Energy loss curves

Energy release and energy loss curves for an irreversible reaction in a flow reactor. 

However, the characteristics of point b with regard to temperature fluctuations are quite different. At this point the slope of the energy release curve is greater than the slope of the energy loss curve. If a small positive temperature fluctuation were to occur, one would be in a... 

If the temperature intercept of the energy loss curve lies between those corresponding to the... 

Fig. 5.2. Energy versus energy loss curves for hydrogen and helium isotopes in silicon.

Figure 8.7 presents ionization energy loss curves for electrons in some common materials. 

The plot of CE = Pout/Ps (from Eqs (5.10.33) and (5.10.37)) versus Ag for AM 1.2 is shown in Fig. 5.65 (curve 1). It has a maximum of 47 per cent at 1100 nm. Thermodynamic considerations, however, show that there are additional energy losses following from the fact that the system is in a thermal equilibrium with the surroundings and also with the radiation of a black body at the same temperature. This causes partial re-emission of the absorbed radiation (principle of detailed balance). If we take into account the equilibrium conditions and also the unavoidable entropy production, the maximum CE drops to 33 per cent at 840 nm (curve 2, Fig. 5.65). 

At steady state the rate of transformation of energy by reaction must be equal to the rate of thermal energy loss. This implies that the intersection ) of the curves given by equations 10.6.6 and 10.6.8 will represent the solution(s) of the combined material and energy balance equations. The positions at which the intersections occur depend on the variables appearing on the right side of equations 10.6.6 and 10.6.8. Figure 10.3 depicts some of the situations that may be encountered. 

To further reduce of the cross section formula (4.11), we note that it is proportional to the area of the curve of Fn(K)/en plotted against In (Kag)2 between the maximum and minimum momentum transfers. Since T is large and the generalized oscillator strength falls rapidly with the momentum transfer, the upper limit may be extended to infinity. In addition, the minimum momentum transfer decreases with T in such a manner that the limit Fn(K) may be replaced by /, the dipole oscillator strength for the same energy loss. This implies that a mean momentum transfer can be defined independently of T such that the relevant area of the curve of Fn(K)/ n is equal to (// ) [ (In Kag)2 - (In Ka0)2]. Thus, by definition (Bethe, 1930 Inokuti, 1971),... 

Figure 11. Electron-energy-loss spectrum of crystalline boron nitride, showing the boron K-edge (at 190 eV) and the nitrogen K-edge (at 400 eV). The background intensity, delineated by the dashed curve arises from inelastic scattering by valence electrons. The hatched areas represent the measured values required for the quantitative analysis of boron ( see text) (50).

The right-hand side (RHS) of Equations (9.116) and (9.119) represent the net heat loss and the left-hand side (LHS) represents the energy gain. The gain and the loss terms can be plotted as a function of the flame temperature for both the diffusion and premixed flames as Semenov combustion diagrams. Intersection of the gain and loss curves indicates a steady solution, while a tangency indicates extinction. 

Figure 2.11 Morse curve for an excited molecule. The energy required for excitation (A) is lost as the molecule returns to the ground state but only the energy lost between states (C) may be emitted as radiation. Energy losses due to internal rearrangements (B and D) are non-radiative.

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