The total thermicity of a gas mixture is defined as [56], [57]

(7–57)

where

(7–58)

is the thermicity coefficient of the kth gas species in the mixture. is the specific volume and is the frozen speed of the sound of the mixture. Since the Zeldovich-von Neumann-Döring (ZND) calculation tracks the same fluid particle behind the detonation wave, the composition evolution of the fluid particle is described by the species conservation equation as

Following the steps described in [57], the species thermicity coefficient can be expressed as

(7–59)

is the thermal expansion coefficient; is the specific internal energy of the gas mixture; and and are the constant pressure and the constant volume specific heat capacities of the gas mixture, respectively.

For an ideal gas mixture, the coefficient of thermal expansion

and

where and are the mean molecular weight of the mixture and the molecular weight of the kth species, respectively.

Thus, the thermicity coefficient (Equation 7–59) of an ideal gas species becomes [57]

(7–60)

And the total thermicity of the ideal gas mixture is given by

(7–61)

The physical significance of the thermicity is manifested by recasting the energy equation with simple thermodynamic relationships into the adiabatic change equation [57]

(7–62)

which indicates that the thermicity represents the pressure change due to chemical reaction [56].

The induction length is defined as the distance of the peak thermicity location behind the shock wave [58].