Critical state for the thermal

As stated in Preface, the basic concept of the thermal explosion theory is that whether the thermal explosion or the spontaneous ignition of a chemical of the TD type, including every gas-permeable oxidatively-heating substance, having an arbitrary shape and an arbitrary size, placed in the atmosphere under isothermal conditions, occurs or not is decided, based on the balance between the rate of heat generation in the chemical and the rate of heat transfer from the chemical to the atmosphere at the critical state for the thermal explosion which exists at the end of the early stages of the self-heating process. 

The critical state for the thermal explosion is a state corresponding to the point of tangency which is shown in Fig. 2 presented in Section 1.2, And, the self-heating process of a chemical of the TD type from a temperature, e.g., the which is also shown in Fig. 2, situated below Ti up to T is referred to as the early stages of the process. 

Now, the Semenov equation is certainly based on the nonstationary theory of the thermal explosion, because this equation holds on the assumption that the spatial distribution of temperature in a fluid fdled in the container and placed in the atmosphere maintained at a temperature situated below the critical state for the thermal explosion, is uniform (refer to Section 1.2). In this regard, it has been ascertained in a series of studies, which are described in Subsections 5.5.3 and 5.7.2, as well that the spatial distribution of temperature in an arbitrary volume of a liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions is perfectly uniform in the early stages of the self-heating process, except the thin upper surface layer, even if it is not stirred mechanically [18]. 

In this connection, the explosion limit, a term used in the F-K s scheme, corresponds to the critical state for the thermal explosion in the Semenov s scheme. 

Now, every liquid may also have the uniform distribution of internal temperature as a kind of fluid. In other words, as stated in Section 1.5, it will be permitted to say that a condition, UKK A, holds at all times, on account of its own fluidity, in an arbitrary volume of every liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions. The problem in considering the critical condition for the thermal explosion of a liquid is, thus, not the heat transfer by the convection in the mass of the liquid, but the heat transfer or the heat loss by the conduction from the liquid charged in an arbitrary container and placed in the atmosphere under isothermal conditions, through the whole liquid surface, across the container walls, to the atmosphere. 

Merzhanov Dubovitskii (Ref 4) formulated a general theory for the thermal explosion of condensed expls, which takes into consideration the removal of particles from the reaction volume. This theory makes it possible to calc all the basic characteristics of thermal explosion such as critical conditions, depth of preexplosion decompn induction period "Detonation is Condensed Explosives is the title of a book by J. Taylor (Ref 3) who discusses in detail the various aspects of the subject. See also studies reports listed as Refs 2, 5 6 Refs 1)L.D.Landau K.P.Stanyukovich, Dokl-AkadN 46, 396-98 (1945) 47, No 4, 273-76 (1945) CA 40, 4523 4217 (1946) 2)G.Morris H.Thomas, "On the Thermochemistry and Equation of State of the Explosion Products of Condensed Explosives , Research (London)... 

The general procedure followed will be outlined briefly here for the thermal conductivity. All available experimental data for the saturated liquid for each molecular species is first plotted in reduced forms vs. the reduced temperature, as shown by the solid lines in Fig. 2. Associated with each molecular species is, of course, a characteristic A. Isotherms are then cross-plotted for /c vs. A, as shown in Fig. 3, from which additional values of k can be obtained for any given A. Then by iteration, the existing data for each molecular species is extrapolated to consistent triple- and critical-point values. In both Figs. 2 and 3 the classical critical and triple points have become lines, since for light molecules the reduced parameters of the critical state are also functions of A as mentioned above. 

For the theoretician, clusters are also convenient model systems to evaluate the performance of dissociation rate theories. By comparing the results of numerically exact molecular dynamics (MD) trajectories to the predictions of rate theories, the various approximations inherent to these theories can be unambiguously tested and possibly improved upon. Previous authors have critically discussed how the Rice-Ramsperger-Kassel (RRK), ° Weisskopf, and Phase Space Theory of Light and Pechukas, Nikitin, Klots, Chesnavich and Bowers respectively compare for the thermal evaporation of atomic clusters. This work was subsequently extended by the present authors to rotating and molecular clusters. From these efforts it was concluded that phase space theory (PST), in its orbiting transition state version, was quantitatively able to describe statistical dissociation. This chapter is not devoted to a detailed presentation of phase space theory and the reader is encouraged to consult the cited work. 

The purpose of this chapter, in a book about transport properties, is to give advice to the reader on the best methods for converting the data, which are usually measured as a function of P and T, to a function of p and T, which is the form required for the correlating equations and, in addition, to provide sources for values of the ideal-gas isobaric heat capacities, which are also required for the transport-property calculations. Both of these purposes can be fulfilled by calculations from a single equation of state which has been fitted to the whole thermodynamic surface. Heat capacities of the real fluid are required only for the calculation of the critical enhancement of the thermal conductivity and viscosity, as described in Chapter 6 discussion of these properties in this chapter will be restricted to Section 8.4.4. 

Hence, in order to evaluate the critical enhancement of the thermal conductivity by means of equation (14.58) apart from the background transport properties, a knowledge of three thermodynamic properties is needed, namely, that of the isochoric and isobaric heat capacities and of the correlation length, all of which can be evaluated from the relevant equation of state. Furthermore, one needs to determine four adjustable parameters (see Chapter 6) which enter the expressions for Q and Qq- Two of these, namely, the system-dependent amplitudes fo and r, have been obtained by the application of the... 

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