Entropy and
Isentropic Processes
Jayani Jayasuriya
ME/NSE 312 - Thermodynamics
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Announcements
• Change in Office hours
• Two attempts for quizzes
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Lecture Outline
• 2st Law – Example problem
• Define Isentropic Processes (Chapter 6.11)
• Use Isentropic Efficiency for Calculating Performance
(Chapter 6.12)
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Control Volume SS Example
Problem 6.6 (8th Edition)
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Maximum Work of Expansion Process
T1
P1
Work
P2
ASSUME
• Adiabatic
• Steady state
• Kinetic and potential energy change negligible
FIND
• Maximum work output per unit mass flow for given ∆P
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Maximum Work of Expansion Process
T1
P1
Work
P2
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Isentropic Processes
Isentropic: Constant entropy
Mollier Diagram: h-s diagram for our turbine:
Smallest allowed value of h2 yields maximum work!
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Isentropic Efficiency - Turbine
Actual expansion h2 > h2s
• Why?
• By how much?
Isentropic turbine efficiency
is the ratio of the actual
turbine work to the maximum
theoretical work, each per
unit of mass flowing:
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Isentropic Efficiency - Compressor
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Isentropic Efficiency – Nozzle
T1
P1
P2
ASSUME
• Adiabatic
• Steady state
• Negligible inlet velocity
FIND
• Isentropic Efficiency
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Isentropic Efficiency – Nozzle
T1
P1
P2
Diffuser – Opposite
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Isentropic Process – Ideal Gas
T1
ASSUME
P1
• Adiabatic
• Isentropic turbine
• Ideal gas
• Constant specific heat
• Steady state
• Kinetic and potential energy change negligible
Work
T2
P2
FIND
• Isentropic efficiency
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Isentropic Process – Ideal Gas
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Isentropic Process – Ideal Gas
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Isentropic Process – Ideal Gas
 T2   P2 
 = 
 T1   P1 
 1
 1− k 


 P2   v2 
 = 
 P1   v1 
k
• Ideal gas
• Constant specific heat ratio (k)
• Polytropic process where n = k
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Review: Reversible Processes
Reversible process: if the system and all parts of its
surroundings can be exactly restored to their
respective initial states after the process has taken
place.
• Pendulum oscillating in a vacuum
• Adiabatic compression and expansion in frictionless
cylinder
Internally Reversible Process: Process where no
irreversibilities within the system.
• Sgen system = 0
• Sgen surroundings may be > 0
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Isentropic vs. Reversible
Isentropic process  ∆S = 0
Reversible process  Sgen = 0 (perfect)
Are all isentropic processes reversible?
S
∆=
2
∫
δQ
1
2
−∫
1
δQ
T
T
+ S gen
=
+ S gen
Isentropic but not reversible
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Isentropic Efficiency - Steam
Superheated steam enters a turbine at a temperature of 400 °C, a
pressure of 20 bar and a flow rate of 1 kg/s. The pressure at the outlet
is 0.4 bar. The isentropic efficiency is 80%.
What is the power output of this turbine?
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Inlet State
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Outlet State
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Isentropic Efficiency – Ideal Gas
6.141: Air modeled as an ideal gas enters an adiabatic turbine
operating at steady state at 1040 K, 278 kPa, and exits at 120 kPa. The
mass flow rate is 5.5 kg/s and the power developed is 1120 kW.
Assuming k = 1.4, find:
• Temperature of the air at the turbine outlet
• Isentropic efficiency
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Isentropic Efficiency – Ideal Gas
6.141: Air modeled as an ideal gas enters an adiabatic turbine
operating at steady state at 1040 K, 278 kPa, and exits at 120 kPa. The
mass flow rate is 5.5 kg/s and the power developed is 1120 kW.
Do not assume constant specific heat, find:
• Temperature of the air at the turbine outlet
• Isentropic efficiency
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