Gradient intensive parameter

The affinities that define the rate of entropy production in continuous systems are therefore gradients of intensive parameters (in entropy representation) rather than discrete differences. For instance, the affinities associated with the z-components of energy and matter flow for constituent k, in this notation would be... 

Chemical potential, as the concentration, is intensive parameter and does not depend on the amoxmt of solution. It serves the main criterion of the balance in the composition and the state of a system. Exactly gradients of the chemical potential, and not the concentration is the motivating force of mass exchange, hke the presstue gradients are the motivating force of flow. Equilibrium is reached when not the concentration but the chemical potentials of dissolved components become equal in the entire volume of the medium or in compared media. At equal chemical potentials the concentration of components may be totally different. That is why for the determination of the rate and direction of chemical processes or mass exchanges it is necessary to know how to meastue chemical potentials. 

The flux of mass and energy in a continuum occurs in the presence of spatial gradients of state parameters, such as temperature, pressure, or electrical potential. Variables such as the volume of a system, its mass, or the number of moles are called extensive variables because their values depend on the total quantity of substance in the system. On the other hand, variables such as temperature, pressure, mole fraction of components, or electrical potential constitute intensive variables because they have certain values at each point in the system. Therefore, constitutive equations express the connection between fluxes and gradients of the intensive parameters. In the constitutive equations listed above, the flux de-... 

Consider the serial array shown in Fig. 5., where both the thermodynamic subsystems have identical thermodynamic currents, and its thermodynamic forces are additive values, because they are originated from the gradients of intensive parameters by line-integration). The dissipation potentials are given for each current-tube. 

Consider, for example, a crystallized, binary solid made up of A and B elements. If this solid does not present any point defects, its composition is uniform, and if all other intensive parameters are also uniform, the solid is said to be in internal equilibrium. The diffusion of one of the species A or B can be considered only if the solid presents other structrrre elements than the oires of the ideal crystal, that is, point defects. Indeed, on the contrary there is no gradient of chemical potential, so atoms or molecules of A or B cotrld not diffuse. 

The quantity k is related to the intensity of the turbulent fluctuations in the three directions, k = 0.5 u u. Equation 41 is derived from the Navier-Stokes equations and relates the rate of change of k to the advective transport by the mean motion, turbulent transport by diffusion, generation by interaction of turbulent stresses and mean velocity gradients, and destmction by the dissipation S. One-equation models retain an algebraic length scale, which is dependent only on local parameters. The Kohnogorov-Prandtl model (21) is a one-dimensional model in which the eddy viscosity is given by... 

Fig. 4. Quadrupolar powder patterns (a) Spin NMR powder pattern showing that the central -)<- ) transition is broadened only by dipolar coupling, chemical shift anisotropy, and the second-order quadrupolar interactions, (b) Spin 1 NMR powder pattern for a nucleus in an axially symmetric electric field gradient (see text). The central doublet corresponds to 6 = 90° in Eq. (10). The other features of low intensity correspond to 6 = 0° and 6 = 180°. (c) Theoretical line shape of the ) - -) transition of a quadrupolar nuclear spin in a powder with fast magic-angle spinning for different values of the asymmetry parameter t (IS) ...

The increase in vertical turbulence intensity caused by cooling tower plumes can be estimated for each temperature gradient and increment of distance from the tower. This can be represented by well-known turbulence parameters developed for Gaussian plume models ... 

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