Abel’s equation

Section 1 lists those subjects from "Abel s Equation of State to "Detonating Relays which were either already described in Vols 1,... 

In conclusion, it may be said that van der Waals equations can only provide reasonably accurate representation over limited ranges of variation of the pressure and temperature. For this reason many attempts were made to produce a more satisfactory equation by modifying vanderWaals equations. Such modifications were made by Berthelot (See item b ), Callendar (See item c-2), Clausius (See item C3), Dieterici (See item d2), Hirschfelder et al (See item 113), Keyes (See item ki), Lees (See item I3), and Macleod (See item mi) Accdg to Dunkle (Ref 17), for high temps and moderate pressures which give rise to large values of V so that P55>a/v2, van der Waals equation reduces to Abel s equation (See item ai)... 

Since the combustion gases of powders satisfy Abel s equation of state to a good approximation, it is possible by using the auxiliary... 

The energy equation reduces to the form of Abel s differential equation of the 2nd type. 

Explosive Mixtures of Gases, Flome Propagation in. A system of differential equations of flame propagation is sec up and discussed. The energy equation reduces to the form of Abel s differential equation of the 2nd type. 

An equivalent relation to Eq. (4.1), derived by Panaiotov Petrov (1968/69) via Abel s integral equation, has the following form. 

By using the inverse function = z(n), we can rewrite (5) as a linear equation of Abel s type (note also, that > 0 implies n < 0 < 0), so... 

Very little has been published covering such nonideal, but very realistic, situations. Two publications by Wiederman (1986a,b) treat nonideal gases. He uses a co-volume parameter, which is apparent in the Nobel-Abel equation of state of a nonideal gas, in order to quantify the influence on flragment velocity. The co-volume parameter is deflned as the difference between a gas s initial-stage speciflc volume and its associated perfect gas value. 

State" (See item a ). For a detailed description of LS equation, see Ref If Ref 10, p 194 Ref 12a, p 246 and Ref 12b, Chapter 14. Briefly the equation is based on the assumption that decomposition products formed on detonation are, because of their high density, not gases, but rather liquids whose particles are in a state of oscillation. This conditions the course of expansion of the decomposition products. L S replaced R of die Abel equation by a coefficient depending on the number of degrees of molecular freedom. We are not describing here the LS equation because the modification by Zel dovich Kompaneets seems to replace it (See next item... 

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