Exergy
1
Advanced Thermo-fluids
Exergy
What? Exergy? Can I
eat it? What? No?
Contents:
1. What is exergy?
2. Reversible work
3. Second law efficiency
*~#$!
4. Forms of exergy
5. Exergy change
6. Exergy transfer
7. Exergy balance
What is Exergy?
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Advanced Thermo-fluids
Exergy
Exergy:
=> Useful work potential of a system at specified state
=> Represent maximum useful work obtainable from a system
=> Also called availability or available energy
=> Exergy is a thermodynamic property
=> Value depends on:
a the state of the system
a the surroundings
What is Exergy?
Considerations in exergy analysis:
cInitial state is specified
dProcess path is reversible
eFinal state is at dead state, i.e.
H temperature and pressure
equal to the surroundings
H no kinetic and potential energy
H chemically innert
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Advanced Thermo-fluids
Exergy
Reversible work
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Advanced Thermo-fluids
Exergy
Process involving boundary work:
Expansion => part of work produced
is used to push atmospheric pressure
Compression => part of work applied
is helped by atmospheric pressure
Surroundings work Wsurr => work done by or
against surroundings during a process
Wsurr = P0 (V2 − V1 )
Useful work Wu => difference between
actual work and surrounding work
Wu = W − Wsurr
Reversible work
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Advanced Thermo-fluids
Exergy
Reversible work Wrev: => max useful work obtainable from a
reversible process between specified initial and final states
If final state = dead state,
=> reversible work equals exergy
Irreversibility => difference between
reversible work and useful work
I = Wrev ,out − Wu ,out
I = Wu ,in − Wrev ,in
For work producing
process e.g.
expansion, turbine
For work consuming
process e.g. compression,
compressor
Second Law Efficiency
6
1st. Law efficiency:
=> a measure of performance of a device
=> doesn’t relate to its best possible performance
1st. Law efficiency =
ηth =
Wnet ,out
QH
Desired output
Required input
QL
COPR =
Win
COPHP
QH
=
Win
Advanced Thermo-fluids
Exergy
Second Law Efficiency
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Advanced Thermo-fluids
Exergy
2nd. Law efficiency => a measure of performance of
a device relative to its best possible performance
Best possible performance => reversible condition
η th
η II =
η th , rev
 Wu
 W for work - producing device
 rev
=
 W rev for work - consuming device
 Wu
COP
COPII =
COPrev
2nd. Law efficiency of all
reversible devices is 100%
Forms of Exergy
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Advanced Thermo-fluids
Exergy
Forms of energy of a system:
Energy of
a system
=
Kinetic
Energy
+
Potential
Energy
+
Internal
Energy
1 v2
1 v2
Q − W + m(h + V + gz)in − m(h + V + gz) out = (∆U + ∆KE + ∆PE) system
2
2
Each form of energy has a potential to produce work
Each form of energy has work potential (i.e. exergy)
Not all energy can be converted to work
Mechanical form of energy can
be converted all to exergy
Exergy of a system is the sum of all exergies
from each form of energy in the system
Forms of Exergy
Exergy of kinetic energy:
Exergy of potential energy:
xke = ke =
9
V
Advanced Thermo-fluids
Exergy
2
2
x pe = pe = gz
Exergy of internal energy:
xu = (u − u0 ) + P0 (v − v0 ) − T0 ( s − s0 )
Exergy of system:
1
xsys = xu + xke + x pe
xsys = [(u − u0 ) + P0 (v − v0 ) − T0 ( s − s0 )] +
V
2
2
+ gz
Forms of Exergy
Exergy of system:
Advanced Thermo-fluids
Exergy
10
x sys = x u + x ke + x pe
x sys = [( u − u 0 ) + P0 ( v − v 0 ) − T 0 ( s − s 0 ) ] +
Exergy change of system:
+ gz
2
∆ x sys = ∆ x u + ∆ x ke + ∆ x pe
∆ x sys = [( u 2 − u 1 ) + P0 ( v 2 − v1 ) − T 0 ( s 2 − s1 ) ] +
V2
∆ X sys = [(U 2 − U 1 ) + P0 (V 2 − V1 ) − T 0 ( S 2 − S 1 ) ] + m
V2
ϕ = x sys
2
− V1
2
+ g ( z 2 − z1 )
2
∆ X sys = [( E 2 − E1 ) + P0 (V 2 − V1 ) − T0 ( S 2 − S1 ) ]
ϕ => exergy of closed system
(no mass flow) per unit mass
2
V
2
− V1
2
2
+ mg ( z 2 − z 1 )
X sys = mx sys = m ϕ
Exergy Transfer
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Advanced Thermo-fluids
Exergy
Exergy can be transferred to or from a
system in three forms (like energy):
n heat
o work
p mass flow
Exergy transfer equation is derived from
energy transfer components:
1 v2
1 v2
Q − W + m(h + V + gz)in − m(h + V + gz) out = (∆U + ∆KE + ∆PE) system
2
2
Exergy Transfer
Exergy transfer
by heat:
X heat
 T0 
= 1 − Q
 T
Exergy transfer by heat is
zero for adiabatic systems
Adiabatic
Q=0
Exergy transfer by work:
X work
W − Wsurr
=
W
for boundary work
for other forms of work
It is possible to get all work
potential (i.e. exergy) from work
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Advanced Thermo-fluids
Exergy
Exergy Transfer
13
Exergy transfer by mass flow ψ:
=> derived from flow energy equation
Flow work w flow = h +
V
2
2
+ gz
Flow exergy Ψ = (h − h0 ) − T0 ( s − s0 ) +
mΨ = ( H − H 0 ) − T0 ( S − S 0 ) + m
V
2
2
∆Ψ = (h2 − h1 ) − T0 ( s2 − s1 ) +
2
+ gz
2
+ mgz
V2 − V1
2
V
2
2
+ g ( z 2 − z1 )
Advanced Thermo-fluids
Exergy
Exergy Balance
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Advanced Thermo-fluids
Exergy
Decrease of exergy principle:
Derived from 1st. and 2nd. Law of thermodynamics
States that exergy of isolated system during a
process always decrease. In the limiting case of
a reversible process, exergy remains the same.
∆X isolated = ( X 2 − X 1 ) isolated ≤ 0
Exergy Balance
Decrease of exergy in isolated
system is due to process
irreversibilities => exergy
destruction
Process irreversibilities also cause
entropy generation => increase of
entropy principle
Exergy destruction and entropy
generation are related
X destroyed = T0 S generated ≥ 0
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Advanced Thermo-fluids
Exergy
Exergy Balance
Exergy change of a system
undergoing a process can be
+ve or -ve, BUT exergy
destruction cannot be negative
> 0
S gen = 0
< 0
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 > 0
X des  = 0
< 0
Irreversib le
Reversible
Impossible
Irreversib le
Reversible
Impossible
General exergy balance
equation:
X in − X out − X destroyed = ∆X system
1424
3
1
424
3
1
424
3
Net exergy transfer
by heat, work and mass
Exergy destruction
Advanced Thermo-fluids
Exergy
Change in exergy
Exergy Balance
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Advanced Thermo-fluids
Exergy
Exergy balance for closed system:
X heat − X work − X destroyed = ∆X system
 T0 
∑ 1 − T Q − {W − P0 (V2 − V1 )}− X destroyed = ∆X system
Exergy balance for open system:
X heat − X work + X mass,in − X mass,out − X destroyed = ∆X system
 T0 
∑1− T Q −{W − P0 (V2 −V1)}+ ∑miψi − ∑meψe − Xdestroyed = ∆Xsystem
Summary
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Advanced Thermo-fluids
Exergy
Exergy => Useful work potential of a system at specified state
Reversible work Wrev: => max useful work obtainable from
reversible process between specified initial and final states
2nd. Law efficiency => a measure of performance of
a device relative to its best possible performance
Exergy of a system
xsys = [(u − u0 ) + P0 (v − v0 ) − T0 ( s − s0 )] +
V
2
2
+ gz
Exergy balance:
 T0 
∑1− T Q −{W − P0 (V2 −V1)}+ ∑miψi − ∑meψe − Xdestroyed = ∆Xsystem
Relation between exergy
destroyed and entropy generated
X destroyed = T0 S generated ≥ 0