  The state space for solutions of the compressible Euler equations with a
general equation of state is examined. An arbitrary equation of state is
allowed, subject only to the physical requirements of thermodynamics. An
invariant region of the resulting Euler system is identified and the convexity
property of this region is justified by using only very minimal thermodynamical
assumptions. Finally, we show how an invariant-region-preserving (IRP) limiter
can be constructed for use in high order finite-volume type schemes to solve
the compressible Euler equations with a general constitutive relation.
