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, Iel = delξ/dt [A≡C∙s-1], watt for thermal or heat flow, Ith = dthξ/dt [W≡J∙s-1], and for chemical flow of reaction, Ir = drξ/dt, 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, ΔelF = ∂G/∂elξ [V≡J∙C-1], dimensionless for thermal force, ΔthF = ∂G/∂thξ [J∙J-1], and for chemical force, ΔrF = ∂G/∂rξ, the unit is [J∙mol-1], which deserves a specific acronym [Jol] comparable to volt [V]. 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, νi, associated with each motive component i (transformant [2]).

In a chemical reaction, r, the motive entity is the stoichiometric amount of reactant, drni, with stoichiometric number νi. The advancement of the chemical reaction, drξ [mol], is defined as,

drξ = drni·νi-1

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

Ir = drξ·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],

Advancement.png

Abbreviation: dtrξ [MU]

Reference: Gnaiger (1993) Pure Appl Chem

Communicated by Gnaiger E (last update 2018-11-02)
delQi (dthQi) are the changes in electric charge (heat) at the compartments of high or low electric potential (temperature) within the discontinuous system (from ref. [2]).

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.
The advancement causes a change of concentration due to a transformation, Δtrc, in contrast to a difference of concentrations calculated between difference states, Δtrc.
» Advancement per volume, dtrY = dtrξ∙V-1



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References

  1. De Donder T, Van Rysselberghe P (1936) Thermodynamic theory of affinity: a book of principles. Oxford, England: Oxford University Press:144 pp.
  2. Gnaiger E (1993) Nonequilibrium thermodynamics of energy transformations. Pure Appl Chem 65:1983-2002. - »Bioblast link«
  3. Prigogine I (1967) Introduction to thermodynamics of irreversible processes. Interscience New York, 3rd ed:147 pp. - »Bioblast link«

MitoPedia concepts: MiP concept, Ergodynamics