Frozen versus equilibrium sound speeds

It was shown in Section 2.2 that the downstream Mach number is unity for Chapman-Jouguet waves. When interpreted correctly, this result applies to any combustible gas mixture. However, a possible source of ambiguity for multicomponent systems is the fact that more than one sound speed a can be defined. Since there are iV - - 2 independent thermodynamic variables in an AT-component gas mixture, N parameters besides s must be specified as constants in computing dp/dp to evaluate 

A frozen (constant-composition) sound speed may be defined as 

Mf 5 is the entropy per unit mass, then actually only iV — 1 independent intensive parameters must be specified because p, p, and a are intensive properties that are independent of the size of the system. 

For a small change along the general Hugoniot curve [equation (9)], we find by differentiation that 

The tangent to the Hugoniot curve is a straight line through the point (po, 1/po) provided that, in equation (35), 

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