223 
-12- Eq. 39-45 
(eay 
Sec, 
6. Gaseous Explosions 
Ixplosions of gaseous mixtures such as hydrogen and oxygen provide the 
best experimental test of the validity of the theory. This is true because 
the pressures attained in these explosions are sufficiently moderate so that 
we can use the perfect gas law and the available knowledge of gaseous 
equilibria, Furthermore, results with these mixtures throw considerable 
light on the question of whether equilibrium is really established in the 
detonation process, 
a. Equations. Since the equations used for ideal gases will later 
prove useful as a first step in the treatment of solid explosives, they will 
be fully developed here. Consider first the Chapman-Jouget condition 
(see Eq. (28)). 
D=V, /- ee ) (39) 
\ aVp 78 
For ideal gases, the adiabatic expansion law (S constant) is 
ei 
es ee = const., (40)* 
(the subscript i will denote the ideal gas state). Therefore, 
Fé 
Dy = (V,/Vp;) \/ ¥eiPaVas = (V4No;) \/%2 Yo3RTo; /M, (hu) 
in which np is the number of moles of gas per M grams of burnt gases. 
Furthermore, Uy can be eliminated from the equations for mass and momentum 
(Eq. (7) and (B)), giving the general result (if U; = 0): 
Py MeN DAC Tae ee Oe es (42) 
In the cases of interest P, can be neglected compared with Po. Then 
substitution of iq. (41) for D yields 
Voi 
Va - Voi doi (43 )# 
This expression my be used to reduce the Huzoniot equation (Hq. (12)) toa 
useful form, by elimination of Vj - Vo. The result is 
fe) = Bye Pang Dag nyRT;/ I5M (Udy) 
For a perfect gas, 
*iquations valid for ideal gases only will be marked with the symbol *, 
tThis is only a fair approximation for ordinary gas explosions ou 
is very good for solids. 
