Special Cases
Platinum RTDs
Thermocouples
Liquid in Glass
Platinum RTD Alpha
z The temperature - resistance curve of a
platinum RTD (or platinum resistance
thermometer, PRT) is dependant on the level of
purity of the platinum itself
z Impurities almost always increase the resistivity
of a metal while simultaneously reducing its
temperature coefficient of resistance (TCR)
Platinum RTD Alpha
z The higher the TCR, the purer the metal
z There are three grades of wire used in PRTs
z The unit of measure is alpha (α) and is
calculated as shown:
R(100 oC ) − R(0 o C )
α=
100 R(0 o C )
1
Platinum RTD Alpha
z α = 0.003926/°C: SPRT grade wire for high accuracy
applications
z α = 0.003916 /°C: Secondary grade wire primarily
used in the US for laboratory instruments
z α = 0.00385 /°C: Industrial grade wire with a large
doped impurity content, used in the ASTM and IEC
standards
PRT Curve Fitting
z The temperature - resistance relationship of a
PRT is not perfectly linear, it is described by the
Callendar Van Dusen equation:
R ( t ) = R (0 oC)(1 + At + Bt 2 + C (t − 100) t 3 )
z Where C = 0 above 0 °C
PRT Curve Fitting: Overview
z The values for the coefficients A, B, & C are
specified by the ASTM, IEC, or the
manufacturer of the PRT if the PRT does not fit
a standardized curve
z The fit to a standardized curve is often not
sufficiently accurate for calibration work
2
PRT Curve Fitting: Overview
z Recall the ASTM PRT accuracy classes
ASTM (IEC-751) class A
= ±[0.13 + 0.0017|t|]°C
@ 100 °C = [0.13 + 0.0017|100|] = ±0.30 °C
ASTM (IEC-751) class B
= ±[0.25 + 0.0042|t|]°C
@ 100 °C = [0.25 + 0.0042|100|] = ±0.67 °C
PRT Curve Fitting: Overview
z To improve the accuracy, the PRT can be
calibrated and the curve redefined by
calculating coefficients specific to the PRT.
z Fitting data to a curve in this manner is an
exercise in simultaneously solving a set of
equations
PRT Curve Fitting: Overview
z Software exists that simplifies this exercise
allowing the operator to:
– Chose the type of curve (CVD, ITS-90, polynomial,
etc.)
– Choose the number of calibration points
– Calculate the precision of the fit obtained
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PRT Curve Fitting: Procedure
z Step 1: Rearrange the equation into a
form which is easier to solve
R ( t ) = R (0 oC)(1 + At + Bt 2 + C (t − 100) t 3 )
becomes W ( t ) = R ( t )
R ( 0)
and W (t ) = 1 + At + Bt 2 + Ct 3 ( t − 100)
PRT Curve Fitting: Procedure
z Step 2: Obtain the data
Temperature Measured Ω
0.000°C 99.9791
50.082°C 119.7772
100.115°C 139.2499
149.988°C 158.3689
200.022°C 177.2497
PRT Curve Fitting: Procedure
z Step 3: Calculate W
Temperature Measured UUT R(0) UUT W
°C Resistance
50.062 119.7772 1.198022
100.095 139.2499 1.392790
149.943 158.3689 ÷ 99.9791 = 1.584020
200.022 177.2497 1.772868
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PRT Curve Fitting: Procedure
z Step 4: Compute simultaneous solution
W t 1 = 1 + A ( t 1 ) + B ( t 1 ) + C ( t 1 ) ⋅ (t 1 − 1 00 )
2 3
W t 2 = 1 + A ( t 2 ) + B ( t 2 ) + C ( t 2 ) ⋅ (t 2 − 100 )
2 3
W t 3 = 1 + A ( t 3 ) + B ( t 3 ) + C ( t 3 ) ⋅ (t 3 − 100 )
2 3
W t 4 = 1 + A ( t 4 ) + B ( t 4 ) + C ( t 4 ) ⋅ (t 4 − 100 )
2 3
PRT Curve Fitting: Procedure
z Step 4: Compute simultaneous solution
– Iteration, Least squares, or Matrix math
Matrix 1 Matrix 2
Wt1 − 1 t1 (t1 ) 2
W − 1
T2 t 2 (t2 ) 2
WT3 − 1 t3 (t 3 ) 2
WT4 − 1 t 4 (t4 ) 2
PRT Curve Fitting: Procedure
z Step 4: Compute simultaneous solution
Exact Solution S o l u ti o n = M a tr ix 2 − 1 ⋅ M a t r i x 1
Overdetermined Solution
( )
Τ −1 Τ
Solution = Matrix 2 • Matrix 2 • Matrix2 • Matrix1
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PRT Curve Fitting: Procedure
z Step 5: Calculate residuals
tem perature
PRT Curve Fitting: Procedure
z Step 5: Calculate residuals
Calculated Measured Residuals Residuals
Resistance Resistance (Ω) (°C)
119.7756 119.7772 -0.0016 -0.004
139.2561 139.2499 0.0062 0.016
158.3619 158.3689 -0.0070 -0.018
177.2520 177.2497 0.0023 0.006
PRT Curve Fitting
Questions ?
6
Thermocouple Recalibration
z Can thermocouples be recalibrated?
z Should thermocouples be recalibrated?
z How can you determine if a thermocouple
meets spec in the application?
z Can accuracy be improved by curve fitting?
Thermocouple Recalibration
z Can thermocouples be recalibrated?
– Yes: If a thermocouple is used in an
environment which is benign to the
thermocouple then it may benefit by
recalibration.
– No: If the thermocouple is used in an
environment which is harmful to the
thermocouple, then recalibration
may provide misleading results.
Thermocouple Recalibration
z Can thermocouples be recalibrated?
Furnace
Readout
Gradient
Region
Constant
Temperature
Region
Temperature
Profile
7
Thermocouple Recalibration
z Can thermocouples be recalibrated?
Furnace
Readout
Gradient
Region
Constant
Temperature
Region
Temperature
Profile
Thermocouple Recalibration
z Should thermocouples be recalibrated?
– Only if the thermocouple is used in an application
that does not introduce inhomogeneity
– If the temperature profile in the calibration furnace is
very similar to the temperature profile in the
application
– If the homogeneity will be tested also
Thermocouple Recalibration
z How can you determine if a thermocouple
meets spec in the application?
– In situ calibration using a reference thermometer
– In situ calibration using a reference temperature
calibrator such as a drywell or micro-bath
8
Thermocouple Recalibration
z Can accuracy be improved by curve fitting?
– Thermocouples are not stable chemically
– The rate of degradation increases rapidly with
increases in temperature
– Inhomogeneities evolve in most applications
Thermocouple Recalibration
z Can accuracy be improved by curve fitting?
– The accuracy will be improved in the same manner
as with PRTs, however
the improvement will only be realized to the extent
that the thermocouple remains in the same physical
and chemical condition as it was during calibration
Thermocouple Recalibration
z Can accuracy be improved by curve fitting?
– Not very much and not for very long
9
Thermocouple Recalibration
Questions ?
Liquid in Glass Characterization
z Improved accuracy can be obtained from liquid
in glass thermometers if they are characterized
z To fully realize the improvement in accuracy,
certain procedures must be followed during
calibration and use
Liquid in Glass Characterization
z Characterization exploits the stability of the
relationship between the liquid and glass
system in the LIG thermometer, variables in
this system which may be insignificant in
normal use become significant at increased
levels of accuracy
10
Liquid in Glass Characterization
z Changes in bulb volume and stem cross
section and length with temperature
– The glass bulb and stem expand and contract as
the thermometer is cycled in temperature
– The thermometric liquid reacts almost
instantaneously, the glass will take up to 72 hours to
return to its relaxed dimensions
Liquid in Glass Characterization
z Measurements made at a
lower temperature than a
previous measurement will
indicate a lower, incorrect
temperature -the correction
will be invalid
Liquid in Glass Characterization
z Since most of the volume
change is in the bulb, ice
point corrections can be
made and applied
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Liquid in Glass Characterization
z Changes in bulb volume with time
– Glass is a super-cooled liquid and will flow very
slowly (imperceptibly) over tome.
– The the glass flows toward the bulb increasing the
wall thickness and decreasing the bulb volume
– Thermometers should be stored horizontally to
minimize this effect
Liquid in Glass Characterization
z Since the volume change
affects the bulb only it
creates an offset.
z Ice point corrections can
be applied to correct for
bulb volume offsets
Liquid in Glass Characterization
z Annealing
– Liquid in glass thermometers are annealed at a
temperature which is higher than the highest
temperature that the thermometer is intended to
measure
– Reuniting the liquid column at a temperature which
is higher than the annealing temperature will change
the glass and may cause it to be unstable
12
Liquid in Glass Characterization
z Annealing
– Ice point measurements should be made after the
column is reunited and the bulb has returned to its
relaxed state
– If the ice point value has changed significantly, the
thermometer may be damaged and must be
observed carefully before being placed back into
use
Special Cases
Questions ?
13
