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

2. The Thermodynamics of Temperature Creation
The Gibbsian equation,defines the change in specific entropy of any substance during any reversible process.
Consider a control mass executing a constant volume process:
The relative change in internal energy of a control mass w.r.t. change in entropy at constant volume is called as absolute temperature.

3. The Thermodynamics of Temperature Creation
Consider a control volume executing a reversible constant pressure process:
The relative change in enthalpy of a control volume w.r.t. change in entropy at constant pressure is called as absolute temperature.

4. Entropy change of an ideal gas
From the Gibbsian equations, the change of entropy of a substance can be expressed as
For an ideal gas, u=u(T) and h=h(T),
du=cv(T)dT and dh=cp(T)dT and Pv=RT
By Integration, the change in the entropy is or

5. Ideal Gas with constant specific heats
When specific heats are constant (calorically perfect gas), the integration can be simplified:
If a process is isentropic (that is adiabatic and reversible), ds=0, s1=s2,

6. Isentropic Process with idea gas

8. Isentropic Process by an idea gas with constant propetiesor or
Are the reversible Process practicable?
100% perfection is possible but may not ne practicable..!?!!?!

9. Practical Processes are influenced by Irreversibilities
Fluid friction
Solid friction
Electrical resistance
Thermo-chemical Reactions (Combustion)
Unrestrained motion
Heat Transfer with a finite temperature difference

10. Solid Friction is an IrreversibilityQ PE KE

11. Solid Friction is an IrreversibilityQ PE KE

12. Solid Friction is an IrreversibilityPE KE Q

13. Solid Friction is an IrreversibilityQ Q
THIS IS NOT POSSIBLE.
Reverse ? Q

14. Solid Friction is an IrreversibilityQ 1 2 4 3

15. Irreversible and Reversible engines
HTR
QHEI
QLEI EI
WnetI
QHE
QLE E
QHER
QLER ER
WnetR
Assume that an irreversible
Engine is more efficient than
the reversible engine.
LTR

16. Wnet,I Wnet,R
>
QHEI QHER
For same Wnet, QHEI < QHER
Implies that, |QLEI | < |QLER|
But a reversible engine can be completely reversed and it will work as a heat pump.
For same |Wnet |,
Let us construct a compound machine using an irreversible engine
and reversed reversible engine (reversible Heat Pump).

17. HTR (Sink)
|QHPR | - QHEI
QHEI < |QHPR |
QHPR
QHEI
WnetR R EI
QLPR
QLE
|QLEI| < QLPR
QLPR - |QLEI |
LTR (Source)

18. Irreversible Machines
The efficiency of an irreversible heat engine will always less than the efficiency of a reversible engine working between the same reservoirs.
The COP of an irreversible heat pump will always less than the COP of a reversible heat pump working between the same reservoirs.

19. Further Discussions Isotope Half-Life Decay He-3 Stable N/A He-4
≈ 0.5 x sec - 1 x sec
p or n
He-5
1 x sec n
He-6
0.8 sec β-
5 x sec - 5 x sec
He-7
3 x sec - 4 x sec
He-8
0.1 sec
0.5 x sec - 1 x sec
n/α
He-9
unknown
hirr < hrev
1/hirr >1/hrev but, 1/hrev = brev
1/hirr > brev (Mathematically possible but thermodynamically impossible).
Similarly, birr < brev  1/birr > 1/brev
1/birr >hrev (Mathematically possible but thermodynamically impossible).

20. Increase of Entropy Principle
For a general Process
Define entropy generation Sgen as,
Increase of Entropy Principle
Entropy change
Entropy Transfer
(due to heat transfer)
Entropy Generation
The principle states that for an isolated Or a closed adiabatic Or System + Surroundings;
A process can only take place such that Sgen 0 where Sgen = 0 for a reversible process only and Sgen can never be less than zero.

21. Implications of Increase of Entropy Principle
Entropy, unlike energy, is non-conservative since it is always increasing.
The entropy of the universe is continuously increasing, in other words, it is becoming disorganized and is approaching chaotic.
The entropy generation is due to the presence of irreversibilities.
Therefore, the higher irreversibilities lead to the higher the entropy generation and the lower the efficiency of a device.
The above is Engineering statement of the second law

22. Second Law & Entropy Balance
Increase of Entropy Principle is another way of stating the Second Law of Thermodynamics:
Second Law : Entropy can be created but NOT destroyed
In contrast, the first law states: Energy is always conserved.
Note that this does not mean that the entropy of a system cannot be reduced, it can.
However, total entropy of a system + surroundings cannot be reduced.

23. Entropy of Universe
A quantity of heat dQ is spontaneously transferred from the surroundings at temperature T0 to the control mass at temperature T.
Let the work done during this process be dW.
For this process by control mass and write
For the surroundings at T0, dQ is negative, and we assume a reversible heat extraction so

24. Net Change in Entropy of Universe
The total net change of entropy is therefore
Since T0 > T, the quantity [(1/T) - (1/T0)] is positive, and we conclude that

25. If T > T0, the heat transfer is from the control mass to the surroundings+
It should be noted that the right-hand side of above equation represents an external entropy generation due to heat transfer through a finite temperature difference.

26. The Third Law of Thermodynamics
The entropy change of a system during a reversible isothermal process tends towards zero when the thermodynamic temperature of the system tends towards zero. In the neighbourhood of absolute zero, all reactions in a liquid or solid in internal equilibrium take place with no change in entropy. [Nernst 'principle'].

27. Planck’s statement of the 3rd law
In 1911, Planck one step further and made the hypothesis that not only does the entropy difference vanish as T → 0, but that:
Planck’s statement of the Third Law: The entropy of every solid or liquid substance in internal equilibrium at absolute zero is itself zero.
Planck is just saying:

28. Engineering Relations from Second Law

29. Entropy as A Rate Equation
The second law of thermodynamics was used to write the balance of entropy for a infinitesimal variation for a finite change.
Here the equation is needed in a rate form so that a given process can be tracked in time.
Take the incremental change and divide by dt.
We get

30. For a given control mass we may have more than one source of heat transfer, each at a certain surface temperature (semi-distributed situation).
The rate of entropy change is due to the flux of entropy into the control mass from heat transfer and an increase due to irreversible processes inside the control mass.

31. The Second Law Of Thermodynamics For A Control Volume
The rate of change of property B of the system .
Let B = Entropy of the system, S = ms.

32. Entropy Rate Equation for CV
Rate of change in entropy of a CV = Entropy in flow rate –Entropy out flow rate + the flux of entropy into the control mass from heat transfer + Rate of Entropy generation

33. The Steady State Steady Flow Process
For the steady-state process, which has been defined before, we conclude that there is no change with time of the property (entropy) per unit mass at any point within the control volume.
That is,
so that, for the steady-state process,

34. If in a steady-state process there is only one area over which mass enters the control volume at a uniform rate and only one area over which mass leaves the control volume at a uniform rate,
we can write
and dividing the mass flow rate out gives

35. Since sgen is always greater than or equal to zero, for an adiabatic process it follows that
where the equality holds for a reversible adiabatic process.

36. Geometry of Turbine Blades for High Efficiency

37. Transient Process
For the transient process, the second law for a control volume, it can be written in the following form:
If this is integrated over the time interval t, we have

38. Therefore, for this period of time t, we can write the second law for the transient process as
Since in this process the temperature is uniform throughout the control volume at any instant of time, the integral on the right reduces to

39. and therefore the second law for the transient process can be written

40. Mechanical Engineering Inventions
Carnot Cycle
Lenoir Cycle
Otto Cycle
Stirling Cycle
Atkinson Cycle
Diesel Cycle
Brayton cycle
Rankine Cycle
Vapour Compression Refrigeration Cycle
Vapour Absorption Refrigeration Cycle