234 
Sec. 10 =25— Eq. 74-81 
From these equations, Yo/ ¥o4 can be computed as a function of x5, and 
therefore as a function of x, (essentially the density of loading) through 
iq. (67), provided that Cy; is given. Fortunately the final ratio D/D; is 
not very sensitive to C4 /n so that tables for three different values of 
Cyi/n are adequate for all the explosives considered. 
d. Calculation of To/To3. For imperfect gases the analogue of Eq. 
(45) is 
M(Ep-E,) = Q+ Cy (Tp-T,) + M ie (az/av)p, av, (7h) 
which expresses the application of the first law of thermodynamics. The 
reaction is first carried out to the final temperature at a large volume, 
Such that the product gases are ideal, and these gases are then compressed 
to their final volume with a resultant energy term because of the gas im- 
perfection. 
Using the eaquation of state (62) and standard thermodynamics, one ob- 
tains 
aE ap nRT og x AF 
ane = pe oes oe 
a) sap P = we a (75) 
so that 
Vg 
M i (aB/aT av =+n aah ® (aR /ax Jax 
= NpRTr & Xe Ree = NoRTo Of (Fp-1). (76) 
Eq. (67) can be rearranged to read . 
(V1-V5) = FoVo/¥o Vo, (77) 
with which the Hugoniot equation (12) becomes 
By-Ey=3PoFoVa/¥o Yo = 3noRToFo“/yo BoM (78) 
Therefore, from iq. (74), (75) and (73) 
Q04 (Tp-Ty engRTy OC (Fy-1) = InRIDPD”/yp Wp. (79) 
Rearrangement of this yields 
To [ Gsenak OL (Fp-1) - 3(noRPy /yo 3 2) | = -4C,T), (80) 
compared with 
T4 [8 -E(naa/ Bai) = -eCiTy (81) 
