Isokinetic temperature meaning

Thus, y is the slope of the plot of A// against AG at the harmonic mean temperature, and from y the isokinetic temperature P is calculated. Tomlinson has shown many examples of this type of analysis. 

There is usually a compensation between values of rate constants along a series. That is, when AH increases, AS does so as well (and vice versa). As a consequence, the spread of the rate constant is less than if AH were varied at constant AS (or vice versa). This means that the isokinetic temperature is usually > 0 K, and often 0K. 

Figure 4.35. Effect of catalyst work function on the activation energy EA, preexponential factor k° and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt/YSZ 4 p02=4.8 kPa, Pc2H4=0-4 kPa,4,54 kg is the open-circuit preexponential factor, T is the mean temperature of the kinetic investigation, 375°C.4 T0 is the (experimentally inaccessible) isokinetic temperature, 886°C.4 25,50...

The physical meaning of the constant (3, connected with the reversal of reactivity at the temperature T = /3, is a puzzling corollary of the isokinetic relationship, noted already by older authors (26, 28) and discussed many times since (1-6, 148, 149, 151, 153, 163, 188, 212). Especially when the relative reactivity in a given series is explained in theoretically significant terms, it is hard to believe that the interpretation could lose its validity, when only temperature is changed. The question thus becomes important of whether the isokinetic temperature may in principle be experimentally accessible, or whether it is merely an extrapolation without any immediate physical meaning. 

Practically all values of 3 within the experimental interval claimed in the literature (1-5, 115-119, 153) have been shown to be artifacts (148, 149, 163) resulting from improper statistical treatment (see Sec. IV). Petersen thus believed (148) that actually no such value had been reported, and the meaning was offered that the isokinetic temperature probably is not accessible experimentally (149, 188). This view was supported by the existence of negative... 

It follows that for a special value of one parameter, the observed value of y is independent of the second parameter. This happens at Ii= a2/ai2 or I2 = -ai/ai2 any of these values determines y= a -aia2/ai2, the so called isoparametrical point. The argument can evidently be extended to more than two independently variable parameters. Experimental evidence is scarce. In the field of extrathermodynamic relationships, i.e., when j and 2 are kinds of a constants, eq. (84) was derived by Miller (237) and the isoparametrical point was called the isokinetic point (170). Most of the available examples originate from this area (9), but it is difficult to attribute to the isoparametrical point a definite value and even to obtain a significant proof that a is different from zero (9, 170). It can happen—probably still more frequently than with the isokinetic temperature—that it is merely a product of extrapolation without any immediate physical meaning. 

Since A° is constant for a given series satisfying equation (44), any structural change in the reactants must be reflected in the only parameter, E, determining the rate constant. If T = Tit the rate constants of all reactions in the given set will be identical. For that reason, Tt is called the isokinetic temperature . It is a mathematical consequence of equation (44) and has no physical meaning. (The only physically reasonable isokinetic temperature is the absolute zero.) Nevertheless, the value of as compared with a medium value of the temperature range of experiments (Texp) can help us to classify possible correlations of the Arrhenius parameters (Simonyi, 1967 Tiidos, 1969). 

That means that the phenomenon isokinetic effect is indicated by the observation that the Arrhenius lines of the closely related reactions intersect in only one point, characterized by the isokinetic pre-exponential factor kao and by the isokinetic temperature Tiso, or, in other words, there is a linear relationship between In ko and Ea with the slope IRT so-... 

As seen from Fig. 1, the kinetic data In ko and a strictly follow a compensation line. Two points are worth stressing (a) Independently of the kind of contact mass variation (variation of promoters, copper component, copper content, or Si quality), all data follow the same compensation line. This line is characterized by an isokinetic rate constant of kiso = 7.1 mmolmc/gc.m. h and an isokinetic temperature of 7iso = (603 20) K. (b) The isokinetic temperature is positioned within the range of reaction temperatures applied. That means that a ranking of contact mass reactivities is generally impossible and is possible only at a certain temperature. 

There exists a linear dependence between the enthalpy and entropy values (Fig. 1). The slope of the straight line, which was considered as the isokinetic temperature, amounts to 3K. It was calculated by the least squares method. Similar values of the isokinetic temperature were obtained by means of the method of intersection of the Arrhenius lines. 

Equation 77 shows that, at the isokinetic temperature. Eg is the mean of 1 and 2. Furthermore, inspection of Eq. 79 shows that—contrary to some statements in the literature (3, 64)— the isokinetic temperature does not coincide with Tmax- It turns out that the latter is always below the former, irre-... 

It is irrelevant for this effect whether the isokinetic temperature lies above or below the temperature at which K = 1. However, if these two temperatures coincide, then the Arrhenius plot passes smoothly from one slope to the other, without a transition curve (64). At that point, Ea is the mean of Ei and 2. 

In these expressions, use has been made of (8.4.4) A and A" are constants for the reactions or elementary steps of a given family. Therefore the meaning of 0 is that of an isokinetic temperature, i.e., a temperature at which rate constants for ail reactions or elementary steps of a family have the same value. Below that temperature, the reactions with a smaller activation energy are faster. Above the isokinetic temperature, the faster reactions are the ones with the larger values of the activation energy. These relations are illustrated in the Arrhenius diagram of Fig. 8.4.1. 

Downstream of the reactor the temperature and the gas flow is measured and the chemical analysis of the gas is performed concerning the concentration of the relevant components furthermore an isokinetic sampling is performed the particles with a diameter greater than 0.05 pm are collected on a membrane filter and successively analyzed all the remaining soluble substances are taken off by means of a series of distilled water filled impingeis and also analyzed. 

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