text: # Isentropic process is related to
  
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  3. Isothermal Expansion
  4. Reversible Isothermal Expansion
  
  Option 2 : Reversible Adiabatic Expansion
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  ## Detailed Solution
  
  Concept:
  
  In thermodynamics, an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible. The work transfers of the system are frictionless, and there is no transfer of heat or matter.
  
  $$dS = \frac{{d{Q_{rev}}}}{T}$$
  
  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: