Exergy

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Exergy

• Phase 2

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Exergy destruction

• Caused by irreversibilities such as
• Friction, mixing, chemical reactions, heat
  transfer through a finite temperature difference,
  unrestrained expansion, non-quasi-equilibrium
  compression or expansion anything that cause
  entropy generation
• Anything that generates entropy, destroys exergy

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Exergy destruction

• Exergy destroyed is proportional to entropy
  generated
• Xdestroyed T0Sgen 0
• Exergy destroyed represents the lost work
  potential, also called irreversibility or lost
  work

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Exergy destruction

• gt 0 irreversible system
• Xdestroyed 0 reversible system
• lt 0 impossible system
• Apply to all systems since we can make the
  boundary of the system large enough to enclose
  surroundings in system

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Exergy Balance

• Exergy balance any system
• Xin Xout Xdestroyed ?Xsystem (kJ)
• Exergy balance any system, unit mass
• xin xout xdestroyed ?xsystem (kJ/kg)
• Exergy balance rate form

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Exergy Balance

• Closed systems

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Exergy destruction

• In the rate form

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Exergy destruction

• For unit-mass
  (xinxout) xdestroyed ?xsystem (kJ/kg)
• For reversible process xdestroyed term goes to 0
• Xdestroyed T0Sgen

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Exergy destruction

• The exergy change of the system, if the
  environment is known, can be determined from the
  end states, (?Xsystem X2X1) however, the exergy
  transfer for the heat, work and mass transfer
  must be determined with knowledge of the states
  and process.

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Exergy destruction

• For closed system (no mass flow)
• XheatXwork- Xdestroyed ?Xsystem
• ?(1-T0/Tk)Qk W-P0 (V2V1) T0Sgen X2- X1
  where Qk is the heat transferred through the
  boundary at temperature Tk at location k.
• Also a rate form

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Exergy destruction

• Wrev can be found by setting W Wrev and
  Xdestroyed T0Sgen 0
• Equation represents the exergy destroyed within
  the system boundaries only, so if 0 may be
  internally reversible only
• Expand system boundaries to include surroundings
  to find irreversibilities in surroundings

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Exergy destruction

• For a reversible process, entropy generation and
  exergy destruction are zero, exergy balance
  becomes similar to energy balance
• Energy change of a system for any process equals
  the energy transfer. For exergy the change
  equals the transfer for only reversible processes

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Exergy destruction

• The quantity of energy remains constant (1st law)
  for actual processes but the quality of the
  energy (2nd law) decreases.
• Accompanied by an increase in entropy and
  decrease in exergy

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Exergy Balance

• Control volumes, add mass flow
• XheatXwork(Xmass in Xmass out ) - Xdestroyed
  ?XCV
• ?(1-T0/Tk)Qk W-P0 (V2V1)?mi?i ?me?e-T0Sgen
  (X2- X1)CV
• Also a rate form

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Exergy Balance

• The rate equation is the rate of exergy change
  within the control volume during a process is
  equal to the rate of net exergy transfer through
  the control volume boundary by heat, work, and
  mass flow minus the rate of exergy destruction
  within the boundaries of the control volume.

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Exergy Balance

• When the initial and final states of the control
  volume are known then
• X2X1 m2F2- m1F1

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Exergy Balance

• Steady-flow systems (Fig 7-43)
• Amount of exergy entering must equal amount
  leaving and destroyed.

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Exergy Balance steady flow

• Control volumes used the most are turbines,
  nozzles, diffusers, heat exchangers, pipes,
  compressors, and ducts
• Operate steady state, no change in mass, energy,
  entropy, exergy, volume
• Amount of exergy entering must equal amount
  leaving and destroyed