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As \( M_1 \) grows without bound, the limiting density ratio across a normal shock in air is

  • A.2.4
  • B.1.0
  • C.6.0
  • D.Unbounded

Answer: C

The limit is \( (\gamma+1)/(\gamma-1) = 2.4/0.4 = 6 \). Pressure and temperature ratios keep growing indefinitely, but the density cannot: the gas simply cannot be packed more tightly by a shock. At genuinely hypersonic speeds dissociation lowers the effective specific heat ratio and pushes the limit higher.

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