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<p>This research presents a quadratic extrapolation derived through parametric optimisation for the estimation of resistance ratio value at the triple point of mercury using the resistance ratio value at the melting point of gallium based on interpolation equation defined in the subrange between these two fixed points by the International Temperature Scale of 1990. The specific correlation between these two fixed points when they are expressed in <i>S</i> values is also incorporated in derivation. Extrapolation errors of the proposed quadratic equation are looked into with a data sample of 30 standard platinum resistance thermometers. Maximum absolute error observed at the triple point of mercury is 1.14 mK. Mean value of the extrapolation errors is 0.32 mK with a standard deviation of 0.52 mK. Application of the proposed quadratic equation would eliminate the need for actual measurement of the triple point of mercury and maintain a reasonable accuracy at the same time. The proposed extrapolation is of both technical and practical significance and relevance for cryogenic processes from −&#xa0;40&#xa0;°C to 0&#xa0;°C.</p>

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An Extrapolation for Temperature Range from the Triple Point of Mercury to the Triple Point of Water

  • 期刊论文

  • 发表日期：

    2026年7月16日

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  • Kang Lan,
  • Lide Fang,
  • Jianping Sun

摘要

This research presents a quadratic extrapolation derived through parametric optimisation for the estimation of resistance ratio value at the triple point of mercury using the resistance ratio value at the melting point of gallium based on interpolation equation defined in the subrange between these two fixed points by the International Temperature Scale of 1990. The specific correlation between these two fixed points when they are expressed in S values is also incorporated in derivation. Extrapolation errors of the proposed quadratic equation are looked into with a data sample of 30 standard platinum resistance thermometers. Maximum absolute error observed at the triple point of mercury is 1.14 mK. Mean value of the extrapolation errors is 0.32 mK with a standard deviation of 0.52 mK. Application of the proposed quadratic equation would eliminate the need for actual measurement of the triple point of mercury and maintain a reasonable accuracy at the same time. The proposed extrapolation is of both technical and practical significance and relevance for cryogenic processes from − 40 °C to 0 °C.