Comments on the equation of state of the products of high density explosives

The problem of the thermal equation of state of the products of solid explosives is considered. It is assumed that the products are in chemical equilibrium, that the specific chemical heat released is independent of the loading density, and that the detonation density is proportional to the loading density. Using the energy conservation equation and thermodynamic relationships, it is then shown that the thermal equation of state must satisfy the following relationship:

$F[T^{(1?K)/2K}\upsilon ;{\upsilon }^{(1+K)/(1?K)}p]=0$

. where K is a constant and F is an arbitrary function of its two arguments. It is then argued that the experimental knowledge of detonation velocity, pressure, density, and particle velocity versus loading density is not enough to check the validity of an assumed thermal equation of state of the products and to compute the detonation temperature. In particular, it is explained why similar detonation pressures, densities, and particle velocities, but completely different detonation temperatures have been calculated by various authors, using similar detonation velocity data but different thermal equations of state.