SO345: Atmospheric Thermodynamics

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SO345 Atmospheric Thermodynamics

• CHAPTER 16 THERMODYNAMIC DIAGRAMS

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THERMODYNAMIC 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.

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a , 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.

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WHY 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.

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PRIMARY 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).
•  
• The use of graphical representations greatly
  simplifies analyses of the different
  thermodynamic processes just listed.

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DESIRED 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.

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DIFFERENT 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 diagram 

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a , -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.

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a , -p DIAGRAM Fig. 16.1 An a,
-p thermodynamic diagram.
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STUVE 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.

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ATMOSPHERIC 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

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Stuve DiagramFig. 16.2 The
Stuve Diagram.
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EMAGRAM

• 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.

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Emagramfig. 16.3 The Emagram.
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TEPHIGRAM

• 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.

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TEPHIGRAM

• 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.

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TephigramFig. 16.4 The
Tephigram.
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SKEW 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.

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SKEW 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.

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Skew T/ log p Diagram Fig. 16.5
The Skew T/ log p Diagram
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COMPARISON 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.

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UTILITY 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.

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UTILITY 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.

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STRENGTHS AND WEAKNESSES OF CHARTS
Table 16.1Summary of strengths and weaknesses of
the different Thermodynamic Diagrams.
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Fig. 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).