Adiabatic hypothesis

Ehrenfest calls this postulate, that, in the limiting case of infinitely slow changes, the principles of classical mechanics remain valid, the adiabatic hypothesis, by analogy with the terminology of thermodynamics 1 Bohr speaks of the principle of mechanical transform-ability. 

As the skewing angle increases, however, the simple adiabatic hypothesis becomes less and less satisfactory, as the H+H2 case shows. Figure 7 [5l]. The clear inadequacy of this oversimplified approach to deal with the general case has pointed out the need for the semiclassical treatment of nonadiabatic coupling. 

This counting is based on the assumption (which is satisfied for many spectra) that in the first instance the motion of the model is determined by the principal and secondary quantum numbers of the single electrons, that then in the next instance the interaction of the vectors 1 with each other and the St with each other and only then in the third instance the interaction of I and s can be added as a small perturbation. This pictorial model even leads (adiabatic hypothesis) to a correct counting of the terms if the interaction ratio no longer represents reality, but the model in this case no longer yields the correct position of the terms, and the quantum numbers no longer represent the mechanical quantities of the model (which is apparent from the invalidity of the Lande interval rule for multiplets and the g-formula). 

In this paper we consider protoceUs composed by a finite volume enclosed by a membrane that - for simplicity - is assumed to be permeable only to short molecules. The transmembrane motion of the permeable species is here supposed to be ruled by the difference of their chemical potentials in the internal aqueous volume of the protocell and in the external aqueous environment. We assume that transmembrane diffusion is extremely fast, so that there is always equilibrium between the internal and external concentrations of the permeable species (this adiabatic hypothesis could be... 

Design of explosion suppression systems is clearly complex, since the effectiveness of an explosion suppression system is dependent on a large number of parameters. One Hypothesis of suppression system design identifies a limiting combustion wave adiabatic flame temperature, below which combustion reactions are not sustained. Suppression is thus attained, provided that sufficient thermal quenching results in depression of the combustion wave temperature below this critical value. This hypothesis identifies the need to deliver greater than a critical mass of suppressant into the enveloping fireball to effect suppression (see Fig. 26-43). 

In some cases the hypothesis fixes completely which special motions are to be considered as allowed. This occurs if the new class of motions are derived by means of an adiabatic transformation from some class of motions already known (Ehrenfest [1917]). 

Figure 5.18 shows the overall conversion of NCO groups as a function of time for uncatalyzed samples cured at three different temperatures. Points are experimental values, while full curves are predicted results using the kinetic parameters derived in the adiabatic analysis. The predictive capability of the rate equation is very good, in spite of the strong hypothesis regarding the absence of substitution effects. 

Starting with Bowden and Yoffe s adiabatic compression hypothesis, a method and apparatus (the Olin-Mathieson (O-M) drop-weight tester) were adopted by a committee on test methods (11). The technique was... 

The simplest way of taking aceount of vibrational effeets is to assume vibrational adiabatieity during the motion up to the eritieal dividing surface [27]. As mentioned aheady in the Introduetion, mueh of the earlier work on vibrational adiabatieity was concerned with its relationship to transition-state theory, espeeially as applied to the prediction of thermal rate constants [24-26], It is pointed out in [27] that the validity of the vibrationaUy adiabatie assumption is supported by the results of both quasielassieal and quantum seattering ealeulations. The effeetive thresholds indicated by the latter for the D -I- H2(v =1) and O + H2(v =1) reactions [37,38] are similar to those found from vibrationaUy adiabatic transition-state theoiy, which is a strong evidence for the correctness of the hypothesis of vibrational adiabatieity. Similar corroboration is provided by the combined transition-state and quasielassieal trajectory calculations [39-44]. For virtually all the A + BC systems studied [39-44], both collinearly and in three... 

In the present context, the adiabatic elimination leading to (3.38) is called the steady state hypothesis and was introduced by Briggs and Haldane (1925). In the original treatment by Michaelis and Menten (1913) an assumption of equilibrium for the first reaction in (3.27) was made, which leads to the same result (3.39) but with a different expression for Km- The steady state hypothesis can be justified rigourously and is precise as long as Et < Km + S(0) (Segel and Slemrod, 1989). 

It may well be true that the entropy of the universe is increasing (see Chapter 6), but whatever it is doing is quite irrelevant to the study of thermodynamics here on Earth. The difference between the two ways of looking at AS presented above essentially involves two different definitions of the system. In our preferred explanation, the system is the water in the pail, and its entropy decreases spontaneously. In the other view, the system is the universe, by implied hypothesis a closed composite adiabatic system, and the pail a portion of this composite system separated from the rest by diathermal walls. In the overall system, entropy increases. In this view, the choice of system is effectively taken from us—we must choose the universe as our system to preserve the dictum that entropy increases in spontaneous processes. 

In electrochemical kinetics, this model corresponds to the Butler-Vohner equation widely used for the electrode reaction rate. The latter postulates an exponential (Tafel) dependence of both partial faradaic currents, anodic and cathodic, on the overall interfacial potential difference. This assumption can be rationalized if the electron transfer (ET) takes place between the electrode and the reactant separated by the above-mentioned compact layer, that is, across the whole area of the potential variation within the framework of the Helmholtz model. An additional hypothesis is the absence of a strong variation of the electronic transmission coefficient", for example, in the case of adiabatic reactions. 

Recent calculations /16/ for some simple gas reactions show that T is shorter than the periods of vibrations and rotations of the activated complex, therefore, it cannot be considered as a stationary state configuration with a well-defined discrete energy spectrum. This is contrary to the assumption of vibrational-rotational adiabaticity which is related to the equilibrium hypothesis of activated complex theory. 

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