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2. Outline Define terms and conventions Introduce 1 st law of thermodynamics Contrast state and non-state properties Describe the Carnot cycle 2

3. System and environment System = what we wish to study – View as control mass or control volume Control mass (CM) – Define some mass, hold fixed, follow it around Control volume (CV) – Define and monitor a physical space Environment = everything else that may interact with the system 3

4. System states Systems may be open or closed to mass – Open systems permit mass exchange across system boundaries – Our CVs are usually open – Strictly speaking, a CM is closed Closed systems may be isolated or nonisolated – Isolated systems do not permit energy transfer with environment – Closed, isolated system = environment doesnt matter 4

5. Lagrangian vs. Eulerian CM is the Lagrangian viewpoint – Powerful, desirable but often impractical – Total derivatives – Freeway example CV is the Eulerian viewpoint – Observe flow through volume – Partial derivatives 5

6. Air parcel Our most frequently used system CM (usually!) – Lagrangian concept Monitor how T, p, and V change as we follow it around 6

7. Conventions We often use CAPITAL letters for extensive quantities, and lower case for specific quantities – Specific = per unit mass Example: – U is internal energy, in Joules – u is specific internal energy, in J/kg – Unfortunately, u is also zonal wind velocity Exceptions: – Temperature T is essentially specific, but capitalized (and isnt per unit mass anyway) – Pressure p is fundamentally extensive, but lower case 7

8. Energy and the 1 st law Total energy = KE + PE + IE – Conserved in absence of sources and sinks Our main use of 1 st law: monitor changes in internal energy (IE or u) owing to sources and sinks How do we change system u? With energy transfer via – heat Q or q – work W or w Caveat: w is also vertical velocity, and q will be reused (briefly) for water vapor specific humidity 8

9. Work Work = force applied over a distance – Force: N, distance: m – Work: Nm = J = energy Our principal interest: CM volume compression or expansion (dV) in presence of external pressure (p) W > 0 if dV > 0 9

10. Work 10 W > 0 when system expands against environment

11. Heat Diabatic heat – Diabatic: Greek for passable, to be passed through – Internal energy exchanged between system and environment – q > 0 when energy flow is INTO system Adiabatic = system is isolated – Adiabatic: impassable, not to be passed through 11

12. Caution on nomenclature We should use diabatic when the energy exchange is between system and environment But, what if the heat source or sink is inside the system? – Thats adiabatic, but q 0 – Our interior heat source will be water changing phase Dry adiabatic: q = 0 – No heat source, outside OR inside – dry really means no water phase changes Moist adiabatic: q 0, but heat source/sink is inside system – moist implies water phase change – Synonyms include saturated adiabatic and wet adiabatic – Can also be referred to as diabatic! 12

13. 1 st law In the absence of KE and PE Other ways of writing this 13 Most of my examples will be per unit mass.

14. State properties Internal energy u is a state property Changes in state properties are not path- dependent Other state properties include m, T, p,, V, etc. 14

15. State properties 15

16. Path-dependence Work and heat are path-dependent 16

17. Path-dependence A cyclic process starts and ends with the same state property values … but the cyclic process can have net heat exchange and do net work 17

18. Path-dependence 18

19. Path-dependence 19

20. Carnot cycle 4-step piston cycle on a CM 2 steps of volume expansion, 2 of volume compression 2 steps are isothermal, 2 are (dry) adiabatic Warm and cold thermal reservoirs external to system Start and end with temperature T 1 and volume V 1 20

21. Carnot – Step 1 21 Isothermal volume expansion Add heat Q A from warm reservoir T 2 = T 1 V 2 > V 1

22. Carnot – Step 2 22 Adiabatic volume expansion No heat exchange T 3 < T 2 V 3 > V 2

23. Carnot – Step 3 23 Isothermal volume compression Lose heat Q B to cold thermal reservoir T 4 = T 3 V 4 < V 3

24. Carnot – Step 4 24 Adiabatic volume compression No heat exchange T 1 > T 4 V 1 < V 4 Returned to original state T 1, V 1. Cycle is complete.

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26. Apply 1 st law 26

27. Carnot on T-V diagram 27

28. Carnot on T-V diagram 28

29. Carnot on T-V diagram 29

30. Carnot on T-V diagram 30

31. Carnot on T-V diagram 31

32. Carnot on T-V diagram 32

33. Carnot on T-V diagram 33 No net V But did net W

34. Conceptual summary 34 Heat flow diverted to do work

35. Question for thought #1 35 The isothermal expansion (Q A ) occurred at a higher temperature than the Isothermal compression (Q B ). What does this imply for the work? Q B is waste heat. What does this imply for the efficiency of this heat engine? Is there a limit to efficiency? Is the limit found in the 1 st law?

36. Question for thought #2 36 Can you design a cyclic process that does no net work? What would it look like on a T-V diagram?

37. Summary 1 st law says, in essence, if you cant take the heat, you cant do the work Work and heat are path-dependent Carnot cycle illustrates isothermal and (dry) adiabatic processes – Heat diverted to do work, but some is wasted W = Q A - Q B 37