Platinum Resistance Thermometry

INSTITUTE OF PHYSICS PUBLISHING

METROLOGIA

Metrologia 43 (2006) L45–L46

doi:10.1088/0026-1394/43/6/N04

SHORT COMMUNICATION

Platinum resistance thermometry: the conceptual difference between calibration uncertainty and measurement uncertainty M Tischler Instituto Nacional de Tecnolog´ıa Industrial, Argentina

Received 21 July 2006 Published 20 October 2006 Online at stacks.iop.org/Met/43/L45 Abstract The calibration uncertainty of a standard platinum resistance thermometer (SPRT), as reported by a calibration laboratory in terms of the resistance-ratio with respect to the triple point of water (TPW), is strictly zero at the temperature of the TPW. This does not mean that when the instrument is used to measure a temperature close to the TPW the measurement uncertainty is zero. This point is being explicitly emphasized in this short note for the benefit of colleagues at calibration laboratories and users of SPRTs.

The definition of the International Temperature Scale of 1990 (ITS-90) is based on a standard platinum resistance thermometer (SPRT), fixed points and a reference function [1]. The latter is a generic function of temperature T90 , chosen by the CCT at the time of the definition of the ITS90, representing the ratio Wr (T90 ) = R(T90 )/R(273.16 K) between the electrical resistance of an ideal platinum resistance thermometer at T90 and its resistance at the temperature of the triple point of water (TPW). Because of this definition Wr (273.16 K) = 1. The reference function serves as a mathematical tool to help realize the ITS-90 using a real SPRT. The corresponding resistance-ratio for this real SPRT, W (T90 ), differs from Wr (T90 ) by
W (T90 ) = W (T90 ) − Wr (T90 ).
W (T90 ) is determined experimentally during the calibration of the SPRT at the fixed points, as specified in [1]. Since also for the real SPRT W (273.16 K) = 1,
W (273.16 K) = 0 by definition. The uncertainty affecting the determination of
W (T90 ), and therefore the calibration of the SPRT, leads to typical results such as those represented in figure 1. It includes (among other uncertainties) the uncertainty with which each fixed point is realized, and especially the TPW which is needed in order to determine W (T90 ) at each fixed point. However, the calibration uncertainty is zero for T90 = 273.16 K, because W (273.16 K) = 1, regardless of the uncertainty with which the TPW is realized at the calibration laboratory. 0026-1394/06/060045+02$30.00

The purpose of this note is to help clarify this point that seems to produce some confusion. Having said that, it should be emphasized that this does not mean that when a calibrated SPRT is used to measure a temperature close to or at 273.16 K the resulting measurement uncertainty is zero. All it means is that if the user relies on his own TPW, the calibration uncertainty, as reported by the calibration laboratory, contributes zero at the TPW temperature. When the user of the SPRT measures a temperature, the resistance at the unknown temperature has to be measured, followed by a measurement of the resistance at the TPW, in order to calculate W (T90 ). Then, using the calibration data (i.e.
W (T90 )) Wr (T90 ) is calculated. The unknown temperature follows by inverting Wr (T90 ), which is why the definition of the ITS-90 includes the inverse function T90 (Wr ). The result is affected by many sources of uncertainty that the user of the SPRT has to take into account. Among other contributions, the calibration uncertainty, as provided by the calibration laboratory in figure 1, has to be blended in. In the particular case that the unknown temperature is close to 273.16 K, the latter is negligible (exactly zero at T90 = 273.16 K). However, the measurement uncertainty must include the contribution of the uncertainty with which the user realizes his own TPW, properly propagated. If the temperature to be measured is close to 273.16 K, and the user’s own TPW is employed, the realization accuracy of the TPW of the calibration laboratory is irrelevant. Of course, the realization

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Short Communication

Figure 1. Typical calibration uncertainty of an SPRT as determined at a calibration laboratory, as a function of the measured resistance ratio W = R(T90 )/R(273.16 K). (This figure is in colour only in the electronic version)

accuracy of the TPW of the calibration laboratory becomes increasingly important as the temperature to be measured departs from the TPW, and is already included by propagation as part of the calibration uncertainty shown in figure 1. Resistance-ratios versus resistance values. Using resistanceratios instead of just resistance values requires the use of a TPW cell. It provides the practical possibility of reducing to a minimum the temperature measurement uncertainty, since it eliminates factors that affect simultaneously numerator and

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denominator. For instance, inaccuracies in the realization of the unit of electrical resistance are eliminated and only the linearity of the resistance-measuring instrument is important. If, for whatever reason, the user of the SPRT prefers not to use his own TPW cell, he cannot use resistance-ratios. In that case, calibration uncertainties additional to that given in figure 1 have to be included by the user. These additional uncertainties originate from (a) the uncertainty with which the TPW has been realized at the calibration laboratory, (b) the uncertainties of realization and use of the electrical resistance unit, at the calibration laboratory, (c) the uncertainties of realization and use of the electrical resistance unit, at the user’s laboratory, and (d) uncertainties due to possible resistance changes in the SPRT during the period between calibration and use, part of which are also cancelled when using resistance-ratios. The additional information (not contained in figure 1) that the user requires if he does not use his own TPW realization is usually provided by the calibration laboratory in the form of the value of electrical resistance of the SPRT at the TPW measured during the calibration and a corresponding uncertainty reflecting the accuracy of the TPW realization, the accuracy of the resistance measurements and the stability of the SPRT, during the whole calibration process. Finally, to further illustrate the main point of this note, a somewhat analogous situation using a multimeter in order to measure a voltage may be drawn. Since the multimeter can be zeroed by employing the user’s own short circuit before any measurement, if the voltage to be measured happens to be close to 0 V, the calibration uncertainty provided by the calibration laboratory does not contribute to the measurement uncertainty. The user has to realize and evaluate the uncertainty of his own short circuit, which is a voltage reference point, like the TPW is a temperature reference point. Choosing not to use a short circuit before every measurement, but relying on the offset determined during the calibration of the instrument, is bound to increase the measurement uncertainty.

Reference [1] Preston-Thomas H 1990 Metrologia 27 3–10

Metrologia, 43 (2006) L45–L46