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TitleSome mathematical properties of the ITS-90
Publication TypeConference Paper
Year of Publication2013
AuthorsWhite, D.R.
Conference NameAIP Conference Proceedings
Date Published2013
AbstractInvestigations into uncertainty propagation on the standard platinum resistance thermometer (SPRT) subranges of the ITS-90 have yielded insights into some of the mathematical properties of interpolated scales. One of the key observations is that Type 3 non-uniqueness is amplified by the fixed-point sensitivity coefficients, which increases the importance of choosing interpolating functions that yield sensitivity coefficients with a limited magnitude. The use of complete polynomials for the interpolations is necessary to ensure consistent behavior of the scale for all SPRTs. This feature also ensures that linearly related variables such as the SPRT resistance R, the resistance ratio W, and the Cragoe Z variable, all give equivalent interpolations. Although, in principle, the choice of Wr values is arbitrary, Type 1 non-uniqueness (subrange inconsistency) is influenced by the consistency of the set of reference resistance ratios, Wr, assigned to the fixed points. Additionally, having dWr/dW close to unity simplifies the uncertainty propagation equations. Finally, the structure of ITS-90 lends itself to a separation of the attributes of reproducibility and thermodynamic accuracy, a feature not exploited in the development of ITS-90. The paper concludes with a suggested procedure for the design of scales of the same structure as ITS-90. Suggestions are also made for areas of investigation that may support future improvements to the temperature scale. © 2013 AIP Publishing LLC.

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