1. LECTURES IN THERMODYNAMICS Claus Borgnakke CHAPTER 6
For the 8th Edition of:
Fundamentals of Thermodynamics
Claus Borgnakke, Richard Sonntag
John Wiley & Sons, 2013

2. Chapter 6 The Inequality of Clausius Entropy Gibbs Property Relations
Entropy Changes for Solids, Liquids and Ideal Gases
The Polytropic Process in an Ideal Gas
Entropy Generation and The Entropy Balance Equation
Entropy Equation Applied to Heat Engines and Heat Pumps
Entropy and Chaos

3. The Inequality of Clausius

4. The Inequality of Clausius
Remark: For example you may say heat engine cycle is not reversible, i.e. QL should have been smaller (efficiency higher) for it to be reversible.

5. The Entropy

6. The Entropy
Entropy for water, T-s diagram

7. The Entropy T-s diagram from CATT3 for water.
Showing P = 1.55 MPa & v = 0.13 m^3/kg curves with the plot option
Enthalpy-Entropy for water,
h-s diagram, Mollier diagram
Aqua, red separated by P = Pcritical

8. The Entropy

9. The Entropy T-S diagram
Comment: Rev. adiabatic process: no area under curve (vertical) ds = 0
Isothermal process: Rectangle height = T and base = s2 – s1
The two processes and the area below the process curve shows the heat transfer.

10. The Carnot Cycle in a T-s diagram
Carnot Heat Engine
T-S diagram
Carnot Heat Pump

11. The Entropy Change in Evaporation
Constant P process

12. The Carnot Cycle in a T-s diagram
The Work Term
The Carnot Cycle in a T-s diagram
Remark: Notice the process 2-3 has a varying pressure and decrease in s that means work and heat transfer together. Difficult.
Expansion 3-4 goes through the two-phase region also very difficult for a turbine to get work out efficiently.
No current device tries to run a heat engine, heat pump or refrigerator as a Carnot cycle.

13. Work and Heat Transfer in an Isothermal Process

14. Work and Heat Transfer in an Isothermal Process
The T = C curve for superheated vapor only simplifies when we go so far out as having an ideal gas (it becomes a hyperbola).
The work and heat transfers are the area in the P-V and the T-S diagrams respectively. The shape of the T = C
curve in the superheated vapor region makes area determination for work difficult.

15. The Entropy In-text Concept Questions

16. Gibbs Relations Gibbs relations:
Remark: If other work terms are allowed like surface tension, magnetic field etc. the expression for work becomes longer and the equations are known by other names like Gibbs-Duhem.
Gibbs relations:

17. Entropy Change for a Solid or Liquid
For Table B.1.1 entry values for saturated liquid are used.

18. Entropy Change for an Ideal Gas

19. Entropy Change for an Ideal Gas
Notice only one model for specific heat is needed the other is then given.

20. Entropy Change using the Standard Entropy
Notice this is the reason for the remark in all the ideal gas Tables, namely the standard entropy is the entropy at P =100 kPa if P is different you must correct for it. This is not so for the properties u and h as they do not depend on P.

21. Entropy Change Using Different Models
General comment: Use A.8 or constant specific heat for hand calculations. In a spreadsheet you can use Table A.6.

22. Entropy Change Using Different Models

23. Process Equation Using Entropy
Remember math: Cp/R ln(x) = ln( xCp/R )

24. Process Equation Using Entropy

25. Polytropic Process in P-v and T-s diagrams

26. An Isentropic Process

27. Process Equation Using Entropy

28. An Isentropic Process
Notice: We cannot use the polytropic process eq. as it does not apply (it requires constant specific heats).

29. Process Equation Using the Pr , vr Functions

30. Process Equation Using Entropy
Notice: We cannot use the polytropic process eq. as it does not apply (it requires constant specific heats).

31. Work in a Polytropic Process

32. Work and Heat Transfer in a Polytropic Process
The curves are drawn in a spreadsheet using the properties from A.5, but s(T1, P1) is from A.8.
State 2: There is only one point on the process curve at P2, this determines the second property.

33. Work and Heat Transfer in a Polytropic Process
The curves are drawn in a spreadsheet using the properties from A.5, but s(T1, P1) is from A.8.
State 2 is the only point on the process curve with P2,
Due to the low T and small range there is very little difference (Cv, Cp does not change much).

34. The Entropy Change in an Irreversible Process

35. The Entropy Change in an Irreversible Process
Change in S, T can go up or down

36. The Effect of Entropy Generation on Process Work
The lost work is not energy lost, it is a lost opportunity to extract work from process. The energy ends up in a different form.

37. The Entropy Balance Equation

38. The Entropy Balance Equation

39. The Entropy Generation, Heat Transfer over ΔT

40. The Entropy In-text Concept Questions

41. The Entropy Generation, Heat Transfer over ΔT
Add comments about change in S for the ambient as in book. Internally here means water.

42. The Entropy Generation, Conversion of W to Q
Why can more S flow out than in? Because some was made in the CV and we assumed steady state.

43. The Entropy Generation in an A/C Unit

44. The Entropy Generation in an A/C Unit

45. The Entropy Generation in an A/C Unit
The missing part is the heat loss from the house to the ambient, the very reason we need to heat it. It must be = QH = 40 kW that is an additional heat transfer over a ∆T and thus entropy is made there also. This of course is outside the A/C unit.

46. The Statement of Heat Engines From Entropy
Remark: The expression indicate the trend of the work output with temperatures and with the entropy generation. This form is not predictive as we would need to evaluate the entropy generation for the actual device. This is near impossible so manufacturers measure the performance and may provide the actual efficiency which is not a single number but varies with the conditions so a map of the efficiency is needed.

47. The Statement of Refrigerators From Entropy

48. Heat Engines, Refrigerators & Entropy: Conclusions

49. The Statement of Clausius by Entropy Equation