Exergy

1
Exergy

• A Measure of Work Potential

2
Exergy

• Property
• Availability or available work
• Work f(initial state, process path, final state)

3
Exergy

• Dead State
• When system is in thermodynamic equilibrium with
  the environment
• Same temperature and pressure as surroundings, no
  kinetic or potential energy, chemically inert, no
  unbalanced electrical, magnetic, etc effects

4
Exergy

• Exergy
• Useful work
• Upper limit on the amount of work a device can
  deliver without violating any thermodynamic law.
• (always a difference between exergy and actual
  work delivered by a device)

5
Exergy associated with Kinetic and Potential
Energy

• Kinetic energy
• Form of mechanical energy
• Can be converted to work entirely
• xke ke vel2 /2 (kJ/kg)

6
Exergy associated with Kinetic and Potential
Energy

• Potential Energy
• Form of mechanical energy
• Can be converted entirely into work
• xpe pe gz (kJ/kg)
• All ke and pe available for work

7
Reversible Work and Irreversibility

• Exergy
• Work potential for deferent systems
• System operating between high temp and dead state
• Isentropic efficiencies
• Exit conditions differ

8
Reversible Work and Irreversibility

• Reversible Work
• Irreversibility (exergy destruction)
• Surroundings Work
• Work done against the surroundings
• For moveable boundary
• Wsurr P0(V2 V1)
• Wuseful W Wsurr W - P0(V2 V1)

9
Reversible Work and Irreversibility

• Reversible Work, Wrev
• Max amount of useful work produced
• Min amount of work that needs to be supplied
• between initial and final states of a process
• Occurs when process is totally reversible
• If final state is dead state exergy

10
Reversible Work and Irreversibility

• Difference between reversible work and useful
  work is called irreversibility
• Wrev Wuseful I
• Irreversibility is equal to the exergy destroyed
• Totally reversible process, I 0
• I, a positive quantity for actual, irreversible
  processes

11
2nd Law Efficiency

• Second Law Efficiency, ?II
• Ratio of thermal efficiency and reversible
  (maximum) thermal efficiency
• ?II ?th/?th, rev
• Or ?II Wu/Wrev
• Can not exceed 100

12
2nd Law Efficiency

• For work consuming devices
• For ?II Wrev/Wu
• In terms of COP
• ?II COP/COPrev
• General definition
• ? exergy recovered/exergy supplied
• 1 exergy destroyed/exergy supplied

13
Exergy change of a system

• Property
• Work potential in specific environment
• Max amount of useful work when brought into
  equilibrium with environment
• Depends on state of system and state of the
  environment

14
Exergy change of a system

• Look at thermo-mechanical exergy
• Leave out chemical mixing
• Not address ke and pe

15
Exergy of fixed mass

• Non-flow, closed system
• Internal energy, u
• Sensible, latent, nuclear, chemical
• Look at only sensible latent energy
• Can be transferred across boundary only when
  temperature difference exists

16
Exergy of fixed mass

• 2nd law not all heat can be turned into work
• Work potential of internal energy is less than
  the value of internal energy
• Wuseful (U-U0)P0(V V0)T0(S S0)
• X (U-U0)P0(V V0)T0(S S0) ½mVel2mgz

17
Exergy of fixed mass

• F (u-u0)P0(v-v0)-T0(s-s0)½Vel2gz
• or F (e-e0)P0(v-v0)-T0(s-s0)
• Note that F 0 at dead state
• For closes system
• ?X m(F2-F1) (E2-E1)P0(V2-V1)-T0(S2-S1)½m(Vel
  22-Vel12)mg(z2-z1)
• ?F (F2-F1) (e2-e1)P0(v2-v1)-T0(s2-s1) for a
  stationary system the ke pe terms drop out.

18
Exergy of fixed mass

• When properties are not uniform, exergy can be
  determined by integration

19
Exergy of fixed mass

• If the state of system or the state of the
  environment do not change, the exergy does not
  change
• Exergy change of steady flow devices, nozzles,
  compressors, turbines, pumps, heat exchangers is
  zero during steady operation.
• Exergy of a closed system is either positive or
  zero

20
Exergy of a flow stream

• Flow Exergy
• Energy needed to maintain flow in pipe
• wflow Pv where v is specific volume
• Exergy of flow work exergy of boundary work in
  excess of work done against atom pressure (P0) to
  displace it by a volume v, so
• x Pv-P0v (P-P0)v

21
Exergy of a flow stream

• Giving the flow exergy the symbol ?
• Flow exergy
  ?(h-h0)-T0(s-s0)½Vel2gz
• Change in flow exergy from state 1 to state 2 is
  ?? (h2-h1)-T0(s2-s1) ½(Vel22 Vel12)
  g(z2-z1)
• Fig 7-23

22
Exergy transfer by heat, work, and mass

• Like energy, can be transferred in three forms
• Heat
• Work
• Mass
• Recognized at system boundary
• With closed system, only heat work

23
Exergy transfer by heat, work, and mass

• By heat transfer
• Fig 7-26
• Xheat (1-T0/T)Q
• When T not constant, then
  Xheat ?(1-T0/T)dQ
• Fig 7-27
• Heat transfer Q at a location at temperature T is
  always accompanied by an entropy transfer in the
  amount of Q/T, and exergy transfer in the amount
  of (1-T0/T)Q

24
Exergy transfer by heat, work, and mass

• Exergy transfer by work
• Xwork W Wsurr (for boundary work)
• Xwork W (for all other forms of work)
• Where Wwork P0(V2-V1)

25
Exergy transfer by heat, work, and mass

• Exergy transfer by mass
• Mass contains exergy as well as energy and
  entropy
• Xm ?m(h-h0)-T0(s-s0)½Vel2gz
• When properties change during a process then

26
Exergy transfer by heat, work, and mass

• For adiabatic systems, Xheat 0
• For closed systems, Xmass 0
• For isolated systems, no heat, work, or mass
  transfer, ?Xtotal 0

27
Decrease of Exergy Principle

• Conservation of Energy principle energy can
  neither be created nor destroyed (1st law)
• Increase of Entropy principle entropy can be
  created but not destroyed (2nd law)

28
Decrease of Exergy Principle

• Another statement of the 2nd Law of
  Thermodynamics is the Decrease of Exergy
  Principle
• Fig 7-30
• For an isolated system
• Energy balance Ein Eout ?Esystem
  0 E2 E1
• Entropy balance Sin Sout Sgen ?Ssystem Sgen
  S2 S1

29
Decrease of Exergy Principle

• Working with 0 E2 E1 and Sgen S2 S1
• Multiply second and subtract from first
• -T0Sgen E2 E1 -T0(S2 S1)
• Use
• X2X1 (E2-E1)P0(V2-V1)-T0(S2-S1)
• since V1 V2 the P term 0

30
Decrease of Exergy Principle

• Combining we get
• -T0Sgen (X2X1) 0
• Since T is the absolute temperature of the
  environment Tgt0, Sgen 0, so T0Sgen0 so
• ?Xisolated (X2X1)isolated 0

31
Decrease of Exergy Principle

• The decrease in Exergy principle is for an
  isolated system during a process exergy will at
  best remain constant (ideal, reversible case) or
  decrease. It will never increase.
• For an isolated system, the decrease in exergy
  equals the energy destroyed