(T) < 1 mK
High-precision standard resistor RS
including its temperature control
different currents are used
 d RS 

 < 2 ⋅ 10 − 7 a − 1
 d t  rel
I ≈ 1 mA
RS
RT
Resistance Measurement
 RT 
Highest level with
 < 2 ⋅ 10 − 8
U 
commercial equipment
 RS 
Physikalisch-Technische
Bundesanstalt
U(T) < 5 µK
AC-Bridges
Inductive voltage divider (ratio transformer)
typically 25 Hz or 30 Hz
Manufacturer: Automatic Systems Laboratories (ASL)
“DC”-Bridges
Current comparator (current reversal necessary)
Manufacturer: Measurement International, Guildline
Measurement Errors and Corrections
1. Self Heating of the Resistance Thermometer
Physikalisch-Technische
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Typical Measurement Errors
Physikalisch-Technische
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1. Stability of the Thermometer
- resistance might be changed by mechanical shock
or oxidation (SPRT, IPRT)
- Drift even after careful heat treatment (Thermistors)
6. Hysteresis
up to ∆T = 500 mK at IPRTs (not at SPRTs)
- depend on thermal “history” of the IPRT
- caused by thermal expansion of the ceramic substrate / powder
Thermal Measurement Errors
Physikalisch-Technische
Bundesanstalt
A contact thermometer measures only its own temperature.
4.
Change of the temperature of the investigated object
- heat conduction
- heat storage/capacity
5.
Heat dissipation and thermal coupling
i.e. thermometer and object have different temperatures
6.
Dynamic behavior and thermal lag
7.
Radiation errors
Heat Dissipation and Thermal Coupling
TFurnace
TEnvironment
Physikalisch-Technische
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Dynamic Behavior and Thermal Lag
Physikalisch-Technische
Bundesanstalt
T2
T1
The dynamic behavior depend on the construction of
the thermometer and the thermal coupling between object
and thermometer.
Example of an Uncertainty Budget
Physikalisch-Technische
Bundesanstalt
Calibration of a resistance thermometer in a liquid bath
(more details in DKD-R 5-1)
tx = tN + δtKal + δtDrift + cRδRR + δtBr + δtWaN + δtWAP + δtEWN + δtHom + δtStab
tx:
ITS-90 temperature of the resistance thermometer to be calibrated
tN: Mean of the temperature of the SPRT (reference)
δtKal: Correction based on the SPRT calibration
δtDrift: Correction based on the drift of the SPRT
cRδRR: Correction based on the calibration of the standard resistor
c R:
Sensitivity of the bridge
δtBr: Correction based on the bridge calibration
δtWaN: Correction based on heat conduction of the SPRT
δtEWN: Correction based on self-heating of the SPRT
δtWAP: Correction based on heat conduction of the resistance thermometer
δtHom: Correction based on the in-homogeneity of the bath
Example of an Uncertainty Budget
Physikalisch-Technische
Bundesanstalt
Calibration of a resistance thermometer in a liquid bath
(more details in DKD-R 5-1)
Quantity
Estimate
Standard
uncertainty
Probability
distribution
Sensitivity
coefficient
Uncertainty
contribution
tN
Temperature SPRT
180.234 °C
1.2 mK
Normal
1
1.2 mK
δtKal
Calibration SPRT
0K
7.5 mK
Normal
1
7.5 mK
δtDrift
Drift SPRTRef
0K
3.5 mK
Rectang.
1
3.5 mK
δRR
Standard Resistor
0Ω
0.07 mΩ
Normal
10 K/Ω
0.7 mK
δtBr
Bridge
0K
1.5 mK
Normal
1
1.5 mK
δtWaN
Heat cond. SPRT
0K
1.2 mK
Rectang.
1
1.2 mK
δtHom
Homogeneity bath
0K
4.6 mK
Rectang.
1
4.6 mK
δtStab
Stability bath
0K
3.5 mK
Rectang.
1
3.5 mK
tx
Temperature
180,234 °C
10 mK
Summary

Definition of the unit kelvin

International Temperature Scale of 1990

Sensors and instruments

Sources of uncertainty

Uncertainty budget
Physikalisch-Technische
Bundesanstalt