1. Chapter 6: Entropy First law: Energy conservation concept.
Introduction of the concept of internal energy, u, to use the first law quantitatively for a process.
Second law:
Indicates that natural processes proceed in a certain direction but not in the opposite direction – qualitative in nature
The difference between an ideal engine (such as the Carnot engine) and a real engine is that the ideal engine involves reversible processes, but a real engine involves real processes that are irreversible.
Ideal reversible processes in an ideal engine may lead to a maximum engine efficiency
A real process will deviate from the reversible process. Then, how much?

2. Inequality of Clausius
Entropy S:
A parameter introduced to describe the deviation of a real process from the corresponding ideal reversible process, or to measure the irreversibility
A parameter to treat the second law quantitatively
Inequality of Clausius
(6.1)
It can be demonstrated that it is valid for all possible cycles, including both reversible and irreversible heat engines and refrigerators.

3. Inequality of Clausius
For a reversible engine (Carnot engine):

4.  Entropy generation

5. Defining Entropy as a Property of a System
Consider cycle 1-A-2-B-1
(all cycles here are reversible cycles!)
All the processes are reversible here except process d.

6. Defining Entropy as a Property of a System
The change of the entropy following a reversible and an irreversible process (such as process d) between the same initial and final states is identical.

7. Retrieving Entropy Data/The entropy of a pure substance

8. Using the T-ds Equations

9. Entropy change of an ideal gas
Specific heats are not constant. Use of ideal gas tables such as A-22 is more accurate.

10. Entropy change of a solid or liquid

11. Entropy change in Internally Reversible Processes

12. Entropy Balance for Closed Systems

13. Entropy production/Increase of entropy principle Or entropy production
Or entropy production
Entropy is NOT conserved. It may be increased due to the heat transfer into the system or generated because of irreversibility, but it may also be reduced due to the heat transfer out of the system,

14. Entropy Rate Balance for Control Volume

15. Isentropic process for an ideal gas
Differentiating on both sides of the ideal gas law

16. Isentropic process for an ideal gas
The relation is cited here for comparison with the CV related relation to be introduced later.
The above derivation as did in Chapter 2 did not involve entropy concept.

17. Isentropic Efficiencies of Turbines, Nozzles, Compressors, and Pumps
The isentropic efficiencies involve a comparison between the actual performance of a device and the performance that would be achieved under idealized circumstances for the same inlet state and the same exit pressure. In the following analyses, the effects of heat transfer, kinetic energy, and potential energy are ignored.
With the condition of an isentropic process, the state at 2s can be easily determined.

18. Isentropic Efficiencies of Nozzles

19. Isentropic Efficiencies of Compressors and Pumps

20. Heat transfer/work in internally reversible, steady-state flow processes
The work relation of an open system differs from the closed system because of the flow work is included in the inlet and outlet energies in terms of enthalpies h1 and h2.
For an adiabatic process, the same relation may be obtained by noticing that:
Expansion, dp<0, W > 0, turbines
Compression, dp>0, W<0, compressors

21. Work in Polytropic Processes

22. Work in Polytropic Processes with Ideal Gases

23. Work in Polytropic Processes

24. DO NOT confuse with the relations for control mass or system below:

25. Polytropic Processes

26. Polytropic process/Isentropic process
A polytropic process is a quasi-equilibrium process, which consists of a series of equilibrium states.
A polytropic process may be considered as an internally reversible process (p. 246, 7 ed.)
If these is no heat transfer through the polytropic process, the process is an isentropic process.
In this case, n = k.

27. Key equations

28. Key equations
The relative pressure and relative volume are all a function of temperature only.