Macroscopic potential

In addition to the nearest-neighbor interaction, each ion experiences the electrostatic potential generated by the other ions. In the literature this has generally been equated with the macroscopic potential 0 calculated from the Poisson-Boltzmann equation. This corresponds to a mean-field approximation (vide infra), in which correlations between the ions are neglected. This approximation should be the better the low the concentrations of the ions. 

The phenomenological coefficient relating the current density and the macroscopic potential gradient is the conductivity due to the ion, k,. Thus, one has the general relationship... 

In our discussion below, we assume that the binding energy of a CTE is large, and the CTEs are rather stable and do not participate in the photogeneration of free carriers. We will show that the asymmetrical stack of D-A interfaces under pumping of CTEs provides a macroscopic potential drop that can be... 

However, the qualitative features of its dependence on the light intensity can be established on the grounds of simpler considerations. At low intensity of light the steady state CTE concentration, which is dependent on the pumping intensity I of CTEs and their lifetime, will be small and the macroscopic potential drop will be negligible. The macroscopic potential drop V I will be important... 

The extremely complex redox behavior of the tetraheme cytochrome c3 is probably also operative in the other multiheme cytochromes. However, with an even higher number of hemes per subunit it becomes impossible to perform such detailed studies. Hence, the reduction potentials quoted for the cytochromes in the next sections must be considered as apparent macroscopic potentials which simply reproduce the overall redox profile. 

The last form of energy, namely the macroscopic potential energy, is accounted for by considering conservative body forces derivable from a potential, such as the gravity force per unit volume pg, in the term / in the definition of i. Note that relative to the first principle, all forms of energy have an equal status. 

Solution. Since the center of mass of the parcel does not move, there is no change in either the macroscopic potential energy or the kinetic energy of the parcel. Also, the pressure of the system remains constant at 1 atm= 1.013 bar= 1.013 x 10 Pa. Therefore, the first law of thermodynamics in the form of Eq. (2.6) applies, which, for a system as a whole (rather than a unit mass), can be written... 

The macroscopic quantities used for describing the state of internal energy of a system are called state variables. For an ideal gas, these may, for example, be volmne V, pressure p, temperature T, and amount of substance n. Added to these are the mechanical quantities required to determine the macroscopic potential and kinetic energy, i.e. quantities such as the velocity v and position XyXfyZ) of the system. In the following, reference will mainly be made to the internal energy of systems. 

While several calculations have proved that a charge density a = a jl may appear at a surface when the electronic degrees of freedom are taken into account, it should be noted that no one has found a dipole density a"R with a" = ajA. It is likely that, in actual systems with a discrete atomic structure, the oscillating macroscopic potential (G = 0) (Fig. 3.7b) is strongly damped by microscopic non-uniform contributions (Gy f= 0 terms). 

The macroscopic potential energy, Ep, is the energy associated with the bulk (macroscopic) position of the system in a potential field. For example, an object in the Earths gravitational field has a potential energy given by ... 

SOLUTION Can you draw a schematic of this process We need to write the energy balance. This system is at steady-state, with one stream in and one stream out. When working with macroscopic potential energy, it is often convenient to write the balance on a mass (rather than mole) basis. We will neglect the bulk kinetic energy of the water at the inlet and outlet and the heat loss through the pipe. Since there are no frictional losses, the exit temperature is the same as the inlet therefore, their enthalpy is equal. Thus, the first law simplifies to ... 

For systems where macroscopic kinetic energy and macroscopic potential energy are important, we can generalize to ... 

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