Group 'A' Construction of a Thermodynamic Diagram - COMET

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

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,
1
st

Law of Thermodynamics, hydrostatics, and
water substance in the atmosphere

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.


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.

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

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.

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.

Discussion/Reflection


All team members plan to use major
portions of this project in their classrooms
during the 2002
-
3 academic year.

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


Proposed Syllabus Rubric

1.Teach Ideal Gas Law


-
Example Problem

Using

Excel

Create

a

P
a

Diagram

by

plotting

the

200
K,

300
K

and

400
K

isotherms

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?

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





Syllabus Rubric

-
Example Problem


Which line in the P
a

Diagram below indicates an
isobaric change from 200K

to 400 K

a)
A

b)
B

c)
C

Syllabus Rubric

-
Example Problem


Which line in the P
a

Diagram below indicates an
isosteric change from 200K

to 400 K

a)
A

b)
B

c)
C

Syllabus Rubric

-
Example Problem


Which line in the P
a

Diagram below indicates an
isothermal change from 200K

to 400 K

a)
A

b)
B

c)
C

Syllabus Rubric

2.Teach 1
st

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 45
o




Plot sounding


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)


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


Syllabus Rubric

4. Water Vapor Continued


Derive Claussius
-
Claperyon Equation



Students plot lines of constant w
s

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.

Syllabus Rubric

5.Processes in the Atmosphere



Parcel process (definition)



Problems/Exercises


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)

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)



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.

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.

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?

Web
-
driven Interaction

Process


du = (+),

(
-
), or 0


db = (+), (
-
)
or 0


d
q

= (+),

(
-
), or 0


Undetermined


A to B
















B to C
















A to C
















Questions for diagram points
(A


G)


Is d
q

for ‘A to C’ >, <, = ‘A to G’ or cannot be
determined?



Is d
a
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?

Questions for diagram points
(A


G)


‘B to F’ d
a
, (+), (
-
), 0, or cannot be
determined?


‘A to C’ d
a
, (+), (
-
), 0, or cannot be
determined?



‘D to B’ d
a
, (+), (
-
), 0, or cannot be
determined?


Water Vapor Exercises/Problems


Given T, T
d

as a function of pressure

(a) Compute/determine from Skew
-
T diagram at
1000 mb.

[w, w
s
, e, e
s
, T
w
, RH, q, q
s
, T
v
,
θ, ρ, θ
e
, θ
w
]

(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

Water Vapor Exercise/Problems


Wallace & Hobbs (p. 80) question on lifting
parcel over mountain


Perform using a Skew
-
T


Redo using Java Applet

Water Vapor Exercises/Problems


A closed insulated room is initially at 25
°
C,
20% RH. Volume of the room is 400m
3
.


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