R. Meyer J. Köhler A. Homburg Explosives

119 Equation of State
the calculation of thermodynamic data is possible only using a suitable
equation of state, whereby pressure P, temperature T, the density of
Gas r and the specific number of moles ns are associated.
For internal ballistics one ordinarily uses a truncated virial equation
which breaks off after the third term and is in the form:
P= ns·R·T·r (1+ns·r·B+n2 s·r 2 ·C)
P: Pressure [Pa]
ns: Specific number of moles [kmol/kg]
R: Gas constant (J/(kmol·K)]
T: Explosion temperature [K]
p: Density of gas [kg/m3 ]
B: Second viral coefficient [m3 /kmol]
C: Third virial coefficient [m6 /kmol2 ]
The temperature-dependent second and third virial coefficient describe
the increasing two- and three-particle collisions between the
gas molecules and their accompanying increase in gas density. The
virial coefficients are calculated using a suitable intermolecular potential
model (usually a 12-6 Lennard-Jones Potential) from rudimentary
statistical thermodynamics.
The detonation pressure behind the W Shock Wave of a liquid or solid
explosive substance is between 2 GPa and 50 GPa whereby the temperature
at the wave front can reach up to 5000 K.
Next to the W Chapman-Jouget theory, during the last 50 years, the
principal methods of calculating detonation pressure and the velocity
of flat detonation waves have been the Becker-Kistiakowsky-Wilson
(BKW), the Lennard-Jones-Devonshire (LJD) and the Jacobs-Cowperthwaite-Zwisler
(JCZ) equations of state.
All of these methods employ model equations which do not quite
satisfactorily yield the condition of the highly dense and heated detonation
products. This is shown in particular in the semiempirical BKW
equation of state, which in addition to five parameters for the calibrating
of experimental measurements values, requires two separate sets
of data for the calculations involving explosives of either an extrememly
high or slightly negative oxygen balance or a positive oxygen
balance.
The LJD and the JCZ equations of state represent methods, which,
when used in conjunction with an intermolecular potential rudiment,
employ lattice models.
With lattice models it is assumed that the molecules in the fluid phase
repose on the lattice points of three dimensional lattice, while entering
into an exchange effect with the adjacent molecules.
Among the more recent and theoretically-based equations of state in
detonation physics are the perturbation-theoretical methods. First