Adiabatic index

The conditions existing during the adiabatic flow in a pipe may be calculated using the approximate expression Pi/ = a constant to give the relation between the pressure and the specific volume of the fluid. In general, however, the value of the index k may not be known for an irreversible adiabatic process. An alternative approach to the problem is therefore desirable.(2,3)... 

In the MF equation (A7.20) can be simplified essentially only in the particular case of non-adiabatic collisions, which do not change the molecular orientation y(g) = <5(g). In this case operator T = /, and the relaxation part of (A7.20) can be diagonalized over index q ... 

The LDPE reactor is sometimes termed heat transfer limited in conversion. While this is true, the molecular weight (or melt index)—conversion relationship is not since this work shows that a selected initiator can allow conversion improvements to be made under adiabatic conditions for a specified molecular weight. The actual limitation to conversion is the decomposition temperature of the ethylene and given that temperature as a maximum limitation, an initiator (not necessarily commercial or even known with present initiator technology) can be found which will allow any product to be made at the rate dictated by this temperature. Conceptually, this is a constant (maximum) conversion reactor, runnirg at constant operating conditions where the product produced dictates the initiator to be used. 

Simple thermodynamic treatment of gas compression stipulates that the maximum temperature (Tmax) attained is dependent on the adiabatic index (y) of the gas ... 

D. R. Stull11 developed a rating system to establish the relative potential hazards of specific chemicals the rating is called the reaction hazard index (RHI). The RHI is related to the maximum adiabatic temperature reached by the products of a decomposition reaction. It is defined as... 

Let us take a simple example, namely a generic Sn2 reaction mechanism and construct the state functions for the active precursor and successor complexes. To accomplish this task, it is useful to introduce a coordinate set where an interconversion coordinate (%-) can again be defined. This is sketched in Figure 2. The reactant and product channels are labelled as Hc(i) and Hc(j), and the chemical interconversion step can usually be related to a stationary Hamiltonian Hc(ij) whose characterization, at the adiabatic level, corresponds to a saddle point of index one [89, 175]. The stationarity required for the interconversion Hamiltonian Hc(ij) defines a point (geometry) on the configurational space. We assume that the quantum states of the active precursor and successor complexes that have non zero transition matrix elements, if they exist, will be found in the neighborhood of this point. 

If DSC data have been obtained for a pure material or a reaction mixture, several thermal stability indicators (ASTM E 1231-96) may be estimated from the data. These are adiabatic temperature rise, explosion potential, instantaneous power density, time to maximum rate, and NFPA instability index (Leggett 2002). 

From Table I one can conclude that within reasonable ranges for Kq (Z/A) and the adiabatic index T, prompt explosion energies can describe SN1987a or perhaps even more energetic supernovae. A close examination of the work of Shigeyama, Nomoto and Hashimoto [12] leads me to suspect they may have underestimated the energy in 1987a. 

Examples of the reduction of the number of equations abound. With adiabatic reactors in the steady state, the temperature is a function of the composition (see [A, D, F] and the introductions to papers under Adiabatic in the Index of Subjects in Publications.) This is the case also with the catalyst particle (see I, Ch. 2, and [81, 122] and Example 9). Examples of reduction in the number of equations because one or more can be solved immediately are given in Example 12 see also [280] and [310]. 

The general character of the motion is shown in Fig. 1. A shock wave propagates in an unperturbed cold gas the maximum compression, which is dependent on the adiabatic index of the gas, is reached at the front of this wave. The velocity of propagation of the shock wave and the mass velocity at the front are related in an elementary way to the pressure of the shock wave. Behind the front the pressure, density, and velocity decrease.1... 

It is easy to see without calculation that, with time, I1 should increase and E2 should decrease. Thus, we are able in advance, before integration of the equations, and for any adiabatic index, to show that... 

A self-similar solution is found in which the pressure II at the shock wave front propagating in the gas decreases as a power function of the distance traveled, X II X n, where 1 < n < 2. In the general form, for any adiabatic index of the gas, it is proved that 1 < n < 2 for 7 = 7/5 the numerical value of n is 1.333. The law found yields the greatest possible rate of the plane shock wave decay under any circumstances. 

The existence of two types of self-similar solutions, explicitly formulated by Ya.B. for the first time, stimulated extensive studies to clarify the general character of the difference between them and to apply the concept of self-similar solutions of the second kind to various problems in mathematical physics. The present state of the problem can be found in a monograph by G. I. Barenblatt.6 We note also the existence of an exact analytic solution with a rational self-similarity exponent when the adiabatic index is equal to 7/5.7... 

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