Group ‘A’ Construction of a Thermodynamic Diagram

1. Group ‘A’Construction of a Thermodynamic Diagram August 16, 2002 Lynn LeBlanc (coordinator), Chad Kauffman,Greg McFarquhar, David Metzler, Pat Parrish, Robert Pasken, Anthony Rockwood, Jie Song

2. Overview • Students will construct (and use) a Skew-T log-P diagram as an aid in understanding and applying basic thermodynamic concepts. • This will fit in the middle of a standard thermodynamic course covering the gas laws, 1st Law of Thermodynamics, hydrostatics, and water substance in the atmosphere

3. Learning Objectives • Students will learn how to apply the fundamental thermodynamic principles in the construction of the thermodynamic diagram. • Students will learn how to apply the thermodynamic diagram to practical problems.

4. Audience • Intended audience is undergraduate majors in atmospheric science/meteorology. • A knowledge of thermodynamics is essential to understanding why the atmosphere behaves the way it does.

5. Required Resources • Semi-log paper • Hard-copy Skew-T log-P diagrams • Java applets for: • Aircraft Altimetry • Macromedia Flash • p-a diagrams • Skew-T diagrams

6. Assessment Plan • Interactive Web-based exercises to test ability to interpret or analyze thermodynamic diagrams • Quantitative submissions • Textual submissions • Student will use the skew-T log-P diagram to quantify changes in variables during atmospheric processes. • Student will sketch a Skew-T log-P diagram as part of an exam.

7. Learning Activities • Teaching strategy will include lectures, hands-on activities, interactive computer-based instructions. • Multiple instructional methods seemed to be a natural fit for this project. • Because the thermodynamic diagram is a key tool for research meteorologists and operational weather forecasters, this approach grounds the learning of thermodynamic within a professional application. • This strategy offers the advantage of providing inherent interest in the topic and motivation for their learning.

8. Discussion/Reflection • All team members plan to use major portions of this project in their classrooms during the 2002-3 academic year.

9. Proposed Syllabus Rubric 1.Teach Ideal Gas Law -Avagadro’s Principle -Partial Pressure -Gas constant for dry air Plot isotherms on P-alpha diagram Problems/exercises Plot isosteres on p-T diagram (p increasing , T increasing  ) Problems/exercises Plot isosteres on log p-T diagrams Problems/exercises

10. Proposed Syllabus Rubric 1.Teach Ideal Gas Law -Example Problem Using Excel Create a P Diagram by plotting the 200K, 300K and 400K isotherms

11. Syllabus Rubric -Example Problems What happens to the isotherms as the pressure gets closer to 1000 mb? Why does that happen? From the shape of the isotherms what changes to the axis would you suggest to make the isotherms straight?

12. Syllabus Rubric -Example Solutions The isotherms get closer together as the pressure increases. Since the function is hyperbolic a Log-Linear graph is more appropriate

13. Syllabus Rubric -Example Problem Which line in the P Diagram below indicates an isobaric change from 200Kto 400 K • A • B • C

14. Syllabus Rubric -Example Problem Which line in the P Diagram below indicates an isosteric change from 200Kto 400 K • A • B • C

15. Syllabus Rubric -Example Problem Which line in the P Diagram below indicates an isothermal change from 200Kto 400 K • A • B • C

16. Syllabus Rubric 2.Teach 1st Law of Thermodynamics Work, Heat, Energy Problems/Exercises on processes, paths (draw by hand) Problems/Exercises using interactive Java Applets with P-alpha diagram specifications for design of [Java Applet] Plot sounding of T-log p diagram Why does it look odd? Skew isotherms 45o Plot sounding

17. Syllabus Rubric 3.Adiabatic Processes Poisson’s Equation & Hydrostatic Equation -Variation as p, alpha with height Hypsometric Equation, Reduction to sea-level Altimetry Java Applet for aircraft flying at constant pressure Problems and Exercises Derivation of Adiabatic Lapse Rate Student calculates and plots lines of constant theta on skew-T log-P diagram Problems and exercises using paper diagrams or Java Skew-T applet (TBD)

18. Syllabus Rubric 4.Water Vapor in the Atmosphere Define variables Relation between variables Variable Gas Constant Virtual Temperature Problems and Exercises Phase Changes Latent Heats Students use diagram for application

19. Syllabus Rubric 4. Water Vapor Continued Derive Claussius-Claperyon Equation Students plot lines of constant ws on Skew-T, log-P diagram Problems/Exercises on paper or Applet Derive Moist Adiabatic Lapse Rate Students plot lines lines of constant Theta-w given critical values at 1000 mb.

20. Syllabus Rubric 5.Processes in the Atmosphere Parcel process (definition) Problems/Exercises

21. Java Applets • P-alpha diagram Draw paths which describe a process Display changes in all thermodynamic variables (temperature, pressure, volume, internal energy, enthalpy, entropy, work, heat)

22. Java Applets cont’d. • Skew-T log-P Follow a parcel as it moves in the atmosphere vertically (or change temperature at constant pressure) Motions controlled by mouse or specific forcing by synoptic vertical motion Display current values of all thermodynamic variable and derived quantities (latent heat released, liquid water condensed)

23. Questions on Adiabatic Processes 1. Assume that in Denver, CO a station pressure of 850 mb and a station pressure of 10°C are measured. Reduce the station pressure of 850 mb to a sea-level adjusted pressure (assuming a dry atmosphere). • Hint: You can use the U.S. Standard atmosphere lapse rate of 6.5 K/km in your calculation.

24. Adiabatic Processes cont’d. 2. Assume that a beginning aviation student erroneously assumes that the atmosphere is isothermal rather than assuming the standard dry adiabatic lapse rate. What error (%) will be made in the difference between altitudes calculated assuming an isothermal atmosphere and a U.S. Standard Atmosphere? Assume a dry atmosphere in both calculations with a temperature of 15°C, and a surface pressure of 1013.25 mb.

25. Adiabatic Processes cont’d. 3. Calculate the height at which the 500 mb level occurs for a typical tropical, mid-latitude and Arctic atmospheres assume a standard Atmosphere lapse rate of 6.5 K/km and assuming surface temperatures of 30°C, 10°C, -10°C. Determine the thickness of the layer between 500-100 mb for the same three regions assuming mean virtual temperatures of 228K, 223K, 210K. What is the height of the tropopause for the three regions?

26. Process du = (+), (-), or 0 db = (+), (-) or 0 dq = (+), (-), or 0 Undetermined A to B B to C A to C Web-driven Interaction

27. Questions for diagram points (A G) • Is dq for ‘A to C’ >, <, = ‘A to G’ or cannot be determined? • Is da for ‘A to C’ >, <, = ‘A to G’ or cannot be determined? • (Explain or note use of Equation of state to calculate specific volume) • Does the above process represent compressional heating, compressional cooling, expansional heating, expansional cooling?

28. Questions for diagram points (A G) • ‘B to F’ da, (+), (-), 0, or cannot be determined? • ‘A to C’ da, (+), (-), 0, or cannot be determined?  • ‘D to B’ da, (+), (-), 0, or cannot be determined?

29. Water Vapor Exercises/Problems • Given T, Td as a function of pressure (a) Compute/determine from Skew-T diagram at 1000 mb. [w, ws, e, es, Tw, RH, q, qs, Tv, θ, ρ, θe, θw] (b) Lift a parcel at 1000 mb to LCL Compute LCL and all above variables (c) Lift to 6 km (use hypsometric equation to determine pressure level) Compute all above variables Compute latent heat released (per kg of air) (d) Redo with Java Applet

30. Water Vapor Exercise/Problems • Wallace & Hobbs (p. 80) question on lifting parcel over mountain • Perform using a Skew-T • Redo using Java Applet

31. Water Vapor Exercises/Problems • A closed insulated room is initially at 25°C, 20% RH. Volume of the room is 400m3. • How much water must be evaporated to raise RH to 60%? What is the final room temperature (under constant pressure of 1000 mb)? • Validate your answer using your constructed thermodynamic diagram