SO345: Atmospheric Thermodynamics

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SO345 Atmospheric Thermodynamics

• CHAPTER 8
• ENTROPY THE SECOND LAW OF THERMODYNAMICS

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REVERSIBLE AND IRREVERSIBLE PROCESSES

• A reversible process is one in which a system
  Aplus its environment A is restored to its
  original state. It is very important to include
  the fact that it is not only the system that must
  be returned to its original state, but also the
  environment, in order to fit the definition of
  this ideal process. All real processes in nature
  tend to be irreversible processes, but similar to
  our initial discussion of the adiabatic process,
  referring to reversibility allows us to
  mathematically represent, to a reasonable degree,
  some important practical concepts in the
  atmosphere.

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ENTROPY

• As energy is defined as the capacity to do
  work, entropy may be described as the
  unavailability of energy. It is the measure of
  disorder of a system. In further defining a
  reversible process, it can be stated as one in
  which the total entropy (once again the systems
  and the environments) is constant. So total
  entropy tends to increase for all real natural
  processes.

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2ND LAW OF THERMODYNAMICS

• There are different forms of the 2nd Law of
  Thermodynamics some of the related concepts
  include
• - heat not being converted completely to
  work
• - ideal Carnot engines
• - heat flowing only from hot to cold and not
  vice versa
• - nature tending to an increase in total
  entropy.

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2ND LAW OF THERMODYNAMICS

• In a way, the 2nd Law of Thermodynamics gives
  restrictions that are not precluded by the 1st
  Law. Simply stated, there are some things that
  can only happen in one direction, but not the
  other. You can burn a thermodynamics book, but
  you will not be able to return the ashes to its
  original book state once burned. Entropy ends up
  being a fairly peculiar variable to deal with,
  but we will most closely follow the form of the
  2nd Law which references entropy and reversible
  processes.

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2ND LAW OF THERMODYNAMICS

• The 2nd Law of Thermodynamics
• In a thermodynamics process, the total entropy
  (of the system and its environment) either
  remains constant or increases.
•  
• if total entropy stays constant --------gt process
  is reversible,
• if total entropy increases --------------gt
  process is irreversible.

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RELATIONSHIP OF ISENTROPIC, REVERSIBLE, AND
ADIABATIC PROCESSES

• If we assume a reversible process and start with
  the implicit form of the 1st Law of
  Thermodynamics
•  
• dh cpdT adp

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RELATIONSHIP OF ISENTROPIC, REVERSIBLE, AND
ADIABATIC PROCESSES

• dh cpdT adp
• and divide the equation by temperature, we
  can get the expression
• (Eq 8.1)

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RELATIONSHIP OF ISENTROPIC, REVERSIBLE, AND
ADIABATIC PROCESSES

• Through an almost mathematical coincidence,
  dividing by temperature converts an inexact
  differential expression to an exact one, and the
  term on the left side of the equation will be
  called the change in Aspecific entropy_at_, or df.
  The conversion to exact differentials allows us
  to ultimately find a formula relating specific
  entropy (f) with potential temperature (?)
• (Eq. 8.2)
• (The complete derivation of f as a function of ?
  can be found in Appendix E)

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RELATIONSHIP OF ISENTROPIC, REVERSIBLE, AND
ADIABATIC PROCESSES

• Like internal energy, we do not know the actual
  value of specific entropy for a particular
  equilibrium state, however it is once again the
  change in f from one state to another that we are
  most concerned about. From Eq 8.2, we can see
  that if the change in specific entropy (df) is
  zero, then the change in potential temperature
  (d?) must also be zero.
•  
• df 0 (isentropic
  process)
• d? 0 (adiabatic
  process)

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RELATIONSHIP OF ISENTROPIC, REVERSIBLE, AND
ADIABATIC PROCESSES

• This shows us that an adiabatic process is also
  an isentropic process is also a reversible
  process.
•  
• adiabatic isentropic
  reversible
•  
• Though we will use the concepts of entropy and
  reversibility in subsequent topics, the main
  focus for most meteorological applications will
  be the use of potential temperature as a variable
  (of state) rather than entropy.