Gibbs energy dissipation

Fig. 8. Biosynthesis and Gibbs energy dissipation in cellular systems...

Heijnen JJ, van Loosdrecht MCM, Tijhuis L (1992) A black-box mathematical model to calculate auto- and heterotrophic biomass yield based on Gibbs energy dissipation. Biotechnol Bioeng 40 1139-1154... 

An empirical relation was proposed in reference [5] to relate the specific Gibbs energy dissipation to the number of atom of carbon of the energy source... 

Table 22 Enthalpy and Gibbs energy dissipation per C-mole biomass during growth. A / x indicates the change in mole number of the growth reaction per C-mole biomass [24],...

Direct calorimetry gives insight in the thermodynamics of growth. Although Gibbs energy dissipation, which is the fundamental thermodynamic variable to determine, can not be directly measured, the difference with enthalpy production, which is determined by direct calorimetry, is small for aerobic processes, or can be calculated for anaerobic processes. 

In heterogeneous solid state reactions, the phase boundaries move under the action of chemical (electrochemical) potential gradients. If the Gibbs energy of reaction is dissipated mainly at the interface, the reaction is named an interface controlled chemical reaction. Sometimes a thermodynamic pressure (AG/AK) is invoked to formalize the movement of the phase boundaries during heterogeneous reactions. This force, however, is a virtual thermodynamic force and must not be confused with mechanical (electrical) forces. 

These relations limit the extent of the flux coupling and reflect the tendency to reduce the entropy production. Thus, instead of dissipating the Gibbs energy com-... 

In a foregoing section, we mentioned that field forces (e,g., of the electric or elastic field) can cause an interface to move. If they are large enough so that inherent counterforces (such as interface tension or friction) do not bring the boundary to a stop, the interface motion would continue and eventually become uniform. In this section, however, we are primarily concerned with boundary motions caused by chemical potential changes. From irreversible thermodynamics, we know that the dissipated Gibbs energy of the discontinuous system is T-ab, where crb here is the entropy production (see Section 4.2). Since dG/dV = dG/dV = crb- T/ A < ), we have with Eqn. (4.8) at the boundary b... 

By convention, thermodynamic functions of state refer to the system and not the environment, so - AG (exergonic) represents the Gibbs energy potentially available for expenditure and potentially dissipated to the environment. Under suitable conditions, this energy could be made to perform work. An endergonic reaction (+ AG) cannot proceed spontaneously and requires an input of Gibbs energy to proceed from its initial to its final state. 

Since is constant, we find that max Sjs corresponds to max(—Gos) and, hence, to min Gos. In turn, attainment of the minimum possible value of the Gibbs energy means the largest feasible useful transformation and the minimum dissipation of the total energy, i.e., the minimum (in this case a zero one) entropy production in the open subsystem. 

Derivation of the expression for the minimum production of S in the systems with constant T and V (volume) differs from the one above only by replacement of enthalpy by internal energy (U) and the Gibbs energy by the Helmholtz energy in the equations. When we set S and P or S and V dissipation turns out to be zero according to the problem statement. In the case of constant U and V or H and P, the interaction with the environment does not hinder the relaxation of the open subsystem toward the state max Sos. 

The total dissipation, TP = 7 product reaction rate and affinity (the Gibbs energy of reaction), and then we have... 

In other words, as expected, at a spontaneous evolution of the system at fixed p and T, its Gibbs potential decreases, dG < 0. Thus, the rate of entropy pro duction and energy dissipation in an open system at constant temperature and pressure is proportional to the rate of decreasing its Gibbs potential due to occurrence of irreversible spontaneous processes inside the system. 

After one turn of the cycle in time x, the system is returned to its initial state. Hence, the changes in the thermodynamic Gibbs potential of the system wiU be zero in time x AG = 0, while AG < 0 due to the con sumption of alimentary substrates from the surrounding medium. The average rate of energy dissipation in the metabolic cycle is... 

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