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I have read some reports of scientists who are interested in equations of state for unreacted explosives. They want these equations of state to describe the mechanical response of an explosive as it is compressed to high pressure by the detonation shock wave, prior to ignition. Some scientists, e.g. Menikoff have developed "complete" equations of state for these materials, by using the fact that:

$$TdS = dU + PdV \tag{a}$$

See equation (1)in the report below:

https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-12-22592

Of course a consequence of (a), above is that since $dS$ must be an exact differential we end up with the following PDE in T:

$\frac{\partial}{\partial V} \left ( \frac{1}{T} \right )_{U}-\frac{\partial}{\partial U} \left ( \frac{P}{T} \right )_{V}=0$

(b)

See equation 18 in Menikoff's report above.

The relevance of (b) is it can be solved to find T(V,U) if we are given P(V,U).

But my question is the following: Is it reasonable to assume that (a) is true under the conditions of a detonation? Remember I am talking about the moment the unreacted explosive is being compressed by the action of the detonation shock wave, and not the chemical energy release stage that happens subsequently. The reason I ask is that (a) assumes thermodynamics equilibrium. But at such high rates of deformation, is there really thermodynamic equilibrium? In their computer simulations a cell of 1mm of explosive will compress to about 30GPa in roughly 10 nanoseconds. Under these conditions will (a) hold true? If not, then is (a) a reasonable approximation?

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