Electric thermal average

If there were no electric field, the thermal average energy would be deep in the low-energy tail of the DOS. In the presence of a field, the steady-state distribution of energies is no longer that of thermal equilibrium. Nevertheless, as it crosses the sample, a carrier spends most of its time in such low-energy sites. 

Average specific electricity consumption Average specific thermal energy consumption 1.2kWh/kg (best observed value — 0.95 kWh/kg) 15000 kCal/kg (best observed value — 10932 kCal/kg)... 

Note that E denotes a thermal average of the energy, a scalar quantity, not the electric field vector E.) Finally, multiplying Planck s expression for E (Eq. 3.40c) by pv (Eq. 3.39) gives... 

It must be stressed that, unlike our expansion of Eq. [30], which is valid only for vanishingly small values of the order parameter, Eqs. [38] and [39] are valid for arbitrary values of the order parameter. In fact, the magnetic and electric energy density expressions of the elastic continuum theory (Eqs. [3] and [4] of Chapter 8) are special cases of Eqs. [38] and [39]. For example, consider the magnetic energy density of the low temperature, anisotropic phase of a system in which only spatial variation of ri(r) is important. S f) in Eq. [38] can then be replaced by its equilibrium value , where < > denotes thermal averaging. The term proportional to H can be neglected because of its spatial invariance, and one obtains Eq. [3] of Chapter 8 directly. 

In the ESHG experiment a laser beam passes through the sample in a static electric field and a weak, collinear, frequency-doubled beam is detected. Absolute values for the hyperpolarizabilities cannot be extracted the signal from the sample is compared to that of a known buffer gas (ultimately helium, for which there are accurate theoretical values (Bishop and Pipin 1989)) or a solid. In analogy with the derivation for a, the classical thermal averaging yields... 

As we have seen in the previous sections, a crystallizable polymer melt that has been sohdified under quiescent conditions possesses a two-phase structure consisting of chain-folded crystals organized as spherulites in an amorphous matrix. Because the mechanical, optical, electrical, thermal, and transport properties of the two phases are generally quite different from each other, the observed behavior will be a weighted average of the properties of the two phases. We can expect the weighting function to be the fraction of the crystalline or amorphous phase, with the size and size distribution of the domains often playing a relatively minor role. 

IHP) (the Helmholtz condenser formula is used in connection with it), located at the surface of the layer of Stem adsorbed ions, and an outer Helmholtz plane (OHP), located on the plane of centers of the next layer of ions marking the beginning of the diffuse layer. These planes, marked IHP and OHP in Fig. V-3 are merely planes of average electrical property the actual local potentials, if they could be measured, must vary wildly between locations where there is an adsorbed ion and places where only water resides on the surface. For liquid surfaces, discussed in Section V-7C, the interface will not be smooth due to thermal waves (Section IV-3). Sweeney and co-workers applied gradient theory (see Chapter III) to model the electric double layer and interfacial tension of a hydrocarbon-aqueous electrolyte interface [27]. 

Measurement by Thermal Effects. When a fine wire heated electrically is exposed to a flowing gas, it is cooled and its resistance is changed. The hot-wire anemometer makes use of this principle to measure both the average velocity and the turbulent fluctuations in the flowing stream. The fluid velocity, L, is related to the current, /, and the resistances, R, of the wire at wire, and gas, g, temperatures via... 

Charge carriers in a semiconductor are always in random thermal motion with an average thermal speed, given by the equipartion relation of classical thermodynamics as m v /2 = 3KT/2. As a result of this random thermal motion, carriers diffuse from regions of higher concentration. Applying an electric field superposes a drift of carriers on this random thermal motion. Carriers are accelerated by the electric field but lose momentum to collisions with impurities or phonons, ie, quantized lattice vibrations. This results in a drift speed, which is proportional to the electric field = p E where E is the electric field in volts per cm and is the electron s mobility in units of cm /Vs. 

Unlike solar thermal systems or PV concentrator systems, the PV flat plate systems work well in cloudy locations because these latter convert diffuse as well as direct sunlight to electricity. On an aimualized basis, the energy produced by a photovoltaic array varies by only about 25% from an average value for the contiguous 48 states of the United States. As a result, it is practical to use photovoltaic systems in normally cloudy locations such as Seattle or northern Maine. 

Acetylene black is very pure with a carbon content of 99.7%. It has a surface area of about 65 m /g, an average particle diameter of 40 nm, and a very high but rather weak stmcture with a DBPA value of 250 mL/100 g. It is the most crystalline or graphitic of the commercial blacks. These unique features result in high electrical and thermal conductivity, low moisture absorption, and high Hquid absorption. 

Demand for natural gas, in all markets—residential, commercial, and industrial—is projected to grow into the foreseeable future, particularly in the electric power generation market and the industrial sector. Total natural gas use in the United States is projected to grow from 20.1 quadrillion British thermal units in 1992 to 26.1 by 2010, an average growth rate of 1.6 percent per year. 

The dependence of the local Nusselt number on non-dimensional axial distance is shown in Fig. 4.3a. The dependence of the average Nusselt number on the Reynolds number is presented in Fig. 4.3b. The Nusselt number increased drastically with increasing Re at very low Reynolds numbers, 10 < Re < 100, but this increase became smaller for 100 < Re < 450. Such a behavior was attributed to the effect of axial heat conduction along the tube wall. Figure 4.3c shows the dependence of the relation N /N on the Peclet number Pe, where N- is the power conducted axially in the tube wall, and N is total electrical power supplied to the tube. Comparison between the results presented in Fig. 4.3b and those presented in Fig. 4.3c allows one to conclude that the effect of thermal conduction in the solid wall leads to a decrease in the Nusselt number. This effect decreases with an increase in the... 

A strong electric field is formed in very thin films (with a thickness of about 10 5 cm) during current flow. If the average electrochemical potential difference between two neighbouring ions in the lattice is comparable with their energy of thermal motion, kTy then Ohm s law is no longer valid for charge transport in the film. Verwey, Cabrera, and Mott developed a theory of ion transport for this case. 

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