Exergy: A Exergy: A measure of Work measure of Work

PotentialPotentialChapter 8Chapter 8

Work Potential of EnergyWork Potential of Energy

When a new energy source is When a new energy source is discovered, the first thing the discovered, the first thing the explorers do is estimate the amount explorers do is estimate the amount of energy contained in the source.of energy contained in the source.

Work Potential:Work Potential: is the amount of is the amount of energy we can extract as useful work. energy we can extract as useful work. The rest of the energy will eventually The rest of the energy will eventually be discarded as waste energy and is be discarded as waste energy and is not worthy of our consideration..not worthy of our consideration..

ExergyExergy

The property that enables us to The property that enables us to determine the useful work determine the useful work potentialpotential of of a given amount of energy at some a given amount of energy at some specified state is specified state is exergyexergy, which is also , which is also called the availability or available called the availability or available energy.energy.

Exergy is a property and is associated Exergy is a property and is associated with the state of the system and the with the state of the system and the environment.environment.

The property exergy is also called The property exergy is also called availability or available energy.availability or available energy.

Dead StateDead State: A system that is in : A system that is in equilibrium with its surroundings equilibrium with its surroundings has zero exergy and is said to be at has zero exergy and is said to be at the date state.the date state.

At the dead state, a system is at the At the dead state, a system is at the temperature and pressure of its temperature and pressure of its environment; it has no kinetic or environment; it has no kinetic or potential energy relative to the potential energy relative to the environment.environment.

Distinction shoud be made between Distinction shoud be made between the the surroundingssurroundings, , immediate immediate surroundingssurroundings and the and the environmentenvironment..

Surrounding: are everything outside Surrounding: are everything outside the system boundaries.the system boundaries.

Immediate surrounding: the portion Immediate surrounding: the portion of the surrounding that is affected of the surrounding that is affected by the process.by the process.

Environment: the region beyond the Environment: the region beyond the immediate surroundings.immediate surroundings.

A system will deliver the maximum A system will deliver the maximum possible work as it undergoes a possible work as it undergoes a reversible process from the specified reversible process from the specified initial state to the state of its initial state to the state of its environment, that is, the dead state.environment, that is, the dead state.

The exergy of heat supplied by The exergy of heat supplied by thermal energy reservoirs is thermal energy reservoirs is equivalent to the work output of a equivalent to the work output of a Carnot heat engine operating between Carnot heat engine operating between the reservoir and the environment.the reservoir and the environment.

Exergy (Work Potential) Associated with Exergy (Work Potential) Associated with Kinetic and Potential EnergyKinetic and Potential Energy

The work potential or exergy of the The work potential or exergy of the kinetic energy of a system is equal to kinetic energy of a system is equal to the kinetic energy itself regardless of the kinetic energy itself regardless of the temperature and pressure of the the temperature and pressure of the environment.environment.

The exergy of the potential energy of a The exergy of the potential energy of a system is equal to the potential energy system is equal to the potential energy itselfitself regardless of the temperature regardless of the temperature and pressure of the environment.and pressure of the environment.

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Example 1: A windmill with 12 m Example 1: A windmill with 12 m diameter rotor as shown in fig. is to diameter rotor as shown in fig. is to be installed at a location where the be installed at a location where the wind is blowing steadily at an wind is blowing steadily at an average velocity of 10m/s. average velocity of 10m/s. Determine the maximum power that Determine the maximum power that can be generated by the windmill.can be generated by the windmill.

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The work done by work-producing The work done by work-producing devices is not always entirely in a devices is not always entirely in a usable form.usable form.

For example, when a gas in a piston-For example, when a gas in a piston-cylinder device expands, part of the cylinder device expands, part of the work done by the gas is used to push work done by the gas is used to push the atmospheric air out of the way of the atmospheric air out of the way of the piston.the piston.

12 VVPW Osurr

The difference between the actual The difference between the actual work W and the surroundings work work W and the surroundings work WWsurrsurr is called useful work W is called useful work Wuu::

The work done WThe work done Wsurr surr by or against the by or against the atmospheric pressure has atmospheric pressure has significance only for systems whose significance only for systems whose volume changes during the process volume changes during the process (i.e., systems that involve moving (i.e., systems that involve moving boundary work.)boundary work.)

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Work done WWork done Wsurrsurr by or against by or against atmospheric pressure has no atmospheric pressure has no significance for cyclic devices and significance for cyclic devices and systems whose boundaries remain systems whose boundaries remain fixed during a process such as rigid fixed during a process such as rigid tanks and steady-flow devices tanks and steady-flow devices (turbines, compressors, nozzles, heat (turbines, compressors, nozzles, heat exchangers, etc.)exchangers, etc.)

Reversible work WReversible work Wrev.rev. is defined as is defined as the maximum amount of useful work the maximum amount of useful work that can be produced as a system that can be produced as a system undergoes a process between the undergoes a process between the specified initial and final states.specified initial and final states.

The useful work output obtained The useful work output obtained when the process between the initial when the process between the initial and final states is executed in a and final states is executed in a totally reversible manner.totally reversible manner.

The difference between the reversible The difference between the reversible work Wwork Wrevrev and the useful work W and the useful work Wuu is is due to the irreversibilities present due to the irreversibilities present during the process and is called during the process and is called irreversibilityirreversibility I. I.

It is equivalent to the exergy It is equivalent to the exergy destroyed and is expressed asdestroyed and is expressed as

Where SWhere Sgengen is the entropy generated is the entropy generated during the process.during the process.

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For a totally reversible process, the useful For a totally reversible process, the useful and reversible work terms are identical and reversible work terms are identical and thus exergy destruction is zero.and thus exergy destruction is zero.

Irreverisbility can be viewed as the Irreverisbility can be viewed as the wasted work potential or the lost wasted work potential or the lost opportunity to do work.opportunity to do work.

The smaller the irreversibility associated The smaller the irreversibility associated with a process, the greater the work that with a process, the greater the work that will be produced.will be produced.

The performance of a system can be The performance of a system can be improved by minimizing the irreversibility improved by minimizing the irreversibility associated with it.associated with it.

Example: A heat engine receives Example: A heat engine receives heat from a source at 1200 K at a heat from a source at 1200 K at a rate of 500 kJ/s and rejects the rate of 500 kJ/s and rejects the waste heat to a medium at 300 K. waste heat to a medium at 300 K. The power output of the heat engine The power output of the heat engine is 180 kW. Determine the reversible is 180 kW. Determine the reversible power and the irreversibility rate for power and the irreversibility rate for this process.this process.

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Example: A 500 kg iron block shown Example: A 500 kg iron block shown in fig. is initially at 200in fig. is initially at 200OOC and is C and is allowed to cool to 27allowed to cool to 27OOC by C by transferring heat to the surrounding transferring heat to the surrounding air at 27air at 27OOC. Determine the reversible C. Determine the reversible work and the irreversibility for this work and the irreversibility for this process.process.

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Second-Law EfficiencySecond-Law Efficiency

The second-law efficiency is a The second-law efficiency is a measure of the performance under measure of the performance under reversible conditions for the same reversible conditions for the same end states and is given byend states and is given by

For Heat engines and the work-For Heat engines and the work-producing devices producing devices

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For refrigerators, heat pumps and For refrigerators, heat pumps and other work-consuming devices. The other work-consuming devices. The second law efficiency is expressed second law efficiency is expressed as: as:

In general, the second law efficiency In general, the second law efficiency is expressed as:is expressed as:

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Example: A dealer advertises that he Example: A dealer advertises that he has just received a shipment of has just received a shipment of electric resistance heaters for electric resistance heaters for residential buildings that have an residential buildings that have an efficiency of 100%, as shown in fig. efficiency of 100%, as shown in fig. Assuming an indoor temperature of Assuming an indoor temperature of 2121OOC and outdoor temperature of C and outdoor temperature of 1010OOC, determine the second law C, determine the second law efficiency of the heatersefficiency of the heaters 7.26

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The exergies of a fixed mass The exergies of a fixed mass (nonflow exergy) and of a flow (nonflow exergy) and of a flow stream are expressed as:stream are expressed as:

Flow exergy:Flow exergy:

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The exergy change of a fixed mass or The exergy change of a fixed mass or fluid stream as it undergoes a fluid stream as it undergoes a process from state 1 to state 2 is process from state 1 to state 2 is given bygiven by

Nonflow exergy or exergy of fixed Nonflow exergy or exergy of fixed massmass

Flow exergyFlow exergy

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Example: A 200m3 rigid tank Example: A 200m3 rigid tank contains compressed air at 1 MPa contains compressed air at 1 MPa and 300K. Determine how much and 300K. Determine how much work can be obtained from this air if work can be obtained from this air if the environment conditions are 100 the environment conditions are 100 kPa and 300 K.kPa and 300 K.

The mass of air in the tank isThe mass of air in the tank is

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Example: Refrigerant 134a is to be Example: Refrigerant 134a is to be compressed from 0.14 MPa and -10OC compressed from 0.14 MPa and -10OC to 0.8 MPa and 50OC steadily by a to 0.8 MPa and 50OC steadily by a compressor. Taking the environment compressor. Taking the environment conditions to be 20OC and 95kPa, conditions to be 20OC and 95kPa, determine the exergy change of the determine the exergy change of the refrigerant during this process and refrigerant during this process and the minimum work input that needs to the minimum work input that needs to be supplied to the compressor per unit be supplied to the compressor per unit mass of the refrigerant.mass of the refrigerant.

Inlet State:Inlet State:

Exit State:Exit State:

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The exergy change of the refrigerant The exergy change of the refrigerant during this compression process is during this compression process is determined asdetermined as

Therefore, the exergy of the Therefore, the exergy of the refrigerant will increase during refrigerant will increase during compression by 37.9kJ/kgcompression by 37.9kJ/kg

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Exergy can be transferred by heat, Exergy can be transferred by heat, work and mass flowwork and mass flow

Exergy transfer accompanied by Exergy transfer accompanied by heat, work and mass transfer are heat, work and mass transfer are given as:given as:

Exergy transfer by heat:Exergy transfer by heat:

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Exergy transfer by work:Exergy transfer by work:

Exergy transfer by mass:Exergy transfer by mass:

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Decrease of Exergy Decrease of Exergy PrinciplePrinciple

The exergy of an isolated system The exergy of an isolated system during a process always decreases during a process always decreases or in the limiting cases of a or in the limiting cases of a reversible process, remains reversible process, remains constant.constant.

This is known as This is known as the decrease of the decrease of exergy principleexergy principle and is expressed and is expressed as:as:

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Exergy DestructionExergy Destruction Irreversibilites always Irreversibilites always generate entropygenerate entropy, ,

and anything that generates entropy and anything that generates entropy always always destroys exergy.destroys exergy.

The exergy destroyed is proportional to The exergy destroyed is proportional to the entropy generated and is expressed asthe entropy generated and is expressed as

Exergy destroyed is a positive quantityExergy destroyed is a positive quantity for any actual process and becomes for any actual process and becomes zero zero for a reversible process.for a reversible process.

Exergy destroyed represents the lost work Exergy destroyed represents the lost work potential.potential.

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Exergy Balance: Closed Exergy Balance: Closed SystemsSystems

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

General form:General form:

Rate form:Rate form:

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systemdestroyedoutin XXXX

Exergy Balance: Control Exergy Balance: Control VolumeVolume

The rate of exergy change within the The rate of exergy change within the control volume during a process is control volume during a process is equal to the rate of net exergy equal to the rate of net exergy transfer through the control volume transfer through the control volume boundary by heat, work and mass boundary by heat, work and mass flow minus the rate of exergy flow minus the rate of exergy destruction within the boundaries of destruction within the boundaries of the control volumethe control volume

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