Estimation of the extrapolation error in the calibration of type S thermocouples
P. Giorgio, K. M. Garrity, M. Jiménez Rebagliati, and J. García Skabar Citation: AIP Conference Proceedings 1552, 516 (2013); doi: 10.1063/1.4821394 View online: http://dx.doi.org/10.1063/1.4821394 View Table of Contents: http://scitation.aip.org/content/aip/proceeding/aipcp/1552?ver=pdfcov Published by the AIP Publishing
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Estimation of the Extrapolation Error in the Calibration of Type S Thermocouples
P. Giorgio1, K. M. Garrity2, M. Jiménez Rebagliati1, and J. García Skabar1
1 INTI, Buenos Aires, Argentina 2 NIST, Gaithersburg, MD, USA
Abstract. Measurement results from the calibration performed at NIST of ten new type S thermocouples have been analyzed to estimate the extrapolation error. Thermocouples have been calibrated at the fixed points of Zn, Al, Ag and Au and calibration curves were calculated using different numbers of FPs. It was found for these thermocouples that the absolute value of the extrapolation error, evaluated by measurement at the Au freezing-point temperature, is at most 0.10 °C and 0.27 °C when the fixed-points of Zn, Al and Ag, or the fixed-points of Zn and Al, are respectively used to calculate the calibration curve. It is also shown that absolute value of the extrapolation error, evaluated by measurement at the Ag freezing-point temperature is at most 0.25 °C when the fixed-points of Zn and Al, are used to calculate the calibration curve. This study is oriented to help those labs that lack a direct mechanism to achieve a high temperature calibration. It supports, up to 1064 ° C, the application of a similar procedure to that used by Burns and Scroger in NIST SP-250-35 for calibrating a new type S thermocouple. The uncertainty amounts a few tenths of a degree Celsius.
Keywords: extrapolation, calibration, type S thermocouples
INTRODUCTION
Platinum (Pt) based thermocouples were used to define the International Temperature Scale of 1968 in the range from [630 °C to 1064 °C]. It is well known that they are not stable, due to the oxidation, evaporation and migration of rhodium [1]. Currently they are used as secondary standards. Although it is well known that Pt-Pd thermocouples perform better than Pt-PtRh thermocouples [2-13], there are still many national laboratories that have not begun to use those types of thermocouples. It may also happen, due to limited resources, that they do neither have an appropriated high temperature furnace nor adequate fixed points to calibrate them in. Additionally type S thermocouple is still regarded in industry as a reference thermometer. The extrapolation of the calibration of type S thermocouples may be then an adequate solution for this case. We have then focused on the analysis of the error resulting from the application of this method.
each thermocouple was exposed to an electrical anneal consisted of 45 min at 1450 °C and 30 min at 750 °C, as described in >14@. The 1450 °C anneal serves to relieve mechanical strain from packing and handling, as well as to remove the rhodium oxide layer. The 750 °C anneal is designed to stabilize the lattice vacancies and produce a uniform rhodium oxide layer. The final furnace anneal is described in >14@.
Six thermocouples identified as sc-98-03, sc-98-04, sc-98-05, sc-98-06 sc-98-07 and sc-98-08 were made from the same spool of wire, produced by Sigmund Cohn. Other four thermocouples, identified as jm-8819, jm-88-20, jm-88-21and jm-88-22 were made from another identical spool of wire, produced by Johnson Matthey. All thermocouples have 0.5 mm diameter. They were calibrated at NIST, at the fixed points of Zn, Al, Ag and Au with an expanded uncertainty lower than 0.1 °C >15@.
PROCEDURE DESCRIPTION
The calibration consisted of a two-step procedure.
EXPERIMENTAL DETAILS
In the first step, the differences between the measured
electromotive forces and the corresponding NIST 175
The extrapolation procedure to calibrate type S reference values were fitted by a second order
thermocouples up to 1064 °C was applied to a set of polynomial with null constant term. In the second step
ten thermocouples. These thermocouples were a calibration curve was constructed as the fitted curve
assembled at NIST from spools of wire purchased by plus the NIST 175 reference curve [16].
NIST. The wire obtained was high purity 24 gauge
Several fixed points calibration curves were
platinum and platinum/ 10% rhodium alloy wire. The obtained by successively using the freezing
typical length of a thermocouple was 100 cm. Initially temperature of gold, tAu, silver, tAg, and aluminum, tAl,
Temperature: Its Measurement and Control in Science and Industry, Volume 8 AIP Conf. Proc. 1552, 516-519 (2013); doi: 10.1063/1.4821394 © 2013 AIP Publishing LLC 978-0-7354-1178-4/$30.00
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as the highest temperature of calibration. For example, the EMF´s measured at the Au, Ag, Al and Zn fixed points were utilized for the calculation of the calibration curve up to tAu. Similarly, another calibration curve was determined from the same Ag, Al and Zn fixed-points measurements. In this case the extrapolation error was evaluated at tAu. Finally a last fixed point calibration curve was calculated by only using the Zn and Al fixed point measurements. This curve was extrapolated to the Ag and Au points.
From the selected fixed point of highest temperature (FPHT) up to 1100 °C, two possibilities were considered for extending the calibration. The first one consisted in extrapolating the above mentioned differences by means of a straight line (linear extrapolation). This line takes the same value and derivative at the FPHT than the curve obtained by the two-steps procedure. The second possibility consisted in the extrapolation of those differences by means of the second order polynomial mentioned above (parabolic extrapolation).
In all cases the extrapolation error was evaluated as the difference between the EMF value obtained from the incomplete fixed point calibration curve, and the EMF value measured for the fixed point of higher temperature, that was not considered in the calibration curve.
RESULTS
Results are given for linear extrapolations performed successively from the Ag and the Al freezing point temperatures. The extrapolation error, evaluated as the difference between the extrapolated calibration curve and the measurement at the corresponding fixed point is presented. Then the differences resulting from the linear and parabolic extrapolations, up to 1100 °C, are presented. Finally the uncertainty evaluation is described.
Case 1 - Extrapolation from the Ag point
The extrapolation error is evaluated at tAu, as:
eAg ext
(t
Au
)
EMFext (tAu ) EMFmed (tAu )
(1)
Where eextAg (tAu) is the error at tAu resulting from the Ag point extrapolation, EMFext(tAu) is the extrapolated EMF and EMFmed(tAu) is the EMF measured at the Au fixed point.
Table 1 show errors committed at the Au point, calculated by means of equation (1). The extrapolation range is about 100 °C. The mean errors for SC and JM thermocouples are 0.04 °C and 0.07 °C respectively
and the standard deviation of the errors is 0.03 °C. The maximum error is equal to 0.1 °C for SC 98-4 thermocouple.
TABLE 1. Error, E, at tAu corresponding to the
linear extrapolation of the curve calculated by
means of FPMs at tZn, tAl and tAg.
.
TC
E at tAu (°C)
Mean E (°C)
JM 88-19
0.03
JM 88-20
0.06
JM 88-21
0.04
JM 88-22
0.02
0.04
SC 98-3
0.06
SC 98-4
0.10
SC 98-5
0.05
SC 98-6
0.02
SC 98-7
0.08
SC 98-8
0.09
0.07
Case 2 - Extrapolation from the Al point
The extrapolation error is evaluated at tAu, as:
eAl ext
(t
Au
)
EMFext (tAu ) EMFmed (tAu ) (2)
Where eextAl (tAu) is the error at tAu resulting from
the Al point extrapolation, EMFext(tAu) is the
extrapolated EMF and EMFmed(tAu) is the EMF
measured at the Au fixed point.
Similarly the extrapolation error evaluated at tAg is:
eAl ext
(t
Ag
)
EMFext (tAg ) EMFmed (tAg )
(3)
Where eextAl (tAg) is the error at tAu resulting from the Al point extrapolation, EMFext(tAg) is the extrapolated EMF and EMFmed(tAg) is the EMF measured at the Ag fixed point.
Table 2 shows the errors committed at the Au and the Ag points, using equations (2) and (3). The extrapolation range is about 300 °C when the extrapolation is done from tAl up to tAg and about 400 °C when the extrapolation is done from tAl up to tAu.
The mean errors at tAg for the SC and JM thermocouples are respectively 0.01 °C and -0.17 °C . The standard deviation of the errors is 0.10 °C. The largest difference is -0.25 °C and occurred for the thermocouple SC-98-5.
The mean errors at tAu for SC and JM thermocouples are respectively 0.06 °C and -0.16 °C. The standard deviation of the errors is 0.12 °C. The largest difference -0.27 °C occurred for the same
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thermocouple SC-98-5, as in the previous extrapolation to tAg.
TABLE 2. Error, E, at tAu and tAg corresponding to the extrapolation of the curve calculated by means of FPMs at tZn and tAl
TC
E at tAu , Mean E E at tAg Mean E
°C
(°C) (°C ) (°C)
JM 88-19 JM 88-20 JM 88-21 JM 88-22 SC 98-3 SC 98-4 SC 98-5 SC 98-6 SC 98-7 SC 98-8
0.04 0.09 0.06 0.04 -0.22 -0.08 -0.27 -0.12 -0.14 -0.14
0.06 -0.16
0.00 0.03 0.01 0.01 -0.21 -0.12 -0.25 -0.09 -0.15 -0.16
0.01 -0.16
temperature difference , °C
0 .0 0 4
0 .0 0 2
0
0.002
0.004
0.006 0.008 0.01 0.012 0.014
SC 98-3 SC 98-4 SC 98-5 SC 98-6 SC 98-7 SC 98-8 JM 88-19
0.016 0.018
JM 88-20 JM 88-21 JM 88-22
0.02 960 980 1000 1020 1040 1060 1080 1100 1120
t , °C
FIGURE 1 Temperature differences = (parabolic – linear) extrapolations, for a Zn, Al and Ag FPs calibration.
Linear vs. parabolic extrapolation
Temperature differences resulting from the application of the linear and parabolic extrapolation are shown in Figures 1 and 2.
In Fig. 1 can be seen that, for the extrapolation from the Ag point up to tAu, the difference is less than 0.010 °C and 0.002 °C for thermocouples SC and JM respectively. From the foregoing values, it follows that for both set of thermocouples the difference between the linear and parabolic extrapolations is negligible, one magnitude order smaller than the measurement uncertainty at the Au point.
As shown in Fig. 2, the difference, when extrapolating from the Al point to tAu, is less than 0.13 °C and 0.03 °C for thermocouples SC and JM respectively. For the SC thermocouples the difference is of the same order as the measurement uncertainty at the Au point.
temperature difference , °C
0 .0 3
0 .0 2
0 .0 1
0
0.01
0.02
0.03
0.04
SC 98-3
0.05
SC 98-4
0.06 0.07
SC 98-5 SC 98-6
0.08
SC 98-7
0.09 0.1 0.11 0.12 0.13
SC 98-8 JM 88-19 JM 88-20 JM 88-21 JM 88-22
0.14 660 710 760 810 860 910 960 1010 1060
t , °C
FIGURE 2 Temperature differences = (parabolic – linear) extrapolation, for a Zn and Al FPs calibration.
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UNCERTAINTY EVALUATION
The combined uncertainty (k=1), u, of the extrapolation error has been estimated for equations (1), (2) and (3) as:
u|
u2 extrap
u
2 fp
um2 o d
Where uextrap is the uncertainty assigned to the extrapolated fem. Its value was estimated as follows. First for every fixed-point temperature tfp, a new extrapolated curve for the thermocouple´s emf was calculated by incrementing the emf at tfp in its corresponding calibration uncertainty (ufp = 0.05 °C, k = 1). At a second step, the differences between the emfs obtained in this way and the not incremented emfs were calculated. These differences were then added in quadrature to obtain uextrap as a function of temperature. ufp is the measurement uncertainty at the fixed point to which the extrapolation is performed. umod is the uncertainty assigned to the extrapolation mechanism. It was estimated as the difference between the linear and the parabolic extrapolated values.
The maximum absolute value of the extrapolation error, the corresponding combined uncertainty and its components are given in tables 3 and 4 for the cases corresponding to equations (1), (2) and (3).
TABLE 3. Uncertainty components (k=1)
t
FP used
uextrap
ufp
°C
°C
tAu Zn, Al, Ag 0.07
0.05
tAu
Zn, Al
0.18
0.05
tAg
Zn, Al
0.15
0.05
umod °C
0.006 0.081 0.046
TABLE 4. Maximum error and corresponding
combined uncertainty (k=1)
t FP used Error
u
°C
°C
tAu Zn, Al, Ag 0.10
0.08
tAu
Zn, Al
0.27
0.21
tAg
Zn, Al
0.25
0.16
CONCLUSIONS
The results presented suggest that the calibration of the ten type S thermocouples in Zn, Al and Ag fixed points, could be extrapolated about 100 °C up to the Au point with an error whose maximum absolute value is about 0.10 °C (uk=1 = 0.08 °C). When the calibration is performed only by using the Zn and Al points, it might be extrapolated about 300 °C up to the Ag or even about 400 °C to the Au point, with maximum absolute values of the extrapolation errors that are respectively 0.25 °C (uk=1 = 0.16 °C) and 0.27 °C (uk=1 = 0.21 °C).
The use of linear or parabolic extrapolation is irrelevant in terms of the error due to extrapolation from the Ag to the Au point. (|Δt| < 0.01 °C at tAu) but it increases significantly up to 0.14 °C when the extrapolation is performed from the Al to the Au point.
ACKNOWLEDGEMENTS
We gratefully thank Dr. G. Strouse for encouraging us to write this paper and for helping in its revision.
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