Adiabatic traversal

The behavior of a colliding system at the avoided crossing depends on the speed with which the crossing is traversed, as well as the separation and slopes of the adiabatic curves. If the atoms approach slowly enough on the covalent curve, the... 

Hoskin Lambourn (Ref 26) examined the system of a detonation initiated simultaneously at the expl face in contact with one of two metal plates, ie, an asymmetric metal/expl/metal sandwich . They assumed that the detonation products are isentropic with a constant adiabatic exponent = 3, and showed that the motion of both plates can be determined by the continued reflection of centered simple waves. The path of the reflected shock was followed by an approximate method for two traverses of the detonation products, and the process can be continued indefinitely... 

What conditions must be fulfilled for the ionization process to occur in the adiabatic fashion we have just described First, the transition from the zero field ntm states to the intermediate field Stark states must be adiabatic. Second, the traversal of the avoided crossings in the strong field regime, E > l/3n5 must be adiabatic as well. Finally, ionization only occurs at E > W2/4 if the ionization rate exceeds the inverse of the time the pulse spends with E > W2/4. 

If S Sx the avoided crossing is traversed diabatically and if S Sx it is traversed adiabatically. Between the two extremes of purely adiabatic and purely diabatic traversals, the probability of making the diabatic transition is given by the Landau-Zener transition probability, as has been demonstrated by Rubbmark et... 

Adiabatic fixed-bed reactors constitute the oldest fixed-bed reactor configuration. In the simplest case they consist of a cylindrical jacket in which the catalyst is loosely packed on a screen support and is traversed in the axial direction (Fig. 9A). To avoid catalyst abrasion by partial fluidization, random catalyst packings arc always traversed from top to bottom. If fixed-beds composed of monolith catalyst sections are used, the flow direction is arbitrary. 

An adiabatic reactor with a regular flow pattern is much simpler to work with than one with exchange of heat. Except for resistance to exchange of material and heat between fluid and catalyst, the space velocity is the only significant space variable. The natural independent variable to use is space velocity, or the volume traversed divided by the total molar flow. The relation between the concentration and the reciprocal space velocity is given by the equation... 

Our purpo se now is to show that Eq. (5.9), applicable to the reversible Carnot cycle, also applies to otlrer reversible cycles. The closed curve on the P V diagram of Fig. 5.4 represents an arbitrary reversible cycle traversed by an arbitrary fluid. Divide the enclosed area by a series of reversible adiabatic curves since such curves camiot intersect (Pb. 5.1), they may be drawn arbitrarily close to one anotlier. Several such curves are shown on the figure as long dashed lines. Coimect adjacent adiabatic curves by two short reversible isotherms which approximate tire curve of tlie arbitrary cycle as closely as possible. The approximation clearly improves as the adiabatic curves are more closely spaced. When the separation becomes arbitrarily small, the original cycle is faithfully represented. Each pair of adjacent adiabatic curves and their isothenrral comrectiirg curves represeirt a Carnot cycle for which Eq. (5.9) applies. 

In a Camot cycle (Fig. 13.5), a system traverses two isothermal and two adiabatic paths to return to its original state. Each path is carried out reversibly (that is, in thermal equilibrium, with internal and external forces nearly balanced at every step). As the system proceeds from state A to C through state B, the system performs work (Fig. 13.5a) ... 

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