1. Chapter 3: Conservation of Energy

2. Important Notation 2

3. Conservation of Energy Ṁ2Ṁ2 Ṁ1Ṁ1 Ṁ3Ṁ3 ṀkṀk Let us take  to be the sum of the internal, kinetic, and potential energy of the system. 3

4. -Here U is the total internal energy, v 2 /2 is the kinetic energy per unit mass, and  is the potential energy per unit mass. - If gravity is the only force field present, then  = gh where h is the height of the center of mass with respect to some reference, and g is the force of gravity per unit mass. To complete the balance it remains only to identify the various mechanisms by which energy can enter and leave the system. These are: 4

5. Energy flow accompanying mass flow Heat Work Work of a flowing fluid against pressure These are: Energy flow accompanying mass flow 5

6. Work Sign convention: - positive for work done on the system - negative for work done by the system The total energy flow into the system due to work will be divided into several parts: - Shaft work, W s, is the mechanical energy flow that occurs without deforming the system boundaries. -Work resulting from deforming the system boundaries -Work of a flowing fluid against pressure 6

7. Work resulting from deforming the system boundaries 7

8. Per unit of time 8

9. Work of a flowing fluid against pressure Work done by surrounding fluid in pushing fluid element of mass into the valve 9

10. Work of a flowing fluid against pressure Work done on surrounding fluid by moving fluid element of mass out of the valve 10

11. Work of a flowing fluid against pressure Net work done on the system due to movement of the fluid 11

12. Work of a flowing fluid against pressure With several mass ports 12

13. Work of a flowing fluid against pressure In rate form 13

14. Collecting all terms 14

15. Collecting all terms Can you identify the meaning of each term? 15

16. Defining a new function – the enthalpy Defining a symbol to represent the combination of shaft and expansion work 16

17. Putting everything together once more On molar basis 17

18. Putting everything together once more On molar basis They represent the complete energy balance: first law of thermodynamics 18

19. Lots of simplifications in many practical problems Closed system 0 Then: 19

20. Lots of simplifications in many practical problems Closed system not changing speed and position 00 Then: Additionally, if there is no shaft work: 20

21. Lots of simplifications in many practical problems Open system at steady state 0 Then: 21

22. Lots of simplifications in many practical problems Open system at steady state with negligible kinetic and potential energy effects at the mass ports 0 Then: 0 22

23. Lots of simplifications in many practical problems Additionally, if there is no deformation of the system boundaries: These are just a few of the many ways the energy balance can be written to address specific cases. 23

24. Heat capacities Heat capacities are system properties, which do not depend on the process. However, to simplify the way to introduce them, consider a simple closed system, with no shaft work, and negligible changes in kinetic and potential energy. The energy balance is: Consider a process at constant volume (an isochoric process): The heat transferred is expected to change the system’s temperature. The temperature change depends on the material. The heat capacity at constant volume is defined as: 24

25. Heat capacities Now, consider a process at constant pressure (an isobaric process): The heat capacity at constant pressure is defined as: 25

26. Heat capacities of solids and liquids For solids and liquids, the heat capacities at constant volume and at constant pressure are similar (Why?): 26

27. Heat capacities of ideal gases Pure ideal gases obey the following two relationships: Comments: For mixtures, the ideal gas heat capacity also depends on composition. 27

28. Heat capacities of ideal gases Consider the enthalpy change between two states, “1” and “2”: Then, for ideal gases: 28

29. Summary of the formulas 29

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31. 31

32. Summary Energy cannot be created, cannot be destroyed: it is always conserved – first law of thermodynamics. The first law of thermodynamics is powerful and general but it has no information about the direction of phenomena in nature. The second law of thermodynamics will bring such information into the formulation. A system can store energy in many ways, but heat and work are not forms of energy storage and are not system properties. Heat and work are forms of energy transfer and depend on the process. Properties are necessary for practical calculations, usually available as tables, diagrams, or analytical (mathematical) formulas. 32

33. Recommendation Read chapter 3 in the textbook and review all examples. 33