Which of the following represents the isentropic process?

Explanation:

An isentropic process is also known as a reversible adiabatic process.

\(dS = \frac{{d{Q_{rev}}}}{T}\)

If the process is reversible and adiabatic: dQrev = 0 ⇒ dS = 0

\({Q_{rev}} = \smallint TdS\)

Entropy analysis for a closed system:

\(ds=(\frac{\delta Q}{T} )+ (\delta S)_{gen}\)

Case 1: For internally reversible process (δs)gen = 0

• When heat is added to the system ⇒ (δQ) = +ve ⇒ ds = +ve
• When heat is rejected from the system ⇒ (δQ) = -ve ⇒ ds = -ve
• For adiabatic process ⇒ (δQ) = 0 ⇒ ds = 0 (ISENTROPIC)

Case 2: For internally irreversible process (δs)gen ≠ 0 ⇒ (δs)gen = +ve

• When heat is added to the system ⇒ (δQ) = +ve ⇒ ds = +ve
• When heat is rejected from the system ⇒ (δQ) = -ve ⇒ ds = -ve or +ve or zero
  • ​Since (δs)gen = +ve and (δQ) = -ve so change in entropy, ds can be zero is (δQ/T) = δs)gen, In this case, the process will be ISENTROPIC
• For adiabatic process ⇒ (δQ) = 0 ⇒ ds = +ve

Thus for a process to be isentropic there are two cases:

1. Reversible adiabatic process
2. An irreversible process where (δQ/T) = δs)gen

Note: Irreversible adiabatic process is not an isentropic process.

In this irreversible adiabatic process dQ = 0, but ds > 0, hence, an irreversible adiabatic process is not isentropic.