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  Purpose  to provide a graphical display of lines representing major kinds of atmospheric processes such as:  Isobaric (constant pressure)  Isothermal (constant temperature)

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

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)!

Thermodynamic diagram and upper air information.  1st characteristic:  P vs.  A vs. B

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, , ln[p], etc….)  We must also make sure that variables A and B are readily measurable quantities (Why?)

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

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.

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

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 , and p. Thus, the equation of state is very useful here! B = (p  / R) A = (P  / T) ln[p]

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

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

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!

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

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?

Thermodynamic diagram and upper air information.  Questions?  Comments?  Criticisms?

Thermodynamic diagram and upper air information.  The end!