Difference between revisions of "Template:Base quantities and count"

Latest revision as of 08:02, 6 July 2023

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 = N·U_X	X	elementary unit	x
amount of substance ^*,§	n_X = N_X·N_A^-1	N	mole	mol
charge ^*,€	Q_el = z_X·e·N_X	I·T	coulomb	C = A·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	Θ	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].

^§ 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.

^€ 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·F·n_X

@@ Line 1: / Line 1: @@
+[[File:SI-units-elementary quantities.png|right|400px|link=Gnaiger 2020 MitoFit x]]
 ::::: {| class="wikitable"
 |-
-! Base quantity !! Symbol for quantity !! Symbol for dimension !! Name of SI unit !! Symbol for SI unit
+! Quantity !! Symbol for quantity ''Q'' !! Symbol for dimension !! Name of abstract unit ''u''<sub>''Q''</sub> !! Symbol for unit ''u''<sub>''Q''</sub> [*]
 |-
-| length || ''l'' || L || meter || m
+| [[elementary entity]] <sup>*,$</sup> || ''U''<sub>''X''</sub> || U || [[elementary unit]] || x
 |-
-| mass || ''m'' || M || kilogram || kg
+| [[count]] <sup>*,$</sup> || ''N''<sub>''X''</sub> = ''N''·''U''<sub>''X''</sub> || X || [[elementary unit]] || x
 |-
-| time || ''t'' || T || second || s
+| [[amount]] of substance <sup>*,§</sup> || ''n''<sub>''X''</sub> = ''N''<sub>''X''</sub>·''N''<sub>A</sub><sup>-1</sup> || N || [[mole]] || mol
 |-
-| electric current || ''I'' || I || ampere || A
+| [[Elementary charge |charge]] <sup>*,€</sup> || ''Q''<sub>el</sub> = ''z''<sub>''X''</sub>·''e''·''N''<sub>''X''</sub> || I·T || coulomb || C = A·s
 |-
-| thermodynamic temperature || ''T'' || Θ || kelvin || K
+|  ||  ||  ||  ||
 |-
-| [[amount]] of substance<sup>*</sup> || ''n'' || N || mole || mol
+| [[length]] || ''l'' || L || [[meter]] || m
 |-
-| count; [[number of entities]]<sup>*,#</sup> || ''N'' || C || counting unit || x
+| [[mass]] || ''m'' || M || [[kilogram]] || kg
 |-
-| luminous intensity || ''I''<sub>v</sub> || J || candela || cd
+| time || ''t'' || T || [[second]] || s
+|-
+| electric current || ''I'' || I || [[ampere]] || A
+|-
+| thermodynamic temperature || ''T'' || Θ || [[kelvin]] || K
+|-
+| luminous intensity || ''I''<sub>v</sub> || J || [[candela]] || cd
 |}
-:::: <sup>*</sup> For the quantities ''n'' and ''N'', the entities X have to be specified and should always be indicated by a subscript or in parentheses (IUPAC).
+::::: [*] SI units, except for the canonical '[[elementary unit]]' [x]. The following footnotes are canonical comments, related to [[iconic symbols]].
-:::: <sup>#</sup> 'Count' is synonymous with 'number of entities' and is one of the most fundamental quantities in physics, but the name, symbol and unit are not included in the SI as a base quantity or base unit. Not all sample types contain countable objects. An 'entity', X, is a countable object or event. Countable objects are particles, such as electrons, molecules, packaging units (parcels), cells, organisms, individuals, patients. 'Number of entities' and 'number' are distinguished (in German: Anzahl ''versus'' Zahl). The count is not a pure dimensionless number, but the dimension of the count, C, is the entity. The magnitude of a count, ''N'', is expressed by a pure number times the 'counting unit' [x], indicating how many times different members of the defined entity are ''accounted'' for in a defined system (not how many times the same member of the defined entity is re-counted in the system — consider the political problem in counting votes), or how many times a defined event is counted during a defined period of time. ''N'' [x] is the count, and ''N''/''t'' [x·s<sup>-1</sup>] is the frequency (counts per time in units of counting units per second). A prefix can be used with the unit [x], like with any other symbol of SI units: Mx = 10<sup>6</sup> x; µx = 10<sup>-6</sup> x; Gx = 10<sup>9</sup> x; nx = 10<sup>-9</sup> x.
+::::: <sup>*</sup> For the elementary quantities ''N''<sub>''X''</sub>, ''n''<sub>''X''</sub>, and ''Q''<sub>el</sub>, the entity-type ''X'' of the elementary entity ''U''<sub>''X''</sub> has to be specified in the text and indicated by a subscript: ''n''<sub>O<sub>2</sub></sub>; ''N''<sub>ce</sub>; ''Q''<sub>el</sub>.
+::::: <sup>$</sup> [[Count]] ''N''<sub>''X''</sub> equals the number of elementary entities ''U''<sub>''X''</sub>. 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 [[count]]s, are derived quantities" ([[Bureau International des Poids et Mesures 2019 The International System of Units (SI)]]). An elementary entity ''U''<sub>''X''</sub> is a material unit, it is not a count (''U''<sub>''X''</sub> is not a number of ''U''<sub>''X''</sub>). ''N''<sub>''X''</sub> has the dimension X of a count and ''U''<sub>''X''</sub> has the dimension U of an elementary entity; both quantities have the same abstract unit, the 'elementary unit' [x].
+::::: <sup>§</sup> [[Amount]] ''n''<sub>''X''</sub> is an elementary quantity, converting the elementary unit [x] into the [[SI base units |SI base unit]] mole [mol] using the [[Avogadro constant]] ''N''<sub>A</sub>.
+::::: <sup>€</sup> [[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''<sub>''X''</sub> is the charge number per elementary entity ''U''<sub>''X''</sub>, which is a constant for any defined elementary entity ''U''<sub>''X''</sub>. ''Q''<sub>el</sub> = ''z''<sub>''X''</sub>·''F''·''n''<sub>''X''</sub>