Thermodynamics: An Engineering Approach, 6th Edition

Yunus A. Cengel, Michael A. Boles

McGraw-Hill, 2008

Chapter 8
EXERGY: A MEASURE OF
WORK POTENTIAL

Objectives
Examine the performance of engineering devices in light
of the second law of thermodynamics.
Define exergy, which is the maximum useful work that
could be obtained from the system at a given state in a
specified environment.
Define reversible work, which is the maximum useful
work that can be obtained as a system undergoes a
process between two specified states.
Define the exergy destruction, which is the wasted work
potential during a process as a result of irreversibilities.
Define the second-law efficiency.
Develop the exergy balance relation.
Apply exergy balance to closed systems and control
volumes.

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EXERGY: WORK POTENTIAL OF ENERGY
The useful work potential of a given amount of energy at some
specified state is called exergy, which is also called the availability or
available energy.
A system is said to be in the dead state when it is in thermodynamic
equilibrium with the environment it is in.

At the dead state, the useful

work potential (exergy) of a
system is zero.

A system that is in equilibrium with its

environment is said to be at the dead
state.

A system delivers the maximum possible work as it undergoes a reversible

process from the specified initial state to the state of its environment, that is,
the dead state.
This represents the useful work potential of the system at the specified state
and is called exergy.
Exergy represents the upper limit on the amount of work a device can deliver
without violating any thermodynamic laws.

The immediate surroundings of a hot The atmosphere contains a

potato are simply the temperature tremendous amount of energy, but
gradient zone of the air next to the no exergy.
potato.

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Exergy (Work Potential) Associated with Kinetic and
Potential Energy
Exergy of kinetic energy:

Exergy of potential energy:

The work
potential or
exergy of
potential energy
The exergies of is equal to the
kinetic and potential energy
potential energies itself.
are equal to
themselves, and
they are entirely
Unavailable energy is
available for work.
the portion of energy
that cannot be
converted to work by
even a reversible heat
engine.

Example 8-1

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Solution

REVERSIBLE WORK AND IRREVERSIBILITY

Reversible work Wrev: The maximum amount of
useful work that can be produced (or the
minimum work that needs to be supplied) as a
system undergoes a process between the
specified initial and final states.
As a closed
system expands,
some work needs
to be done to push
the atmospheric
air out of the way
(Wsurr).

The difference between

reversible work and
actual useful work is the
irreversibility.

For constant-volume
systems, the total
actual and useful
works are identical
(Wu = W).

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Example 8-3

Solution

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 Solve and Study Example 8-4

SECOND-LAW EFFICIENCY, II

Two heat engines that have

Second-law efficiency is a the same thermal efficiency,
measure of the performance of a but different maximum
device relative to its performance thermal efficiencies.
under reversible conditions.

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 General definition of
exergy efficiency

The second-law efficiency of

naturally occurring processes is
zero if none of the work potential is
recovered.
Second-law efficiency of all
reversible devices is 100%.

Example 8-6

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Solution

EXERGY CHANGE OF A SYSTEM

Exergy of a Fixed Mass: Nonflow
(or Closed System) Exergy

The exergy of a specified mass

at a specified state is the useful
work that can be produced as
the mass undergoes a
Exergy of a closed system reversible process to the state
of the environment.

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 Closed system
exergy per unit
mass

Exergy
change of
a closed
system

When the properties of a system are

not uniform, the exergy of the system is

The exergy of a cold

medium is also a
positive quantity since
work can be produced
by transferring heat to it.

Exergy of a Flow Stream: Flow (or Stream) Exergy

Exergy of flow energy

Flow
exergy
Exergy change of flow

The exergy
associated with
flow energy is the
useful work that
would be
delivered by an
imaginary piston
in the flow
section.

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 The energy and
exergy contents of
(a) a fixed mass
(b) a fluid stream.

Example 8-7

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Solution

Solution

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Example 8-8

Solution

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EXERGY TRANSFER BY
HEAT, WORK, AND MASS
Exergy by Heat Transfer, Q
Exergy
transfer by
heat
When
temperature is
not constant

The transfer and

destruction of exergy
during a heat transfer
process through a finite
temperature difference.

The Carnot efficiency c=1T0 /T represents the

fraction of the energy transferred from a heat source
at temperature T that can be converted to work in an
environment at temperature T0.

Exergy Transfer by Work, W

Exergy Transfer by Mass, m

There is no useful work
transfer associated with
boundary work when the
pressure of the system is
maintained constant at
atmospheric pressure.

Mass contains energy,

entropy, and exergy, and
thus mass flow into or out of
a system is accompanied
by energy, entropy, and
exergy transfer.

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THE DECREASE OF EXERGY PRINCIPLE
AND EXERGY DESTRUCTION

The isolated system

considered in the
development of the
decrease of exergy
principle.
The exergy of an isolated system during a process always decreases or, in
the limiting case of a reversible process, remains constant. In other words, it
never increases and exergy is destroyed during an actual process. This is
known as the decrease of exergy principle.

Exergy Destruction

Exergy destroyed is a positive quantity for

any actual process and becomes zero for a
reversible process.
Exergy destroyed represents the lost work
potential and is also called the
irreversibility or lost work.
Can the exergy change The exergy change of a system
of a system during a can be negative, but the exergy
process be negative? destruction cannot.

Consider heat transfer from a system to its surroundings. How do you

compare exergy changes of the system and the surroundings?

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 EXERGY BALANCE: CLOSED SYSTEMS
The exergy change
of a system during
a process is equal
to the difference
between the net
exergy transfer
through the system
boundary and the
exergy destroyed
within the system
boundaries as a
result of
irreversibilities.

Mechanisms
of exergy
transfer.

The heat transfer to

a system and work
done by the system
are taken to be
positive quantities.

Qk is the heat transfer through the boundary at temperature Tk at location k.

Exergy
destroyed
Exergy outside system
balance for boundaries can
a closed be accounted for
system by writing an
when heat exergy balance
transfer is on the extended
to the system that
system and includes the
the work is system and its
from the immediate
system. surroundings.

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EXAMPLES
Exergy balance for heat conduction

Exergy balance for expansion of steam

The exergy balance applied on the extended
system (system + immediate surroundings)
whose boundary is at the environment
temperature of T0 gives

Exergy balance for an air tank

20C 54C

20.6 kJ

= 1 kJ 1 kJ

20C Wpw,in=U=20.6 kJ
Wrev,in = 1 kJ
19.6 kJ
1 kg
20C
140 kPa
20C
The same effect on the insulated
tank system can be accomplished by
a reversible heat pump that
consumes only 1 kJ of work.

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Example 8-10

Solution

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Example 8-11

Solution

18
Solution

Solution

19
Solution

Solution

20
Solution

Example 8-12

21
Solution

Solution

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Example 8-13

Solution

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Solution

Solution

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EXERGY BALANCE: CONTROL VOLUMES

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.
Exergy is transferred into or out
of a control volume by mass as
well as heat and work transfer.

Exergy Balance for Steady-Flow Systems

Most control volumes encountered in practice such as turbines, compressors, nozzles,
diffusers, heat exchangers, pipes, and ducts operate steadily, and thus they experience
no changes in their mass, energy, entropy, and exergy contents as well as their volumes.
Therefore, dVCV/dt = 0 and dXCV/dt = 0 for such systems.

The exergy transfer to a

steady-flow system is
equal to the exergy
transfer from it plus the
exergy destruction
within the system.

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 Reversible Work, Wrev
The exergy balance relations presented above can be used to
determine the reversible work Wrev by setting the exergy destroyed
equal to zero. The work W in that case becomes the reversible work.

The exergy destroyed is zero only for a reversible process, and

reversible work represents the maximum work output for work-
producing devices such as turbines and the minimum work input for
work-consuming devices such as compressors.

Second-Law Efficiency of Steady-Flow Devices, II

The second-law efficiency of various steady-flow devices can be determined from
its general definition, II = (Exergy recovered)/(Exergy supplied). When the changes
in kinetic and potential energies are negligible and the devices are adiabatic:

Turbine

Compressor

Heat
exchanger

Mixing
chamber A heat exchanger with two unmixed
fluid streams.

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 EXAMPLES
Exergy analysis of a steam turbine

Exergy balance for a charging process

Example 8-15

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Solution

Solution

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Solution

Example 8-17

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Solution

Solution

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 Summary
Exergy: Work potential of energy
Exergy (work potential) associated with kinetic and potential energy
Reversible work and irreversibility
Second-law efficiency
Exergy change of a system
Exergy of a fixed mass: Nonflow (or closed system) exergy
Exergy of a flow stream: Flow (or stream) exergy
Exergy transfer by heat, work, and mass
The decrease of exergy principle and exergy destruction
Exergy balance: Closed systems
Exergy balance: Control volumes
Exergy balance for steady-flow systems
Reversible work
Second-law efficiency of steady-flow devices

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