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7.1
ME 200 –Thermodynamics I
Lecture 34: Exergy Analysis-
Concept
Yong Li
Shanghai Jiao Tong University
Institute of Refrigeration and Cryogenics
800 Dong Chuan Road Shanghai, 200240, P. R. China
Email : liyo@sjtu.edu.cn
Phone: 86-21-34206056; Fax: 86-21-34206056
7.2
Previous energy analysis
All considered the isentropic process as the goal to
strive for.
Maximize adiabatic and isentropic efficiency
This approach is short sighted for three reasons:
1. It ignores processes where heat transfer is
present.(The majority of all practical processes.)
2. It assumes that reversibility can be obtained.
3. It assumes that the exit state of a device can
“float”, i.e., cases where the exit pressure is
fixed, but the exit temperature is allowed to fall
below the temperature of the surroundings.
Not so real!
7.3
Example
potential for use, not conserved
Exergy (Availability) Analysis
7.4
Exergy reference environment and dead state
Exergy reference environment:::Large enough portion of
system (CM1) surroundings such that intensive properties (e.g., T0,
p0) are unaffected by interaction with the system (CM2).
» Simple compressible system
»ΔUe = T0 ΔSe - p0 ΔVe Eq(6.10)
» ΔKE = 0, ΔPE=0
Dead state ::: State of system (CM2) when in thermodynamic
equilibrium with the environment (T0 and p0)
» Still possess energy?
Closed
System
Environment @ To,po
Qi
CM2
CM1
Wi
Wuse
Concepts
7.5
Defining exergy
Systems A B (equilibrium): work
Notes:
» Wc = net useful work of
combined system and
environment (CM1)!
» The goal is to maximize
Wc!
Boundary of the combined
system.
Exergy/Availability ::: Maximum
theoretical work output that could
be done by a system if it were to
come into equilibrium with its
environment!
Exergy- E (J)
Concepts
7.6
Exergy Analysis for Closed Systems
1st law Total Energy for CM1:
Assumptions
» Maximize Wc final state of CM1 is the dead state
» Neglect DKECM1 and DPECM1
» Sole effect is work out Qc = 0
c c cE Q WD
c c cW E U D D
0
7.7
Continue Exergy Analysis for Closed Systems
The changes in energy of the combined
system can be calculated by:
Substitution into the equation for useful
work leads to:
2( )c o CM eE U E UD D
Constant for environment
0 2 0 0( ) ( )c CM o eW E U p V V T S D
c cW E D
Exergy reference environment ΔUe = T0ΔSe - p0 ΔVe
2 0 0( ) ( )c o CM e eE U E T S p VD D D
7.8
Continue Exergy Analysis for Closed Systems
Note:
ΔVe = – ΔVCM2
and ΔSc=c=ΔSCM1 = ΔSCM2 + Δse
ΔSe = ΔSCM1 – ΔSCM2 = ΔSCM1 – (S0– S)CM2
= ΔSCM1 + (S – S0)CM2
Then, substituting ΔVe and ΔSe into the equation for useful
work:
Wc = (E – U0)CM2 + p0(V – V0)CM2
– T0 (S – S0)CM2 – T0ΔSCM1
= – (V0 – V)CM2 = (V – V0)CM2
0 2 0 0( ) ( )c CM o eW E U p V V T S D
7.9
Continue Exergy Analysis for Closed Systems
In order to maximize Wc, assume a reversible process for
CM1 and thus, ΔSCM1 = 0!
In addition, drop the subscript CM2:
Wrev,c,max = E– U0 + p0 (V – V0) – T0 (S – S0)
Definition of closed system exergy (availability):
E = Wrev,c,max
Wc = (E – U0)CM2 + p0(V – V0)CM2– T0 (S – S0)CM2 – T0ΔSCM1
E = E – U0 + p0(V – V0) – T0 (S – S0)
7.10
Continue Exergy Analysis for Closed Systems
In specific terms:
e o o o o oe u p v v T s s
Change in Exergy:
2 1 o 2 1 o 2 1U U p V V T S S2 1E = E -ED
2 / 2e o o o o ou V gz u p v v T s s
2 / 2e o o o o ou u p v v T s s V gz
7.11
Notes for Exergy Analysis
It can be used for both adiabatic and non-adiabatic
processes.
It shows how close a device operating between two
fixed end states is to its optimum performance.
It identifies the system components most responsible
for sub-optimum system performance.
7.12
Notes on exergy
Exergy is a measure of the departure of the state of a system
from that of the environment.
Exergy can be regarded as a property of the system, once
the environment is specified.
Exergy cannot be negative!
Exergy is not conserved but is destroyed by irreversibilities.
Exergy E does not include chemical availability.
Exergy viewed as the maximum theoretical work
Exergy can be regarded as the minimum theoretical work
input required to bring the system from the dead state to the
given state.
7.13
Closed System Exergy Balance Energy balance
Entropy balance
Multiply the entropy balance by the temperature T0 and
subtract the resulting expression from the energy balance
use the change in exergy
change
in exergy
closed system
exergy balance
7.14
Closed System Exergy Balance
Obtained by deduction from the energy and entropy balances
can be used in place of the entropy balance as an
expression of the second law.
The exergy balance can be used to determine the locations,
types, and magnitudes of energy resource waste
7.15
Closed System Exergy Balance
The value of the exergy destruction cannot be negative. It is not
a property.
destruction of
exergy
Exergy is a property
the change in exergy of a system
can be positive, negative, or zero
7.16
Closed System Exergy Rate Balance
For an isolated system, no heat or work interactions with
the surroundings occur
no transfers of exergy
the counterpart of the
increase of entropy
principle regarded as an alternative
statement of the second law
7.17
specific flow
exergy
Flow exergy
7.18
Exergy Rate Balance for Control Volumes
Closed System
Exergy Rate
Balance
specific flow
exergy
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