Hirschfelder Roseveare

The change of state across the shock front is given by the adiabatic Rankine-Hugoniot (R-H) Equation  

In these equations e denotes the unit of internal energy, p = pressure, v-specific volume and Q-chemical energy released per unit mass of substance. Subscripts 1 and 2 of eq (1) denote conditions ahead and behind shock front, whereas subscripts 2 3 of eq (2) denote conditions ahead and behind the combustion front. The internal energy, e, being a state function, can be expressed in terms of pressure, p, and speci- 

There are several other formulations of H R-H equations than given above. For example, Taylor (Ref 7) lists equations (VI. 45), p 80, (VII.4), p 86 and (VII.36), p 99 as versions of R-H equation 

It must be noted that R-H. equations, being derived from the Conservation equations, are valid regardless of the equation of state of the medium. Nevertheless, they cannot be solved explicitly, nor even plotted without specifying a suitable equation of state. This can be done as explained in Ref 4, p 951 Ref 7, pp 66-72 and Ref 10, pp 45, 127 165-66 

Rankine-Hugoniot equation is also discussed under Detonation, Theories of  

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This equation, modified by Hirschfelder Roseveare, was found to be suitable for moderatelyriiigh pressures. It is given in Ref 8e, p 262 in the following form ... 

The Boltzmann equation (See item bg) is also of the third degree, but Hirschfelder Roseveare s modification of Boltzmann equation (See under item bg) is of the fourth degree... 

Pure shock waves) 4) G.B. Kistiakowsky, p 951 in Kirk Othmer 5 (1950), pp given in the text (Not included in the 2nd edition) 5) Corner, Ballistics (1950), 100-01 (Corner Noble-Abel equations of state) 6) SAC MS, Ballistics (1951), 18 (Covolume and equation of state of propint gases) 7) Taylor(1952), 34 (Boltzmann and Hirschfelder Roseveare equation of state for the expln products) 69-72 (Rankine-Hugoniot equation of state) 87-98 (Abel, Boltzmann and other equations of state applicable to deton of condensed expls yielding only gaseous products) 114 (Equations of state applicable to deton of condensed expls whose products contain a condensed phase)... 

First we consider the virial expansion in density originally due to Boltzmann and derived from the kinetic theory of gases for hard-sphere molecules. This equation was modified by Hirschfelder and Roseveare, and covolume terms for product species were adjusted to high temperature by setting them equal to the high-temperature second virial coeflficientz. The equation is... 

Hirschfelder and Roseveare, using the (6 12) Lennard Jones potential, obtained a value of 0.024 for the constant on the right-hand side of equation (6.126), while Corner, using the (6 9) potential, arrived at a value of 0.013. Corner also tried to express the remaining constants in the form of... 

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