Difference between revisions of "Advancement"

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Advancement

Description

In an isomorphic analysis, any form of flow is the advancement of a process per unit of time, expressed in a specific motive unit [MU∙s^-1], e.g., ampere for electric flow or current [A≡C∙s^-1], watt for heat flow [W≡J∙s^-1], and for chemical flow the unit is [mol∙s^-1] (extent of reaction per time). The corresponding motive forces are the partial exergy (Gibbs energy) changes per advancement [J∙MU^-1], expressed in volt for electric force [V≡J∙C^-1], dimensionless for thermal force [J∙J^-1], and for chemical force the unit is [J∙mol^-1], which deserves a specific acronym ([Jol]) comparable to volt. For chemical processes of reaction (spontaneous from high-potential substrates to low-potential products) and compartmental diffusion (spontaneous from a high-potential compartment to a low-potential compartment), the advancement is the amount of motive substance that has undergone a compartmental transformation [mol]. The concept was originally introduced by De Donder [1]. Central to the concept of advancement is the stoichiometric number, ν_i, associated with each motive component i (transformant [2]).

In a chemical reaction, r, the motive entity is the stoichiometric amount of reactant, d_rn_i, with stoichiometric number ν_i. The advancement of the chemical reaction, d_rξ [mol], is then defined as

d_rξ = d_rn_i·ν_i^-1

The flow of the chemical reaction, I_r [mol·s^-1], is advancement per time,

I_r = d_rξ·dt^-1

This concept of advancement is extended to compartmental diffusion and the advancement of charged particles [3], and to any discontinuous transformation in compartmental systems [2],

Abbreviation: d_trξ

Reference: Gnaiger (1993) Pure Appl Chem

Communicated by Gnaiger E 2018-11-01, 2018-10-16

Advancement per volume

The advancement of a transformation in a closed homogenous system (chemical reaction) or discontinuous system (diffusion) causes a change of concentration of substances i.

» Advancement per volume, d_trY = d_trξ∙V^-1

References

De Donder T (1936) Thermodynamic theory of affinity: a book of principles. Oxford, England: Oxford University Press.
Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«

Prigogine I (1967) Introduction to thermodynamics of irreversible processes. Interscience New York, 3rd ed:147pp. - »Bioblast link«

MitoPedia concepts: MiP concept, Ergodynamics

@@ Line 1: / Line 1: @@
 {{MitoPedia
 |abbr=d<sub>tr</sub>''ξ''
-|description=In an isomorphic analysis, any form of [[flow]] is the '''advancement''' of a process per unit of time, expressed in a specific [[motive unit]] [MU∙s<sup>-1</sup>], ''e.g.'', ampere for electric flow or current [A≡C∙s<sup>-1</sup>], watt for heat flow [W≡J∙s<sup>-1</sup>], and for chemical flow the unit is [mol∙s<sup>-1</sup>] ('''extent of reaction''' per time). The corresponding motive [[force]]s are the partial exergy (Gibbs energy) changes per advancement [J∙MU<sup>-1</sup>], expressed in volt for electric force [V≡J∙C<sup>-1</sup>], dimensionless for thermal force [J∙J<sup>-1</sup>], and for chemical force the unit is [J∙mol<sup>-1</sup>], which deserves a specific acronym ([Jol]) comparable to volt. For chemical processes of reaction and diffusion, the advancement is the amount of motive substance [mol]. The concept was originally introduced by De Donder [1]. Central to the concept of advancement is the [[stoichiometric number]], ''ν''<sub>X</sub>, associated with each motive component X (transformant [2]).
+|description=In an isomorphic analysis, any form of [[flow]] is the '''advancement''' of a process per unit of time, expressed in a specific [[motive unit]] [MU∙s<sup>-1</sup>], ''e.g.'', ampere for electric flow or current [A≡C∙s<sup>-1</sup>], watt for heat flow [W≡J∙s<sup>-1</sup>], and for chemical flow the unit is [mol∙s<sup>-1</sup>] ('''extent of reaction''' per time). The corresponding motive [[force]]s are the partial exergy (Gibbs energy) changes per advancement [J∙MU<sup>-1</sup>], expressed in volt for electric force [V≡J∙C<sup>-1</sup>], dimensionless for thermal force [J∙J<sup>-1</sup>], and for chemical force the unit is [J∙mol<sup>-1</sup>], which deserves a specific acronym ([Jol]) comparable to volt. For chemical processes of reaction (spontaneous from high-potential substrates to low-potential products) and compartmental diffusion (spontaneous from a high-potential compartment to a low-potential compartment), the advancement is the amount of motive substance that has undergone a compartmental transformation [mol]. The concept was originally introduced by De Donder [1]. Central to the concept of advancement is the [[stoichiometric number]], ''ν''<sub>''i''</sub>, associated with each motive component ''i'' (transformant [2]).
-In a chemical reaction, r, the motive entity is the stoichiometric amount of reactant, d<sub>r</sub>''n''<sub>X</sub>, with stoichiometric number ''ν''<sub>X</sub>. The advancement of the chemical reaction, d<sub>r</sub>''ξ'' [mol], is then defined as
+In a chemical reaction, r, the motive entity is the stoichiometric amount of reactant, d<sub>r</sub>''n''<sub>''i''</sub>, with stoichiometric number ''ν''<sub>''i''</sub>. The advancement of the chemical reaction, d<sub>r</sub>''ξ'' [mol], is then defined as
-  d<sub>r</sub>''ξ'' = d<sub>r</sub>''n''<sub>X</sub>·''ν''<sub>X</sub><sup>-1</sup>
+  d<sub>r</sub>''ξ'' = d<sub>r</sub>''n''<sub>''i''</sub>·''ν''<sub>''i''</sub><sup>-1</sup>
 The flow of the chemical reaction, ''I''<sub>r</sub> [mol·s<sup>-1</sup>], is advancement per time,
   ''I''<sub>r</sub> = d<sub>r</sub>''ξ''·d''t''<sup>-1</sup>
+This concept of advancement is extended to compartmental diffusion and the advancement of charged particles [3], and to any discontinuous transformation in compartmental systems [2],
+:::: [[File:Advancement.png|100px]]
 |info=[[Gnaiger_1993_Pure Appl Chem |Gnaiger (1993) Pure Appl Chem]]
 }}
-  Communicated by [[Gnaiger E]] 2018-10-16
+  Communicated by [[Gnaiger E]] 2018-11-01, 2018-10-16
+== Advancement per volume ==
+:::: The advancement of a transformation in a closed homogenous system (chemical reaction) or discontinuous system (diffusion) causes a change of [[concentration]] of substances ''i''.
 ::::» [[Advancement per volume]], d<sub>tr</sub>''Y'' = d<sub>tr</sub>''ξ''∙V<sup>-1</sup>
@@ Line 18: / Line 23: @@
 :::# De Donder T (1936) Thermodynamic theory of affinity: a book of principles. Oxford, England: Oxford University Press.
 :::# Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - [[Gnaiger 1993 Pure Appl Chem |»Bioblast link«]]
+::::# Prigogine I (1967) Introduction to thermodynamics of irreversible processes. Interscience New York, 3rd ed:147pp. - [[Prigogine 1967 Interscience |»Bioblast link«]]
 {{MitoPedia concepts
 |mitopedia concept=MiP concept, Ergodynamics
 }}