Exergy

1
Exergy

• Thermodynamics
• Professor Lee Carkner
• Lecture 15

2
PAL 14 Reversibility

• Air compressed with constant specific heats
• R 0.287 (Table A-1), k 1.4 (Table A-2)
• (T2/T1) (P2/P1)(k-1)/k
• T2 T1(P2/P1)(k-1)/k (290)(800/100)(0.4/1.4)
  525.3 K
• w Du cvDT 0.727(525.3-290)

3
PAL 14 Reversibility

• Air compressed with non-constant specific heats
• Need to use reduced pressure table (A-17)
• For T1 290, Pr1 1.2311 and u1 206.91
• Pr2 (P2/P1)Pr1 (800/100)(1.2311) 9.849
• For table A-17 this corresponds to T2 522.4 K
  and u2 376.16
• w u2-u1 (376.16-206.91)

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Exergy

• Exergy (x) is a measure of the work potential of
  an energy source
• Defined as
• The dead state is defined as the state in
  thermodynamic equilibrium with the environment
• Exergy is the upper limit for the work an actual
  device could produce

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Exergy Systems

• e.g. the amount of work you can generate from a
  geothermal well depends on where you dump the
  waste heat
• Kinetic energy
• Potential Energy
• Both KE and PE can be completely converted to
  work
• n.b. V and z are relative to the environment

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Kinds of Work

• Surroundings Work
• Wsurr P0(V2-V1)
• Useful work
• Wa W P0(V2-V1)
• Reversible work
• If the final state is the dead state the
  reversible work equals the exergy
• Irreversibility
• I Wrev - Wu

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Second Law Efficiency

• Our standard thermal efficiency has 100 as an
  upper limit
• We instead want to compare the work output to the
  true maximum that given by a reversible engine
• The second law efficiency is
• hth,rev is the Carnot Efficiency

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Comparing With Efficiency
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Efficiencies

• Work producing devices
• hII
• Work consuming devices
• hII
• Refrigerators
• hII
• General Definition
• hII xrecovered/xsupplied 1
  (xdestroyed/xsupplied)

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Exergy of a Closed System

• The exergy per unit mass (f) is
• f (u-u0)P0(v-v0)-T0(s-s0)V2/2gz
• For a process we can subtract the exergies at the
  two states
• Df (u2-u1)P0(v2-v1)-T0(s2-s1)(V22-V21)/2g(z2-
  z1)

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Flow Exergy

• The flow energy is Pv and we can find its exergy
  by subtracting the work needed to displace the
  fluid against the atmosphere
• By including this in our previous relationship we
  find the flow or stream exergy, y
• y (h-h0)-T0(s-s0)V2/2gz
• Exergy change of a fluid stream is
• Dy (h2-h1)-T0(s2-s1)(V22-V21)/2g(z2-z1)

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Exergy Transfer Heat

• The most work that a given amount of heat can
  generate is through a Carnot cycle, so we can use
  the reversible efficiency to find the exergy
• Where T0 is the temperature of the environment

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Transferring Exergy
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Exergy Transfer Work

• One exception is overcoming atmospheric pressure
  for moving boundary work
• Xwork W Wsurr W P0(V2-V1)
• e.g. shaft work, electrical work, etc.

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Exergy Transfer Mass

• Mass flow carries exergy into or out of a system
  just as it does energy
• May have to integrate if fluid properties are
  variable
• Xmass
• Xheat

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Next Time

• Next class Tuesday, April 18
• Exam 2 Wednesday, April 19
• Read 8.6-8.8
• Homework Ch 8, P 38, 42, 64, 75