Modelling and Measurand Identification Required for Defining the Mise en Pratique of the kelvin Franco Pavese INRIM, Thermodynamic Division, Torino, Italy f.pavese@inrim.it F.Pavese 1
Temperature scales Temperature, is an intensive quantity, requiring: the definition of a scale as the measurement standard beside the definition of the unit the measurement of a quantity different from temperature i.e. indirect measurement, different measurand(s) From 1927 on, the international written standard changed from the thermodynamic scale into one called practical temperature scale, of an empirical type. However, a sufficient degree of uniqueness of the temperature values obtained with the latter scale was guaranteed by limiting the differences between the thermodynamic temperature scale and the empirical scale to values lower than the combined uncertainties of the realisations (exceptions applied). In all instances, the definition of a practical temperature scale (more recently labelled simply as international ) also entails preliminary work for implementing the thermodynamic temperature scale, but the two types of scales are of distinct nature and require studies to establish the differences between them. F.Pavese 2
Temperature scales This presentation will illustrate the following issues: Meaning of mise en pratique of the unit and consequences for the definition of temperature scales General classes of models used by the temperature scales Suitable for artefacts (class 1) vs. physical states or laws (class 2) Model parameters: variables vs. stipulated values Exact identification of the measurand in different scale realisations Classes of standards (Special status standards) Standards with a stipulated value (Ambiguities arising from the written standard) The measurand in (key) comparisons The measurand in different ways to implement the prescriptions of the written standard Realisation vs. approximation Realisation vs. conservation and dissemination F.Pavese 3
The kelvin and the Mise en pratique of the unit - 1 In 2005, the CIPM, on input of the CCT, made a substantial change in the definition of the written standards of the unit of the quantity temperature, the kelvin, by transforming all temperature written standards (at present the temperature scales ITS-90 and PLTS-2000) into the mise en pratique of the kelvin. Thermometers calibrated using different mise en pratique implementations should provide the same numerical value for temperature when placed all together in the same isothermal enceinte, within the stated level of uncertainty. The usual way to express this concept is that the different mise en pratique implementations must provide compatible measures in order to preserve the uniqueness of the definition of the standard. F.Pavese 4
The kelvin and the Mise en pratique of the unit - 2 Contrarily to the testing field, the metrologist was already entitled to use its own method to implement the definition of the written standard. The metrologist is now allowed, in principle, to relax also the requirement that a single definition has to be used to measure temperature in a certain range: much more flexibility is now provided, in perspective, by choosing the definition, in a set made available for the implementation of the mise en pratique, considered more convenient in a particular Institution for the realisation of its standards. The only requirement for this choice is the definition being included in the list of the allowed definitions of the mise en pratique : the only technical requirement for inclusion in this list is that there is a firm experimental evidence of the degree of equivalence between the allowed definitions, determined by the level of their compatibility with each other. F.Pavese 5
The kelvin and the Mise en pratique of the unit - 3 Compatibility of implementation methods with each other can be considered the only necessary metrological requisite of the mise en pratique. Definition of Compatibility VIM III (2.47-2007) property of a set of measurement results for a specified measurand, such that the absolute value of the difference of any pair of measured quantity values from two different measurement results is smaller than some chosen multiple of the standard measurement uncertainty of that difference, noting that Metrological compatibility of measurement results replaces the traditional concept of staying within the error, as it represents the criterion for deciding whether two measurement results refer to the same measurand or not. If in a set of measurements of a measurand, thought to be constant, a measurement result is not compatible with the others, either the measurement was not correct (e.g. its measurement uncertainty was assessed as being too narrow) or the measured quantity changed between measurements. F.Pavese 6
The kelvin and the Mise en pratique of the unit - 4 In fact, the basic requisite of any written standard is to be unique within a given uncertainty. For temperature, already there were several intrinsic reasons in a single written standard limiting uniqueness. Until 2005, the uncertainty to be attributed to realisation of a specific Scale according to its definition was determined by the state-of-the art uncertainty of its experimental implementation and by those non-uniqueness components intrinsic to the definition itself, which in several ranges were the major source of uncertainty. All significant deviations between realisations of the same definition, detected through comparison exercises, were attributed to unresolved systematic effects, i.e., to systematic errors in the realisations, to be studied and eventually eliminated by the relevant NMI(s). Now, significant deviations could also arise from the use of different ways to implement the mise en pratique, if compatibility is not ensured. F.Pavese 7
The kelvin and the Mise en pratique of the unit: 1 - Inclusion of the thermodynamic scale The thermodynamic scale is in itself unique, however one must prove that a specific realisation of it is exempt of significant systematic deviations. No practical and technical details for thermodynamic temperature implementation can be specified (modelled) in the mise en pratique, since they only concern the level of attainable state-of-the-art uncertainty of technical realisations. No specific implementation of the mise en pratique called thermodynamic temperature scale, i.e. no method, need be specified, excluding others by not specifying them. At present for some implementations below 30 K (NMi-VSL, NPL, PTB, VNIIFTRI) the CCT Key Comparison 1 supplied the required evidence of compatibility. In the future it may apply to further implementations. This would resolve the dicothomy introduced since 1927 between thermodynamic and practical empirical scales. In fact, at present, T 90 is construed as an approximation of T. Conversely, T is an approximation of T 90, not a realisation of T 90. Adopted in the mise en pratique, both will instead gain the same status. F.Pavese 8
The kelvin and the Mise en pratique of the unit: 2 - Definitions covering several decades of precision levels Until 2005 the temperature written standards were supposed to define only top-level temperature scales. Every user needing temperature measurements of lesser quality needed to trace directly to the top-quality definition, even if several order of magnitude better in uncertainty than the user needs (for most of them a 0.1 K uncertainty is sufficient). The new possibility of inclusion of different methods in the mise en pratique can, in perspective, bridge this gap: basically they only need to prove to be compatible with each other. This requirement is also sufficient, because neither mise en pratique concept nor compatibility include the need for all methods to provide the same uncertainty level. Some knowledge of a Scale structure is first needed to understand the differences between different options. F.Pavese 9
General structure of a temperature scale A temperature-scale definition comprises three elements (usually different in different temperature ranges): (i) a thermometer, i.e., a transducer providing a continuous relationship between a response quantity and temperature, called interpolating instrument (e.g., R-T for the standard platinum resistance thermometer, SPRT); (ii) a mathematical model for the physical law of transducer function f(t); (iii) a number of calibration points T 0i, necessary to determine the numerical values of the model parameters, when not stipulated, for each individual instrument. The instrument interpolates between the calibration values. These values of the response variable, are determined by measurements at fixed points (e.g., the resistances R for a SPRT and phase transitions of ideally pure substances, respectively). The experimental realisation of the ITS-90 consists of a realisation of the physical law or of the calibration of the thermometers at these fixed points; e.g., of the realisation of the corresponding thermodynamic states. The dissemination of a scale is usually done with calibrated thermometers. F.Pavese 10
The kelvin and the Mise en pratique of the unit: 2 - Definitions covering several decades of precision levels Some possibilities of alternate definitions (in no particular order) a) use of definition fixed points with some relaxed requirements, e.g., use of SRMs for the fixed point realisations or as fixed point devices, instead of realising thermodynamic states; b) use of a different list of definition fixed points, or of an abridged list of them; c) use of a stipulated number of empirical calibration temperatures instead of definition fixed points; d) use of stipulated model functions instead of a given list of calibration temperatures; e) use of a model function and definition fixed points to find the numerical values of its parameters instead of a stipulated function; f) use of a different Scale sub-field structure of the definition; g) use of different interpolating instruments, or of different quality; h) use of a stipulated wire scale ; i) harmonised use of written standards set by other organisations. F.Pavese 11
General classes of models (ii) used by temperature scales Physical: a physical law is used. It includes not only the basic mathematical relationship between the response quantity and temperature, but also the, generally many, corrections (additive) terms to it, dictated by the state-of-the-art knowledge. E.g., constant volume gas thermometer (CVGT) basic equation pv = nrt is integrated by correction terms due to substance non-ideality or ambiguity (virial correction, adsorption of the gas by the bulb), and to technical issues (dead-space effects on n, thermomolecular effect, thermal and mechanical expansion of the bulb). In general, temperature ratios to a reference temperature are used. Semi-empirical: the model formulation is based on a physical law, but empirical terms are then added and/or empirical values are stipulated for the model parameters. E.g., vapour pressure scales of 3 He and 4 He, not requiring calibration fixed points. Or, a thermodynamic thermometer is used with an empirical equation whose parameter values are obtained by calibration at fixed points, like the interpolating CVGT. Empirical: typically, polynomial functions whose parameter values are obtained by calibration at fixed points or partially/totally stipulated. Different models are generally used in different temperature ranges of the definition of ITS-90 (above 0.65 K) and of PLTS-2000 (below 1 K): with the mise en pratique, they can be suitable for implementing different methods in the same temperature range or for different uncertainty levels. F.Pavese 12
Identification of the measurand: 1 - classes of standards Temperature is always measured by using a transducer, i.e. the measurand is never temperature. Two broad classes of temperature standards can be identified, bringing to different data models and statistical treatment: Artefact (class 1 (Pavese), type 2 (Kacker)) An artefact standard can be defined as a device carrying a numerical value of the response quantity obtained by a calibration, which is individual and not constrained to any natural value. The interpolating istruments are usually artefacts, i.e., are devices whose response variable can be electrical resistance or e.m.f., or electrical voltage or length; or, pressure, which is in turn an intensive quantity, so the measurand for pressure can be mass or length or electrical capacitance. Examples: electrical thermometers, pyrometric lamps (in other fields: masses, gauge blocks) Physical quantity or law (class 2 (Pavese), type 1 (Kacker)) For these standards, a natural value exists for each defined thermodynamic state, and the aim of the standard in each Laboratory is to accurately realise that value (generally stipulated by the written standard). The fixed points used for calibrating the interpolating instruments are in general a physical quantity, like a uniquely-defined thermodynamic state, typically a phase transition: triple point, vapour-pressure point for a given pressure value namely the normal boiling point. An interpolating instrument can directly be a thermodynamic relationship or law, like vapour pressure or gas law, where pressure is the measurand, or the radiation Plank law, where radiation energy is measured. F.Pavese 13
Identification of the measurand: special-status of stipulated-value standards - 1 Special status -National measurement standard: the MRA international equivalence is not granted to every type of standards, but only to the set of the National standards. They, in turn, are supposed to realise, when existing, the written standards, not a generic approximation of it. -kilogram: BIPM prototype is the reference standard for mass, not allowing, e.g., any other reference value be used in MRA key comparisons involving it. Stipulated value The value of a standard can be stipulated, i.e., be conventional or a consensus value, and when this is done, the value of the standard is not the measurand of the comparison. When the written standard stipulates the value of a specified calibration point or of the parameters of a physical law, zero uncertainty is associated with the value. On the other hand, only in the case of the triple point of water the conventional numerical value is said to be exact by definition in the definition of the unit, kelvin, of the SI quantity thermodynamic temperature. This is not correct, in general, since it should apply to each numerical value of the parameters stipulated by a written standard. In a MRA key comparison, the definition (stipulated) quantity numerical value has to be attributed in these cases by definition to the KCRV. F.Pavese 14
Identification of the measurand: special-status of stipulated-value standards - 2 Incidentally, the standards of the second class of standards seem to match VIM (2007) definition of intrinsic standard -except that the VIM seems to refer to devices, e.g., water triple point cells, instead to the physical states themselves. The VIM is in fact defining the term intrinsic as the measurement standard based on an inherent and reproducible property of a phenomenon or substance, whose value is assigned by consensus and does not need to be established by relating to another measurement standard of the same type. However, the VIM specifies that this type of standard carries an uncertainty associated with its consensus quantity value, which is to be considered when determining the total measurement uncertainty. This is rarely the case; e.g., it is not for the example reported by the VIM, the triple point of water, with the present kelvin definition. F.Pavese 15
Identification of the measurand: in (key) comparisons (A) Comparison of fixed-point realisations. This type of comparison is aimed at directly comparing fixed-point realisations, each realising the same physical condition defined by the written standard. The measurement standard is a fixed-point cell (a device) but the comparison measurand prescribed by the written standard is the physical state itself, characterised by the single value unequivocally stipulated by the written standard. These realisations can be compared by measuring the differences between the temperature values obtained, so providing international traceability, or, in the case of the MRA, international degree of equivalence. Actually, the differences between realisations (between the same physical conditions realised by the different measuring systems) are the measurand of the comparison. Since the values of these differences are generally very small, the transducer used is generally irrelevant, provided that it has enough and known sensitivity and is stable enough with time throughout the comparison procedure. It does not even need to be calibrated. Note that the exercise does not allow one to attribute the definition value to any of the realisations nor to evaluate their differences from it. F.Pavese 16
Identification of the measurand: in (key) comparisons (B) Comparison of transducers (artefacts). This type of comparison is aimed at comparing the realisations of the written standard as performed by each participant laboratory by directly using the values of the calibrated artefacts. In these cases, the measurand is the response variable of the transducer: the data model and error budget of this type of comparison is substantially different from the previous case, so are the measurands. Thermometers are placed together in an isothermal block and measured at controlled temperatures, close to but not necessarily exactly at the fixed-point temperatures. Then the values of the response variable of calibrated interpolating instruments are measured. In this case, artefacts are compared; e.g., thermometers whose relations between the response variable (e.g., electrical resistance for the SPRTs, R i for the i-th laboratory) and temperature T i are supposed to have been established via calibration of each artefact. The R i values can be quite different from each other, but the values T i are instead generally quite close to each other. F.Pavese 17
Realisation of a written standard vs. Approximation - 1 Written standards in calibrations and in testing which originate from international organizations such as the CIPM or ISO, are based on an agreed text that is promulgated and that precisely indicates the rules to be followed for the standard to be implemented by each laboratory. Similarly, all the allowed alternatives in their definition are also precisely written in the standards, because the prescriptions must be respected. Consequently, any implementation of the written standard respecting the written rules with no exceptions is called a realisation of the written standard, e.g. the realisation of T 90 for the ITS-90. In some cases, the written standard allows the use of different methods, each having the status indicated in the definition, e.g., allowing one to use a preferred specific technique. This also applies to the mise en pratique of a standard, whose allowed methods are all to be considered written standards. F.Pavese 18
Realisation of a written standard vs. Approximation - 2 On the contrary, should alternate methods be considered, not included among the techniques specified by the written standard, they can obviously be adopted by a laboratory, but they remain without formal endorsement. Sometimes, they can be recommended by some technical bodies, but they do not have the international status of written standards unless they are incorporated into a new written standard or in an update of a pre-existing one. An implementation according to one of these non-standardised methods must be called an approximation of the written standard. E.g., the indication T 90 should not be allowed for an approximation of ITS-90. The practical temperature scales can be labelled as approximations of the thermodynamic temperature scale, since the written standards aim at mimicking the thermodynamic temperature scale, but with a different set of rules. Conversely, the thermodynamic temperature scale becomes an approximation of the written standard, whenever its implementation is not undertaken in accordance with the rules set out by the written standard. As said before, this different status can now, in principle, be fixed in the mise en pratique. F.Pavese 19
Realisation of a written standard vs. Conservation and Dissemination The values of interpolating instruments at a set of calibration points are recorded for future scale conservation and dissemination. In fact, in many laboratories the realisation of the fixed points for the calibration of all the thermometers is considered a time-consuming and costly exercise, while the use of the response variable values stored on a restricted set of previously calibrated thermometers much more convenient for calibrating further thermometers on the ITS-90. However, conservation of the scale should be considered a distinct process from scale realisation, allowing the laboratory to preserve the realisation process and for dissemination of its own scale realisation. And, the uncertainty budget is different for the three cases. Therefore, an inter-comparison perfomed by using calibrated thermometers is comparing conserved scales, not scale realisations. Also the inter-comparison exercise itself might be considered to be part of the dissemination process, but generally avoiding the degradation in precision that is the usual perception of the concept of dissemination. F.Pavese 20