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Assertion (A): A Mach wave may be treated as isentropic while a finite shock may not.

Reason (R): The property changes across a Mach wave are infinitesimal, so the entropy rise is of second order.

Select the correct answer from the options below.

  • A.A is true but R is false
  • B.A is false but R is true
  • C.Both A and R are true, and R is the correct explanation of A
  • D.Both A and R are true, but R is not the correct explanation of A

Answer: C

Both statements are true and the second explains the first. Entropy rise across a wave scales with the cube of its strength, so for a vanishingly weak wave it is negligible. This is why expansion fans, built from Mach waves, are isentropic while compression shocks of finite strength are not.

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