The Mole, Avogadro’s Number and Albert Einstein

Molecular Frontiers Journal ◽

10.1142/s2529732521400010 ◽

2021 ◽

pp. 1-13

Author(s):

Bengt Nordén

Keyword(s):

Diffusion Theory ◽

Outer Space ◽

Pollen Grains ◽

Albert Einstein ◽

Milky Way Galaxy ◽

Solar Systems ◽

Avogadro’S Number ◽

Solar Winds ◽

System Of Units ◽

Definition Of

The mole a concept and Avogadro’s number are discussed as sought by Albert Einstein in his PhD thesis of 1905. Einstein would probably have regarded the metric system of units based on centimetre-gram-second (cgs) preferable to today’s SI system and specifically he would have rejected a recent SI suggestion to redefine Avogadro’s constant as based on a nonatomistic continuum description of matter. He would probably also have preferred keeping a dualistic definition of mole able of bookkeeping both mass and number of particles: we advocate that here and call it the ‘Einstein Definition’ and as Avogadro’s number we shall adopt an integer, the cube of 84446888 as suggested by Fox and Hill, providing also a definition of the kilogram based on the atomic mass of the carbon 12 isotope. Einstein was the first to explain the microscopic movements of pollen grains reported by Robert Brown in 1828 and his explanation that the particles move as a result of an unequal number of water molecules bumping into them from opposite sides was what finally made the scientific world accept the atom theory in its modern shape. In a cosmic diffusion analogy, pollen or bacterial spores moving randomly in outer space driven by the solar winds between solar systems can be envisaged. Applying Einstein’s diffusion theory, one can argue that life might have emerged from far outside of our planet from billions of solar systems, though not from outside of our Milky Way galaxy. As a curiosity we note that the number of solar systems (stars) in the Universe has been estimated to be of the order of Avogadro’s number.

Download Full-text

A relationship between the Avogadro’s number NA and the transition frequency of the caesium 133 atom ΔνCs

Physics Essays ◽

10.4006/0836-1398-34.1.12 ◽

2021 ◽

Vol 34 (1) ◽

pp. 12-16

Author(s):

Teodor Ognean

Keyword(s):

Ground State ◽

International System ◽

Transition Frequency ◽

Amount Of Substance ◽

Weights And Measures ◽

Avogadro’S Number ◽

System Of Units ◽

Measurement Units ◽

Definition Of ◽

New Si

At the 26th meeting of the General Conference on Weights and Measures (CGPM) held on 13‐16 November 2018 at Versailles, France, the new International System of Units (SI) was established. Following the CGPM’s decision, the new SI units were established based upon a set of seven defining constants. This set of constants is the most fundamental feature in the definition of the entire system of units. What is truly remarkable about the new SI is the fact that all measurement units, except the amount of substance mole and Avogadro’s number NA , are defined based on the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> <mml:mi>ν</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Cs</mml:mi> </mml:mrow> </mml:msub> </mml:math> equal to 9 192 631 770 Hz. This article, based on dimensional analysis, presents the possibility of connecting the Avogadro’s number NA and the mole, to the transition frequency <mml:math display="inline"> <mml:msub> <mml:mrow> <mml:mo>Δν</mml:mo> </mml:mrow> <mml:mrow> <mml:mtext>Cs</mml:mtext> </mml:mrow> </mml:msub> </mml:math> .

Download Full-text

Investigation on the Noise Separation in Watt Balance Experiments

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.381-382.619 ◽

2008 ◽

Vol 381-382 ◽

pp. 619-622

Author(s):

W. Zeng ◽

Xiang Qian Jiang ◽

P. Scott ◽

L. Blunt

Keyword(s):

Background Noise ◽

International System ◽

Histogram Method ◽

Stationary Noise ◽

Vibration Data ◽

System Of Units ◽

Environmental Vibration ◽

Transient Events ◽

Watt Balance ◽

Definition Of

The detection of stationary and non-stationary noise in environmental vibration data is an important issue when considering the precision of the Watt balance, an electromechanical apparatus for the new definition of the kilogram in the international system of Units (SI). In this paper, the authors propose a frequency histogram method to find the structure of the stationary noise from large amount of datasets. For the non-stationary noise, the authors propose a wavelet based denoising methods to distinguish the transient events from the background “noise”, to find their duration and content and to identify their location in time.

Download Full-text

Space Traffic Management (STM) – Legal Aspects

Polish Political Science Yearbook ◽

10.15804/ppsy202103 ◽

2021 ◽

Vol 50 (1) ◽

pp. 1-11

Author(s):

Małgorzata Polkowska ◽

Keyword(s):

Traffic Management ◽

Outer Space ◽

Air Traffic Management ◽

Legal Aspects ◽

Air Traffic ◽

Civil Aviation ◽

International Civil Aviation Organization ◽

Definition Of ◽

Security Regulations ◽

Space Activities

Space Traffic Management (STM) is a new concept referring to space activities. The highest priority is the safety and security of outer space and all conducted operations. There is no definition of STM. There is an urgent need to regulate STM providing safety and security regulations at the international, regional, and national levels. Because there is no STM definition, the regulator might use the example of existing regulations of the International Civil Aviation Organization on Air Traffic Management (ATM). European EUSST is a good example of being a “precursor” of STM. However, many questions are still open regarding specific regulations needed to create an STM system, such as at which level they should be made: globally, regionally, or nationally.

Download Full-text

Embriología de Pachycereus militaris (Audot) Hunt (Cactaceae)

Botanical Sciences ◽

10.17129/botsci.1632 ◽

2017 ◽

pp. 5

Author(s):

Citlali Núñez-Mariel ◽

E. Mark Engleman ◽

Judith Márquez-Guzmán

Keyword(s):

Pollen Grains ◽

Anther Wall ◽

The Family ◽

Family Level ◽

Taxonomic Importance ◽

Definition Of ◽

Functional Megaspore

This is a contribution to the embryology of cacti and to the definition of their reproductory structures. The development of anthers, ovules and seeds of Pachycereus militaris is described. The type of development of the anther wall is monocotyledonous. This may have taxonomic importance above the family level. The endothecium is formed by a single stratum and the pollen grains are tricolpate, spinulate and punctitegilate. A lineal triad of megaspores was observed. The functional megaspore is the chalazal one. It is proposed that the term campylotropous should be uti lized for describing the ovule type, while the term circinotropous should be reserved for the funicle. In contrast to the stated by other authors, this study suggests that the seeds of Pachycereus militaris should be considered as non-albuminous and non-perispermous.

Download Full-text

Thermodynamic Properties of Seawater, Ice and Humid Air: TEOS-10, Before and Beyond

10.5194/os-2018-19 ◽

2018 ◽

Author(s):

Rainer Feistel

Keyword(s):

Hydrological Cycle ◽

International System ◽

Metrological Traceability ◽

Humid Air ◽

Ongoing Research ◽

Seawater Salinity ◽

System Of Units ◽

Atmospheric Relative Humidity ◽

Definition Of ◽

First Time

Abstract. In the terrestrial climate system, water is a key player in the form of its different ambient phases of ice, liquid and vapour, admixed with sea salt in the ocean and with dry air in the atmosphere. For proper balances of climatic energy and entropy fluxes in models and observation, a highly accurate, consistent and comprehensive thermodynamic standard framework is requisite in geophysics and climate research. The new “Thermodynamic Equation of Seawater – 2010” (TEOS-10) constitutes such a standard for properties of water in its various manifestations in the hydrological cycle. TEOS-10 has been recommended internationally in 2009 by the Intergovernmental Oceanographic Commission (IOC) to replace the previous 1980 seawater standard, EOS-80, and in 2011 by the International Union of Geodesy and Geophysics (IUGG) “as the official description for the properties of seawater, of ice and of humid air”. This paper briefly reviews the development of TEOS-10, its novel axiomatic properties, new oceanographic tools it offers, and important tasks that still await solutions by ongoing research. Among the latter are new definitions and measurement standards for seawater salinity and pH, in order to establish their metrological traceability to the International System of Units (SI), for the first time after a century of widespread use. Of similar climatological relevance is the development and recommendation of a uniform standard definition of atmospheric relative humidity that is unambiguous and rigorously based on physical principles.

Download Full-text

The kelvin redefinition and its mise en pratique

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2015.0037 ◽

2016 ◽

Vol 374 (2064) ◽

pp. 20150037 ◽

Cited By ~ 39

Author(s):

B. Fellmuth ◽

J. Fischer ◽

G. Machin ◽

S. Picard ◽

P. P. M. Steur ◽

...

Keyword(s):

International System ◽

Thermodynamic Temperature ◽

Fundamental Constants ◽

Primary Thermometry ◽

A Value ◽

System Of Units ◽

Mise En Pratique ◽

Explicit Constant ◽

Definition Of ◽

Base Units

In 2018, it is expected that there will be a major revision of the International System of Units (SI) which will result in all of the seven base units being defined by fixing the values of certain atomic or fundamental constants. As part of this revision, the kelvin, unit of thermodynamic temperature, will be redefined by assigning a value to the Boltzmann constant k . This explicit-constant definition will define the kelvin in terms of the SI derived unit of energy, the joule. It is sufficiently wide to encompass any form of thermometry. The planned redefinition has motivated the creation of an extended mise en pratique (‘practical realization’) of the definition of the kelvin ( MeP -K), which describes how the new definition can be put into practice. The MeP -K incorporates both of the defined International Temperature Scales (ITS-90 and PLTS-2000) in current use and approved primary-thermometry methods for determining thermodynamic temperature values. The MeP -K is a guide that provides or makes reference to the information needed to perform measurements of temperature in accord with the SI at the highest level. In this article, the background and the content of the extended second version of the MeP -K are presented.

Download Full-text

Definition of the mole (IUPAC Recommendation 2017)

Pure and Applied Chemistry ◽

10.1515/pac-2017-0106 ◽

2018 ◽

Vol 90 (1) ◽

pp. 175-180 ◽

Cited By ~ 13

Author(s):

Roberto Marquardt ◽

Juris Meija ◽

Zoltán Mester ◽

Marcy Towns ◽

Ron Weir ◽

...

Keyword(s):

International System ◽

International Committee ◽

Fundamental Physical Constants ◽

Weights And Measures ◽

Technical Report ◽

System Of Units ◽

Iupac Recommendation ◽

Definition Of ◽

Base Units ◽

Fundamental Physical

AbstractIn 2011 the General Conference on Weights and Measures (CGPM) noted the intention of the International Committee for Weights and Measures (CIPM) to revise the entire International System of Units (SI) by linking all seven base units to seven fundamental physical constants. Of particular interest to chemists, new definitions for the kilogram and the mole have been proposed. A recent IUPAC Technical Report discussed these new definitions in relation to immediate consequences for the chemical community. This IUPAC Recommendation on the preferred definition of the mole follows from this Technical Report. It supports a definition of the mole based on a specified number of elementary entities, in contrast to the present 1971 definition.

Download Full-text

Space Law and Weapons in Space

Oxford Research Encyclopedia of Planetary Science ◽

10.1093/acrefore/9780190647926.013.74 ◽

2019 ◽

Cited By ~ 2

Author(s):

Sa'id Mosteshar

Keyword(s):

Outer Space ◽

The United States ◽

Great Difficulty ◽

Arms Race ◽

Weapons Of Mass Destruction ◽

Legal Principles ◽

Celestial Bodies ◽

Outer Space Treaty ◽

Space Weapons ◽

Definition Of

Although legal principles to govern space were discussed as early as the mid-1950s, they were not formalized until the Outer Space Treaty (OST) 1967 was adopted and came into force. The OST establishes a number of principles affecting the placement of weapons in outer space. In particular it provides that “the Moon and other celestial bodies shall be used exclusively for peaceful purposes” and prohibits the testing of any types of weapons on such bodies. More generally the OST forbids the placement of nuclear weapons or other weapons of mass destruction in outer space. In addition there are a number of disarmament treaties and agreements emanating from the United Nations Office for Disarmament Affairs and the Conference on Disarmament that are relevant to weapons in space. Although the disarmament provisions and international humanitarian laws place some restrictions on the use or manner of use of space weapons, none prohibit space weaponization. The absence of such prohibition is not due to many attempts over the years to prevent an arms race in space. Notable among these are Prevention of an Arms Race in Space Draft Treaty and the Prevention of the Placement of Weapons in Space Draft Treaty. In considering the laws affecting space weapons a fundamental question that arises is what constitutes a weapon and does its placement in space breach the requirement that outer space be used exclusively for peaceful purposes? As an example, does a satellite used to control and direct an armed drone breach the peaceful use provision of the OST? There may be risks that without international norms governments and substate groups may acquire and use armed drones in ways that threaten regional stability, laws of war, and the role of domestic rule of law in decisions to use force. Given their orbital velocity, any object in space could be a weapon with capability to destroy a satellite or other space object. There is also a growing population of dual-use satellites with military as well as civilian applications. These present great difficulty in arriving at a workable definition of a space weapon in the formulation of a generally acceptable treaty. In addition, there are divergent views of the meaning of peaceful use. Some, in particular the United States, consider the meaning to be “nonaggressive” rather than “nonmilitary.”

Download Full-text

The Aerospace Plane: Collisions and Damage to a Third Party on the Surface of the Earth: Which Liability Regime will Rule?

Leiden Journal of International Law ◽

10.1017/s0922156500002314 ◽

1991 ◽

Vol 4 (2) ◽

pp. 249-280

Author(s):

Lousewies S.A.L.B van der Laan

Keyword(s):

Outer Space ◽

Third Party ◽

Chicago Convention ◽

Legal Regime ◽

The Earth ◽

Legal Questions ◽

Starting Point ◽

Outer Space Treaty ◽

Definition Of ◽

Aerospace Plane

The article addresses the establishment of a legal regime concerning liability questions of the aerospace plane. The existing air and space law, as laid down for example in the Chicago Convention and the Outer Space Treaty -especially the definition of the words ‘aircraft’ and ‘space object’-is used as a starting point. The applicability of the existing regimes to the aerospace plane is then evaluated. Two concrete cases, namely liability resulting from damage to third parties on the suiface of the earth and liability after collisions, are presented in depth to illustrate the legal questions that this new hybrid craft will raise. Finally some modest suggestions are made as to the resolution of the conflicts.

Download Full-text