Description
Dimensions are defined in the SI {Quote}: Physical quantities can be organized in a system of dimensions, where the system used is decided by convention. 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, which may be written in terms of base quantities according to the equations of physics. The dimensions of the derived quantities are written as products of powers of the dimensions of the base quantities using the equations that relate the derived quantities to the base quantities.
There are quantities Q for which the defining equation is such that all of the dimensional exponents in the equation for the dimension of Q are zero. This is true in particular for any quantity that is defined as the ratio of two quantities of the same kind. .. There are also some quantities that cannot be described in terms of the seven base quantities of the SI, but have the nature of a count. Examples are a number of molecules, a number of cellular or biomolecular entities (for example copies of a particular nucleic acid sequence), or degeneracy in quantum mechanics. Counting quantities are also quantities with the associated unit one. {end of Quote: p 136, Bureau International des Poids et Mesures 2019 The International System of Units (SI)}
Reference: Bureau International des Poids et Mesures 2019 The International System of Units (SI), Gnaiger MitoFit Preprints 2020.4
Quantity Symbol for quantity Q Symbol for dimension Name of abstract unit u_{Q} Symbol for unit u_{Q} [*] elementary entity ^{*,$} U_{X} U elementary unit x count ^{*,$} N_{X} = NยทU_{X} X elementary unit x amount of substance ^{*,ยง} n_{X} = N_{X}ยทN_{A}^{-1} N mole mol charge ^{*,โฌ} Q_{el} = z_{X}ยทeยทN_{X} IยทT coulomb C = Aยทs length l L meter m mass m M kilogram kg time t T second s electric current I I ampere A thermodynamic temperature T ฮ kelvin K luminous intensity I_{v} 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 N_{X}, n_{X}, and Q_{el}, the entity-type X of the elementary entity U_{X} has to be specified in the text and indicated by a subscript: n_{O2}; N_{ce}; Q_{el}.
- ^{$} Count N_{X} equals the number of elementary entities U_{X}. 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 U_{X} is a material unit, it is not a count (U_{X} is not a number of U_{X}). N_{X} has the dimension X of a count and U_{X} has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
- ^{ยง} Amount n_{X} is an elementary quantity, converting the elementary unit [x] into the SI base unit mole [mol] using the Avogadro constant N_{A}.
- ^{โฌ} 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. z_{X} is the charge number per elementary entity U_{X}, which is a constant for any defined elementary entity U_{X}. Q_{el} = z_{X}ยทFยทn_{X}
References
Bioblast link | Reference | Year |
---|---|---|
Bureau International des Poids et Mesures 2019 The International System of Units (SI) | Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216. ISBN 978-92-822-2272-0 | 2019 |
Gnaiger 2020 BEC MitoPathways | Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5^{th} ed. https://doi.org/10.26124/bec:2020-0002 | 2020 |
Gnaiger 2020 MitoFit x | Gnaiger E (2021) The elementary unit โ canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. https://doi.org/10.26124/mitofit:200004.v2 | 2021 |
BEC 2020.1 doi10.26124bec2020-0001.v1 | Gnaiger E et al โ MitoEAGLE Task Group (2020) Mitochondrial physiology. 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 U_{X} elementary unit [x] U_{X}, U_{B}; [x] not in SI count N_{X} elementary unit [x] N_{X}, N_{B}; [x] not in SI number N - dimensionless = N_{X}ยทU_{X}^{-1} amount of substance n_{B} mole [mol] n_{X}, n_{B} electric current I ampere [A] A = Cยทs^{-1} time t second [s] length l meter [m] SI: metre mass m kilogram [kg] thermodynamic temperature T kelvin [K] luminous intensity I_{V} candela [cd]
- Fundamental relationships
- ยป Avogadro constant N_{A}
- ยป Boltzmann constant k
- ยป elementary charge e
- ยป Faraday constant F
- ยป gas constant R
- ยป electrochemical constant f
- Fundamental relationships
- SI and related concepts
- Bioblast links: Normalization - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>
- Rate
- ยป Normalization of rate
- ยป Flow
- ยป Oxygen flow
- ยป Flux
- ยป Oxygen flux
- ยป Flux control ratio
- ยป Coupling-control ratio
- ยป Pathway control ratio
- ยป Flux control efficiency
- Rate
- Quantities for normalization
- ยป Count in contrast to Number
- ยป Mitochondrial marker
- ยป O2k-Protocols: mitochondrial and marker-enzymes
- ยป Citrate synthase activity
- Quantities for normalization
- General
- ยป Extensive quantity
- ยป Specific quantity
- ยป Advancement
- ยป Motive unit
- ยป Iconic symbols
- General
- Related keyword lists
MitoPedia concepts:
Ergodynamics