1. P M V Subbarao Professor Mechanical Engineering Department
The Entropy Change
P M V Subbarao
Professor
Mechanical Engineering Department
A Single Reason for Every Thing That Happens!!!

2. Carnot Gas Engine : The Reversible Cycle

3. Carnot Engine using Phase Change Substance : SSSF CVs
HTR
Boiler 2 1
Turbine
Compressor 4 3
Condenser
LTR

4. Performance of Reversible Cycle
Use a generalized indices…

5. During a time duration 
For a reversible cycle with n number heat transfer processes
Where, i shows ith process and n is the number of process in a cycle.
But Qi is a path function and depends on process.

6. Therefore,
k is an initial state and k+1 is a final state.
m is the number state Points in a cycle.
Therefore for all reversible cycles.

7. A New cyclic Integral Cyclic integral of this new quantity is zero!
Any quantity whose cyclic integral is zero is a property !
For a reversible process an infinitesimal change in this new property is:
Boltzman named S as Entropy of a substance.
During a reversible process

8. Entropy, S : A Measure of State of Matter
So (J/K•mol)
H2O(liq) 69.95
H2O(gas) 188.8
For a given substance
S (gaseous state) > S (liquid state) > S (solid state)

9. Entropy and Order of Molecules of Matter
S˚(Br2 liq) < S˚(Br2 gas)
S˚(H2O solid) < S˚(H2O liquid)

10. Entropy, S : Molecular Complexity
Increase in molecular complexity generally leads to increase in S.

11. Standard Molar Entropies

12. Entropy and Temperature
S increases slightly with T
S increases a large amount with phase changes

13. Entropy Change during a Reversible Process
From the definition of the entropy, it is known that Q=TdS during a reversible process.
The total heat transfer during this process is given by Qreversible =  TdS
Therefore, it is useful to consider the T-S diagram for a reversible process involving heat transfer
On a T-S diagram, the area under the process curve represents the heat transfer for a reversible process T S
A reversible adiabatic process

14. Flow Boiling Process T h
Liquid
Liquid +Vapour
Vapour
Vapour

15. Steam Generation : Expenditure Vs Wastage
Vapour
Liquid +Vapour h
Liquid s

16. Analysis of Steam Generation at Various Pressures
Specific
Pressure
Enthalpy
Entropy
Temp
Volume
MPa
kJ/kg
kJ/kg/K C
m3/kg 1
3500
7.79
509.9
0.3588 2 5
7.06
528.4 3 10
6.755
549.6 4 15
6.582
569 20
6.461
586.7 6 25
6.37
602.9 7 30
6.297
617.7 8 35
6.235
631.3
0.0102

17. Variable Pressure Steam Gnerationh s

18. Carnot Cycle
Show the Carnot cycle on a T-S diagram and identify the heat transfer at both the high and low temperatures, and the work output from the cycle. S T TH TL
S1=S4
S2=S3 1 2 3 4 A B
1-2, reversible isothermal heat transfer
QH = TdS = TH(S2-S1) area 1-2-B-A
2-3, reversible, adiabatic expansion
isentropic process, S=constant (S2=S3)
3-4, reversible isothermal heat transfer
QL = TdS = TL(S4-S3), area 3-4-A-B
4-1, reversible, adiabatic compression
isentropic process, S1=S4
Net work Wnet = QH - QL, the area enclosed by , the shaded area

19. Nature of Reversible Machines
For all reversible heat engines:
For all reversible heat pumps and refrigerators:
Therefore all reversible machines in this universe :

20. Process : h-s Diagram : Mollier Diagram
Enthalpy-entropy diagram, h-s diagram: it is valuable in analyzing steady-flow devices such as turbines, compressors, etc.
Dh: change of enthalpy from energy balance (from the first law of thermodynamics)
Ds: change of entropy from the second law.
A measure of the irreversibilities during an adiabatic process. Ds Dh h s

21. Enthalpy Vs Entropy Diagram