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When a perfect gas enclosed in cylinder - piston device executes a reversible adiabatic expansion process :

  • A.The entropy change of the surrounding will be zero
  • B.Its entropy will increase
  • C.Its entropy will decrease
  • D.Its entropy change will be zero

Answer: D

The key's answer is its entropy change will be zero.

A reversible adiabatic process is isentropic. Entropy changes by \(dS = \frac{\delta Q_{rev}}{T}\); with no heat transfer and no irreversibility (no friction, no unrestrained expansion), the gas's entropy stays exactly the same.

Entropy would increase only in an irreversible adiabatic process, and it can never decrease in an adiabatic process, since that would violate the second law. The statement about the surroundings is also true in itself, because no heat reaches them, but it describes the surroundings rather than the gas; the defining property of the gas's own process is zero entropy change, which is what the key accepts.

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