Description
An elementary entity XE [x] is a single countable object (E = molecule, cell, organism, particle, party) or single countable event (E = beat, collision, emission, decay, party). A number of defined elementary entities XE is a count, NE = NΒ·XE [x], where N is a dimensionless number. "An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles" (Bureau International des Poids et Mesures 2019).
If an object is defined as a group of particles (a party of two), then the entity is the single group but not the particle. Entity XE is the dimension X of the count NE. The unit of the entity XE and count NE is the 'counting unit' [x]. From the definition of count as the number (N) of entities (X) of type E, it follows that count divided by entity is a pure number, N = NEΒ·XE-1.
Abbreviation: XE [x]
Reference: BEC2020.1 doi10.26124bec2020-0001.v1
Communicated by Gnaiger Erich (2020-05-20) last update 2020-06-05
Base quantities and count
Quantity Symbol for quantity Q Symbol for dimension Name of abstract unit uQ Symbol for unit uQ [*] elementary entity *,$ UX U elementary unit x count *,$ NX = NΒ·UX X elementary unit x amount of substance *,Β§ nX = NXΒ·NA-1 N mole mol charge *,β¬ Qel = zXΒ·eΒ·NX IΒ·T coulomb C = AΒ·s length l L meter m mass m M kilogram kg time t T second s electric current I I ampere A thermodynamic temperature T Ξ kelvin K luminous intensity Iv J candela cd
- [*] SI units, except for the canonical 'elementary unit' [x]. The following footnotes are canonical comments, related to iconic symbols.
- * For the elementary quantities NX, nX, and Qel, the entity-type X of the elementary entity UX has to be specified in the text and indicated by a subscript: nO2; Nce; Qel.
- $ Count NX equals the number of elementary entities UX. In the SI, the quantity 'count' is explicitly considered as an exception: "Each of the seven base quantities used in the SI is regarded as having its own dimension. .. All other quantities, with the exception of counts, are derived quantities" (Bureau International des Poids et Mesures 2019 The International System of Units (SI)). An elementary entity UX is a material unit, it is not a count (UX is not a number of UX). NX has the dimension X of a count and UX has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
- Β§ Amount nX is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant NA.
- β¬ Charge is a derived SI quantity. Charge is an elementary quantity, converting the elementary unit [x] into coulombs [C] using the elementary charge e, or converting moles [mol] into coulombs [C] using the Faraday constant F. zX is the charge number per elementary entity UX, which is a constant for any defined elementary entity UX. Qel = zXΒ·FΒ·nX
References
Bioblast link | Reference | Year |
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Brown 2018 Metrologia | Brown RJC (2018) The evolution of chemical metrology: distinguishing between amount of substance and counting quantities, now and in the future. Metrologia 55:L25. https://doi.org/10.1088/1681-7575/aaace8 | 2018 |
Brown 2021 Metrologia | Brown RJC (2021) A metrological approach to quantities that are counted and the unit one. Metrologia 58:035014. https://doi.org/10.1088/1681-7575/abf7a4 | 2021 |
Cooper 2012 Synthese | Cooper G, Humphry SM (2012) The ontological distinction between units and entities. Synthese 187:393β401. https://doi.org/10.1007/s11229-010-9832-1 | 2012 |
Gnaiger 2020 BEC MitoPathways | Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-0002 | 2020 |
Gnaiger 2020 MitoFit x | Gnaiger E (2021) The elementary unit β canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprints 2020.04.v2. https://doi.org/10.26124/mitofit:200004.v2 | 2021 |
Gnaiger 2024 MitoFit | Gnaiger E (2024) Addressing the ambiguity crisis in bioenergetics and thermodynamics. MitoFit Preprints 2024.3. https://doi.org/10.26124/mitofit:2024-0003 | 2024 |
BEC 2020.1 doi10.26124bec2020-0001.v1 | Gnaiger E et al β MitoEAGLE Task Group (2020) Mitochondrial physiology. Bioenerg Commun 2020.1. https://doi.org/10.26124/bec:2020-0001.v1 | 2020 |
- Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
- Entity, count, and number, and SI base quantities / SI base units
Quantity name Symbol Unit name Symbol Comment elementary UX elementary unit [x] UX, UB; [x] not in SI count NX elementary unit [x] NX, NB; [x] not in SI number N - dimensionless = NXΒ·UX-1 amount of substance nB mole [mol] nX, nB electric current I ampere [A] A = CΒ·s-1 time t second [s] length l meter [m] SI: metre mass m kilogram [kg] thermodynamic temperature T kelvin [K] luminous intensity IV candela [cd]
- Fundamental relationships
- Β» Avogadro constant NA
- Β» Boltzmann constant k
- Β» elementary charge e
- Β» Faraday constant F
- Β» gas constant R
- Β» electrochemical constant f
- Fundamental relationships
- SI and related concepts
MitoPedia concepts:
Ergodynamics