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
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