Description
Gibbs energy G [J] is exergy which cannot be created internally (subscript i), but in contrast to internal-energy (diU/dt = 0) is not conserved but is dissipated (diG/dt < 0) in irreversible energy transformations. Exergy is available as work in reversible energy transformations, and can be partially conserved when the exergonic transformation is coupled to an endergonic transformation.
Abbreviation: G [J]
Reference: Energy
Gibbs energy as a function of advancement
Communicated by Gnaiger E 2022-10-16
- In a transformation tr 0 = -1 A +1 B proceeding in a system with volume V at constant barometric pressure p, the Gibbs energy of reactants A and B is
Eq. 1: G = µA·nA + µB·nB [J]
- A small change dG at constant chemical potentials µi is due to a small advancement of the transformation, in closed or open isothermal systems, exchanging heat in equilibrium with an external thermostat at constant temperature,
Eq. 2: dtrG = µA·dtrnA + µB·dtrnB [J]
- where the advancement dtrξi (i = A or B) is
Eq. 3: dtrξi = dtrnA·νA-1 = dtrnB·νB-1 [mol]
- The isomorphic force of transformation ΔtrFX is the derivative of exergy per advancement,
Eq. 4: ΔtrFX = ∂G/∂trξX [J·mol-1]
- Note that ∂G ≝ dtrG. Then inserting Eq. 2 and Eq. 3 into Eq. 4, the force of transformation is expressed as
Eq. 5: ΔtrFX = (µA·dtrnA + µB·dtrnB)/(dtrnB·νB-1) [J·mol-1]
- which can be rewritten as
Eq. 6: ΔtrFX = µA·dtrnA/(dtrnA·νA-1) + µB·dtrnB/(dtrnB·νB-1) [J·mol-1]
- This yields the force as the sum of stoichiometric potentials, summarized in Figure 8.5 (Chapter 8; Gnaiger 2020 BEC MitoPathways),
Eq. 7: ΔtrFX = µA·νA + µB·νB [J·mol-1]
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- Units
- Joule [J]; 1 J = 1 N·m = 1 V·C; 1 cal = 4.184 J
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Ergodynamics