  We show that shock polars for ideal non-polytropic gas (thermally but not
calorically perfect) have a unique velocity angle maximum, the critical shock,
assuming convex equation of state (positive fundamental derivative) and other
standard conditions. We also show that the critical shock is always transonic.
In the process we show that temperature, pressure, energy, enthalpy, normal
mass flux and entropy are strictly increasing along the forward Hugoniot
curves, and hence along the polar from vanishing to normal shock; speed is
strictly decreasing along the entire polar, mass flux and importantly Mach
number are decreasing on subsonic parts of the polar. If the equation of state
is ideal but not convex, or convex but not ideal, counterexamples can be given
with multiple critical shocks, permitting more than two shocks attaining the
same velocity angle, in particular more than one shock of weak type.
