Conduction proportionality constant

A general observation, verified for nearly all soHds, is a proportionality between current density and field strength, known as Ohm s law. The electrical conductivity is this proportionality constant and is defined as... 

The parameter, K, is a proportionality constant that is known as the hydraulic conductivity. 

The proportionality constant between the current and the electrochemical potential gradient is controlled by the partial electrical conductivity [Pg.546]

The theoretically derived formula (21) relating PMC measurements to the surface concentration of minority carriers and interfacial rate constants contains a proportionality constant, S, the sensitivity factor. This factor depends on both the conductivity distribution in the semiconductor elec-... 

Although the transport properties, conductivity, and viscosity can be obtained quantitatively from fluctuations in a system at equilibrium in the absence of any driving forces, it is most common to determine the values from experiments in which a flux is induced by an external stress. In the case of viscous flow, the shear viscosity r is the proportionality constant connecting the magnitude of shear stress S to the flux of matter relative to a stationary surface. If the flux is measured as a velocity gradient, then... 

Using Eq. (2.6.18) the temperature dependence of various transport properties of polymers, such as diffusion coefficient D, ionic conductivity a and fluidity (reciprocal viscosity) 1/rj are described, since all these quantities are proportional to p. Except for fluidity, the proportionality constant (pre-exponential factor) also depends, however, on temperature,... 

The transport process abont which most of us have an intnitive nnderstanding is heat transfer so we will begin there. In order for heat to flow (from hot to cold), there must be a driving force, namely, a temperature gradient. The heat flow per unit area (Q/A) in one direction, say the y direction, is the heat flux, qy. The temperature difference per unit length for an infinitesimally small unit is the temperature gradient, dT/dy. According to Eq. (4.1), there is then a proportionality constant that relates these two quantifies, which we call the thermal conductivity, k. Do not confuse this quantity with... 

You should be able to see the similarities in Eqs. (4.2) through (4.4). We will use these relationships a great deal in this chapter, so you should understand them fully and do some background reading if they are unfamiliar to you, but we will again concentrate on the proportionality constants thermal conductivity, viscosity, and molecular diffusivity. 

The thermoelectric effect is due to the gradient in electrochemical potential caused by a temperature gradient in a conducting material. The Seebeck coefficient a is the constant of proportionality between the voltage and the temperature gradient which causes it when there is no current flow, and is defined as (A F/A7) as AT- 0 where A Fis the thermo-emf caused by the temperature gradient AT it is related to the entropy transported per charge carrier (a = — S /e). The Peltier coefficient n is the proportionality constant between the heat flux transported by electrons and the current density a and n are related as a = Tr/T. 

For thermal conductivity, the SI units are W/(m K). In laminar flow, the thermal conductivity, A, and the diffiisivity, D, are constant with respect to their respective gradients. Eqn. (3.4-3) indicates that the diffusion flux of solute [mol A/(m2 s)] is proportional to the transverse concentration gradient, with D as the proportionality constant. The dimensions of D are length2/ time, and its units are m2/s in the SI. Eqn. (3.4-2) states that the heat flux [in J/ (m2.s) = W/m2] is proportional to the temperature gradient, with a constant a = A/(p cp) that is called the thermal diffusivity. Its dimensions are length2/time and its SI units are m2/s. Thus, it is not unexpected that the coefficient v = p/p has the same dimensions and units, m2/s. The coefficient v is called the kinematic viscosity, and it clearly has a more fundamental significance than the dynamic viscosity. The usual unit for kinematic viscosity is the Stokes (St) and submultiples such as the centistokes (cSt). In many viscometers, readings... 

From Equation 8.20 we see that the current in a conductor is proportional to the voltage across it. The proportionality constant Ka/f is defined as the conductance G ... 

The determination of r is made easier because of several aspects of Eq. (4.32). It is not necessary to know the real zero point (/ = 0) of the relaxation curve moreover, a physical property such as absorbance or conductance related to concentration is measured in relaxation studies rather than actual concentrations. With first-order reactions, one does not need to know the proportionality constant between the physical property and the concentration of the respective species. This is valid only if one or all of the species present in the system contributes to the physical property (Bernasconi, 1976). Another basic feature of chemical relaxation that should be mentioned is that the forward and backward reactions of Eq. (4.1) contribute additively to r l (Bernasconi, 1976). Thus, it is the faster of the two processes which contributes most to r-1. 

Although irreversible thermodynamics neatly defines the driving forces behind associated flows, so far it has not told us about the relationship between these two properties. Such relations have been obtained from experiment, and famous empirical laws have been established like those of Fourier for heat conduction, Fick for simple binary material diffusion, and Ohm for electrical conductance. These laws are linear relations between force and associated flow rates that, close to equilibrium, seem to be valid. The heat conductivity, diffusion coefficient, and electrical conductivity, or reciprocal resistance, are well-known proportionality constants and as they have been obtained from experiment, they are called phenomenological coefficients Li /... 

Molecular Flow Under molecular flow conditions, conductance is independent of pressure. It is proportional to VT/M , with the proportionality constant a function of geometry. For fully developed pipe flow,... 

If the concentration of tracer in the outlet stream is not measured directly, a quantity Rj(t), which is proportional to C(t), must be measured. For example, Rj(t) may be light absorbance if the tracer is a dye, a conductance if the tracer is an electrolyte, or a counting rate if a radioactive tracer is used. If C(t) = kR[(t), where k is the proportionality constant, it can be substituted in Equation 8-54 to give the residence time density function E(t) as... 

The proportionality constant k is called the thermal conductivity of the material. Heat is transferred from regions of high temperatures to low temperatures - hence the negative sign in front of k. Equation (1) holds for liquids and gases, as well as for solids, as long as convection and radiation are prevented. 

The proportionality constant h is designated as the heat-transfer coefficient, and it is a function of the type of agitation and the nature of the fluid. The heat-transfer coefficient, like the thermal conductivity k, is often detennined on the basis of experimental data. For steady-state conditions, Eq. (3) becomes... 

The Proportionality Constant Relating Electric Field and Current Density Specific Conductivity... 

The proportionality constant between the applied electric field and the resulting drift velocity is called the charge carrier mobility, jx. For electrons, = q r /ml ), for holes, ftp = 7(Trn/mj ). It should be noted that, owing to differences in the effective masses of electrons and holes, their mobilities within a semiconductor may be markedly different. The electrical conductivity, a, of a semiconductor is related to the free carrier concentrations by ... 

Here the proportionality constant icditf >s Ihc diffusion coefficient of the medium, which is a measure of how fast a commodity diffuses in (he medium, and the negative sign is to make the flow in the positive direction a positive quantity (note that dOdx is a negative quantity since concentration decreases in the flow direction). You may recall that Fourier s law of heat conduction. Ohm s law of electrical conduction, and Newton s law of viscosity are all in tlie form of Eq. 14-1. 

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