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Thermodynamic diagram and upper air information.

Thermodynamic diagram and upper air information. Atms Sc 4310 / 7310 Lab 1 Anthony R. Lupo. Thermodynamic diagram and upper air information. Example: The Pseudo adiabatic diagram, or the Stueve. Thermodynamic diagram and upper air information. Thermodynamic diagrams

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Thermodynamic diagram and upper air information.

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  1. Thermodynamic diagram and upper air information. Atms Sc 4310 / 7310 Lab 1 Anthony R. Lupo

  2. Thermodynamic diagram and upper air information. • Example: The Pseudo adiabatic diagram, or the Stueve.

  3. Thermodynamic diagram and upper air information. • Thermodynamic diagrams • Purpose  to provide a graphical display of lines representing major kinds of atmospheric processes such as: • Isobaric (constant pressure) • Isothermal (constant temperature)

  4. Thermodynamic diagram and upper air information. • Dry adiabatic (constant potential temperature) • Isosteric (constant specific volume) • Pseudoadiabatic processes

  5. Thermodynamic diagram and upper air information. • Three desired characteristics of these diagrams: • 1) area of enclosed by the lines be proportional to the change in energy or the work done in the process. • 2) Most of the fundamental lines be straight (constant slope) • 3) Angle between the dry adiabats and isotherms be large (near 90 degrees)!

  6. Thermodynamic diagram and upper air information. • 1st characteristic: • P vs. a A vs. B

  7. Thermodynamic diagram and upper air information. • We shall require that the area enclosed on one diagram is equal to the area on the other. • We must make sure this is an equal area transformation from alpha and P to A and B which are a function of one or more thermodynamic (state) variables. (e.g., T, q, ln[p], etc….) • We must also make sure that variables A and B are readily measurable quantities (Why?)

  8. Thermodynamic diagram and upper air information. • Thus we require differentials to be exact • Thus: Exactness? What do we mean?

  9. Thermodynamic diagram and upper air information. • However, this can be equivalently stated from conformal mapping, that there needs to be a one-to-one transformation, i.e. the Jacobean = 1 (Jacobean – Jacobean notation). • Physically, the Jacobean is a transformation or map factor.

  10. Thermodynamic diagram and upper air information. • Show Jacobean (how to evaluate) • If the above is equal to 1, then your thermodynamic diagram is true.

  11. Thermodynamic diagram and upper air information. • The Emagram (Canada’s AES uses this diagram): B = T A = -R ln[p] • Step 1: Get rid of variables T and R as much as possible in favor of a, and p. Thus, the equation of state is very useful here! B = (pa / R) A = (P a / T) ln[p]

  12. Thermodynamic diagram and upper air information. • Step 2: Evaluate the Jacobean

  13. Thermodynamic diagram and upper air information. • Step 3 plug and chug! ? check!

  14. Thermodynamic diagram and upper air information. • Then, if you wish to create your own thermodynamic diagram: • Then take one half the Jacobean expression and set it equal to one. The other half can be set to zero using arbitrary constants!

  15. Thermodynamic diagram and upper air information. • If B = T (get the Emagram back)

  16. Thermodynamic diagram and upper air information. • Then integrate, • Now, we need to put RHS in terms of a only! Use equation of state. • Did YOU forget your “arbitary” constant on the indefinite integral?

  17. Thermodynamic diagram and upper air information. • Questions? • Comments? • Criticisms?

  18. Thermodynamic diagram and upper air information. • The end!

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