Title: SO345: Atmospheric Thermodynamics
1SO345 Atmospheric Thermodynamics
- CHAPTER 16 THERMODYNAMIC DIAGRAMS
2THERMODYNAMIC DIAGRAMS
- You have already been exposed to thermodynamic
diagrams in the early chapters when certain
concepts such as work were best elaborated on
through the use of certain graphs. - The first thermodynamic diagrams presented to
you were an a vs T diagram and an a vs p diagram
(Figures 3.2 3.3) in describing Charles Law
and Boyles Law. Since then you have also seen
the a , -p diagram and the a , e and T, e phase
diagrams.
3a , p DIAGRAM
- Probably the most fundamental of the
thermodynamic diagrams is the a , p diagram.
Since we express work in the atmosphere by pda ,
this type of diagram becomes important in
illustrating the concept of work which is
represented by any enclosed area within the
diagram. - As discussed earlier, in order to model the
diagram more like our atmosphere, the pressure
axis has been adjusted to increase downward
instead of the usual convention of increasing
values going upward.
4WHY USE THERMODYNAMIC DIAGRAMS?
- One of the simplest ways of convincing someone of
the utility of thermodynamic diagrams is to solve
for different values during a dry adiabatic
process by either solving Poissons Equation
(equation 7.1), or by using any thermodynamic
diagram where a dry adiabatic process is simply
any path along or parallel to a dry adiabat
curve.
5PRIMARY FUNCTION
- The main function of thermodynamic diagrams, is
to graphically depict major atmospheric processes
such as - - isobaric (pconstant),
- - isothermal (Tconstant),
- - dry adiabatic (?constant),
- - pseudoadiabatic (?Econstant),
- - constant moisture content (wsconstant).
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- The use of graphical representations greatly
simplifies analyses of the different
thermodynamic processes just listed.
6DESIRED CHARACTERISTICS OF A GOOD THERMODYNAMIC
DIAGRAM
- Important desired characteristics in a
thermodynamic diagram include - The axes are represented by commonly measured
meteorological variables. - The area enclosed by any series of thermodynamic
processes is proportional to work or energy. - As many of the process lines as possible
(isothermal, isobaric, dry adiabatic, etc.) are
straight or nearly straight. - The angle between isotherms and dry adiabats is
as close to 90deg as possible.
7DIFFERENT TYPES OF THERMODYNAMIC DIAGRAMS
- The different kinds of diagrams which we shall
discuss and evaluate are the - 1) a , -p diagram
- 2) Stuve diagram
- 3) Emagram
- 4) Tephigram
- 5) Skew T/ log p diagramÂ
8a , -p DIAGRAM
- As discussed, the a , -p diagram (Figure 16.1) is
a good fundamental diagram used to illustrate
some basics of atmospheric thermodynamics. Since
its x-axis, specific volume (or density), is not
a commonly measured or observed meteorological
variable, it is not routinely used by
meteorologists. - Work is defined by pda , so the enclosed area is
directly equal to work done by the process. The
only straight lines in this diagram are the
isobars. The angle between the isotherms and dry
adiabats is fairly small and varies depending on
location on the graph.
9a , -p DIAGRAM Fig. 16.1 An a,
-p thermodynamic diagram.
10STUVE DIAGRAM
- The Stuve diagram (along with the other
additional diagrams to be discussed) uses
commonly measured and observed meteorological
variables (T and -p) for its x and y axes.
Temperature is linear, while the pressure axis is
actually -p?, (where ?R/cp). All the dry
adiabat lines intersect at zero temperature and
pressure.
11ATMOSPHERIC RANGE OF VARIABLES
- The boxed region in Figure 16.2 shows the
applicable range of meteorological values in the
atmosphere that we are normally interested in.
Enclosed areas in this diagram are not
proportional to work or energy, and all process
lines are straight with the exception of the
pseudoadiabats. (It is not possible to have all
process lines straight in any diagram and still
perfectly satisfy all criteria). The
adiabat-isotherm angle is closer to 45deg than
90deg and does vary depending on location in the
diagram
12Stuve DiagramFig. 16.2 The
Stuve Diagram.
13EMAGRAM
- The Emagram (Figure 16.3) is also known as the
energy-per-unit-mass diagram. The x-axis is
linear temperature, and the y-axis is -ln p. - Areas in this diagram are proportional to energy,
and all process lines except pseudoadiabats are
straight or nearly straight (the dry adiabats and
ws lines are slightly curved). - The adiabat-isotherm angle is made to be about
45deg.
14Emagramfig. 16.3 The Emagram.
15TEPHIGRAM
- The Tephigrams x-axis is linear temperature and
the y-axis is actually cpln? which you may (or
may not) recall is equal to specific entropy (f
or phi), hence T-f diagram. With the y-axis
being composed of constant entropy lines (or
isentropes), isobars may be depicted as shown in
Figure 16.4.
16TEPHIGRAM
- The figure also encloses the diagrams region
of meteorological conditions which we would be
interested in. You would therefore view a
tephigram with isotherms slanting upward and to
the right, while isobars would appear to be
nearly straight horizontal looking lines. - Area is proportional to energy, and once
again all lines except for pseudoadiabats are
straight or nearly straight (isobars and ws
curves are slightly curved). - By the nature of this diagram, the
adiabat-isotherm angle is exactly 90deg.
17TephigramFig. 16.4 The
Tephigram.
18SKEW T/ LOG P DIAGRAM
- The Skew T/ log p diagram (or simply Skew T)
(Figure 16.5) is a modified version of the
emagram having more of a 90deg adiabat-isotherm
angle. The x-axis is linear temperature (skewed)
and the y-axis, like the emagram, is -ln p.
19SKEW T/ LOG P DIAGRAM
- Areas in a Skew T diagram are proportional to
energy. Pseudoadiabat lines are curved, while
dry adiabats are gently curved. ws lines are
essentially straight (very slightly curved), and
isotherms and isobars are exactly straight. - The adiabat-isotherm angles vary depending on
location, but the angle is close to 90deg. - About the most negative thing about this diagram
is the USAF printed at the top.
20Skew T/ log p Diagram Fig. 16.5
The Skew T/ log p Diagram
21COMPARISON OF DIAGRAMS
- There are different factors in determining the
personal desirability of one thermodynamic
diagram over another. Despite the objective
criteria presented here, there may be other
personal or practical preferences to be taken
into account. - Often times the meteorologists evaluation is
based on the diagram that he or she is most
familiar using. Table 16.1 summarizes relative
strengths and weaknesses based on the
desirability criteria presented. The students
should be able to justify in their own minds a
relative ranking of the thermodynamic diagrams
given.
22UTILITY OF THERMODYNAMIC DIAGRAMS
- Exposing you to these different types of
thermodynamic diagrams does not imply the
necessity to be totally proficient at using each
and every one of them. You will most probably
use and become very familiar with one particular
diagram (for example the Skew T), and that may
become your favorite. - If faced with using a different one, however,
knowing its particular characteristics and
relative advantages and disadvantages may be
helpful. Figure 16.6 provides basic comparative
illustrations of each of the diagram presented.
23UTILITY OF THERMODYNAMIC DIAGRAMS
- Often the student is easily intimidated by the
thermodynamic diagram upon first being introduced
to it. - After the initial shock, however, its relative
ease of use becomes apparent. You may find
shortly, certain situations which are more easily
described through processes outlined in a
thermodynamic diagram than through any other
method.
24STRENGTHS AND WEAKNESSES OF CHARTS
Table 16.1Summary of strengths and weaknesses of
the different Thermodynamic Diagrams.
25Fig. 16.6 Comparative illustrations of the
different Thermodynamic Diagrams. (T, p, and ?
curves are labeled a representative
pseudoadiabat (?E curve) is shown as a dashed
curved line, and a representative ws curve is
shown as a dark solid straight line).