Thermodynamic minimum free-energy temperature

As compared to ECC produced under equilibrium conditions, ECC formed af a considerable supercooling are at thermodynamic equilibrium only from the standpoint of thermokinetics60). Indeed, under chosen conditions (fi and crystallization temperatures), these crystals exhibit some equilibrium degree of crystallinity at which a minimum free energy of the system is attained compared to all other possible states. In this sense, the system is in a state of thermodynamic equilibrium and is stable, i.e. it will maintain this state for any period of time after the field is removed. However, with respect to crystals with completely extended chains obtained under equilibrium conditions, this system corresponds only to a relative minimum of free energy, i.e. its state is metastable from the standpoint of equilibrium thermodynamics60,61). 

Rates of reaction vary with changes in temperature or concentration. All reactions are reversible (i.e., have a forward and a reverse reaction). When the rate of the forward reaction equals the rate of the reverse reaction, there is no net change in concentrations of any component, and the system is said to be at thermodynamic equilibrium. This condition represents a minimum free energy of the system and determines the limits of conversion. The overall rate of reaction equals zero at equilibrium. A relationship can be derived between the forward and reverse rate constants and the overall thermodynamic equilibrium constant. For example, consider the reaction... 

For processes in test tubes in laboratory heat baths, or processes open to the air, or processes in biological systems, it is not the work or heat flow that you control at the boundaries. It is the temperature and the pressure. This apparently slight change in conditions actually requires new thermodynamic quantities, the free energy and the enthalpy, and new extremum principles. S> stems held at constant temperature do not tend toward their states of maximum entropy. They tend toward their states of minimum free energy. 

The equilibrium state of a system at constant temperature and pressure is characterized by a minimum in the Gibbs free energy of the system according to the second law of thermodynamics. For a multicomponent, multiphase (bulk) system, the minimum free energy corresponds to uniformity of the chemical potential (yu,) of each component throughout the system as demonstrated below. For a binary system, the molar free energy (G) and chemical potentials are related by... 

Cell Volta.ge a.ndIts Components. The minimum voltage required for electrolysis to begin for a given set of cell conditions, such as an operational temperature of 95°C, is the sum of the cathodic and anodic reversible potentials and is known as the thermodynamic decomposition voltage, is related to the standard free energy change, AG°C, for the overall chemical reaction,... 

If the polymer system was able to exist in an equilibrium state only, then a strictly defined correlation between (a, ph) and (a, ph) would exist in particular conditions, according to minimum of free energy of system formation. Consequently, there would occur only one temperature at which process initiation is thermodynamically probable. In rare ca.ses there may occur different correlations between ( ph, a) and ( ph, a ), which display one and the same value of free energy minimum of system formation. 

The calculation is based on the rule of thermodynamics, which states that a system will be in equilibrium when the Gibbs free energy is at a minimum. Cl The objective then is the minimization of the total free energy of the system and the calculation of equilibria at constant temperature and volume or at constant pressure. It is a complicated and lengthy calculation but, fortunately, several computer programs are now available that considerably simplify the task. PI... 

We have seen several examples of a technique for separation of gas mixtures which, in contrast with most commercial processes, requires no physical transfer of solvent, handling of solids, or cycling of temperature or pressure. The energy requirements can also be far lower The thermodynamic minimum work of separation is, under isothermal conditions, the free energy difference between the process stream and byproduct, or permeate, stream. When this difference is due only to the partial pressure difference of component 1, it becomes ... 

The stable equilibrium thermodynamic state of a system at constant pressure and temperature is the one with the minimum Gibbs free energy, G. This thermodynamic condition is defined as ... 

Careri (Ref 7b) suggested a procedure for computing exactly the thermodynamic functions of a nonequilibrium system. The state of the system was then varied, at fixed volume and temperature, so as to give a minimum Helmholz free energy, consistent with such conditions as are imposed to permit the exact computation. The condition under which this method leads to self-consistent equations is discussed in detail. The method is then applied in a way that is very close to the Lennard-Jones and Devonshire cell method, bur with cells of variable size. The distribution within a cell is assumed to be Gaussian. Mayer Careri claimed that the method is easier to apply than the cell method, but it seems to be rather complicated... 

Thermodynamic calculations presented here are based on Gibbs free energy minimization and were carried out using HSC Chemistry. The equilibrium amount of each species that is formed is normalized on the basis of one mole of n-Ci6, a model compound for diesel fuel, fed to the reactor. Carbon formation is a function of both the S/C ratio and reforming temperature. Figure 17 shows the minimum amount of S/C ratio thermodynamically required for carbon-free SR of n-Ci6 at a given temperature. Carbon-free operation of n-Cig is thermodynamically possible above the curve. Higher temperatures and S/C ratios inhibit carbon formation. 

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