Classroom note: Using the binomial series to prove the arithmetic mean–geometric mean inequality

In 1968, Leon Gerber compared (1 + x) ^a to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean–geometric mean inequality is presented.     

The Boltzmann Constant for the Definition and Realization of the Kelvin

In November 2018, the four base units, kilogram, ampere, kelvin, and mole, of the International System of Units (SI) are redefined in terms of fundamental physical constants. The redefinition comes into force on World Metrology Day, 20 May 2019. The kelvin, the base unit of thermodynamic temperature, from then is to be founded on a fixed numerical value of the Boltzmann constant. Herein, the change in the definition of the kelvin and the consequences for practical temperature measurement are explained. The primary thermometry methods applied to determine the numerical value of the Boltzmann constant for the redefinition are reviewed. The prospects for the future application of these methods are outlined.     

摩尔的重新定义

摩尔是物质的量的单位,在化学和生物等学科中具有广泛的应用。1971年,摩尔被采纳为第7个国际单位制基本单位,并一直沿用了将近50年。2018年11月16日的国际计量大会上摩尔被重新定义,并于2019年5月20日开始实施。本文阐述重新定义摩尔的原因,摩尔新定义的内涵,重新定义摩尔之后带来的变化。     

能量天平及千克单位重新定义研究进展

质量单位千克是国际单位制7个基本单位中惟一一个仍以实物定义和复现的基本单位.作为一种实物,其量值必然会因为环境因素及使用时的磨损而发生变化.但由于缺少更高一级的参考标准对其进行考察,国际千克原器的真实变化情况无从得知.国际计量委员会建议采用普朗克常数对千克重新定义,号召各个国家开展普朗克常数的精密测量研究工作,并要求至少有三种独立方案提供有效测量数据.自20世纪70年代起,英、美等国采用功率天平方案进行研究,国际阿伏伽德罗常数合作组织则采用了X射线单晶硅密度的方案.为了应对国际单位制的重大变革,2006年中国计量科学研究院提出了用能量天平法测量普朗克常数的新方案,其特点是可避免国外方案中困难的动态测量.2013年原型实验装置研制成功,证实了能量天平方案原理可行.此后,中国计量科学研究院开始了新一代能量天平装置的研制.2017年5月,中国计量科学研究院提交了普朗克常数的测量结果,不确定度为2.4×10~(-7)(k=1),该数据被国际科学数据委员会收入参考数据库.但由于数据的不确定度尚未进入10~(-8)量级,未被用于普朗克常数的定值.目前中国计量科学研究院正对几项主要的不确定度来源进行研究,预计在未来的两年内达可到10-8量级的不确定度.     

Understanding the Revised SI: Background,Consequences, and Perspectives

This article expounds the significance of the revision of the international system of units, the SI, approved by the General Conference on Weights and Measures (CGPM) in 2018. The revised SI implements a construct of a system of units based on fixing the numerical values of constants of nature, the “defining constants.” This fundamental development in the SI is not only elegant and infinitely sustainable, but moreover will drive future technological innovation. This article provides an historical overview and discusses the underlying principles and consequences of the revised SI: from the history of Planck's proposal for creating a system of units “valid for all times and civilizations,” to the scientific and technological motivations for the revision and the expected resulting innovations.