Exergy: A measure of Work Potential

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Exergy A measure of Work Potential

• Chapter 8

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Work Potential of Energy

• When a new energy source is discovered, the first
  thing the explorers do is estimate the amount of
  energy contained in the source.
• Work Potential is the amount of energy we can
  extract as useful work. The rest of the energy
  will eventually be discarded as waste energy and
  is not worthy of our consideration..

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Exergy

• The property that enables us to determine the
  useful work potential of a given amount of energy
  at some specified state is exergy, which is also
  called the availability or available energy.
• Exergy is a property and is associated with the
  state of the system and the environment.
• The property exergy is also called availability
  or available energy.

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• Dead State A system that is in equilibrium with
  its surroundings has zero exergy and is said to
  be at the date state.
• At the dead state, a system is at the temperature
  and pressure of its environment it has no
  kinetic or potential energy relative to the
  environment.

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• Distinction shoud be made between the
  surroundings, immediate surroundings and the
  environment.
• Surrounding are everything outside the system
  boundaries.
• Immediate surrounding the portion of the
  surrounding that is affected by the process.
• Environment the region beyond the immediate
  surroundings.

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

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• Exergy (Work Potential) Associated with Kinetic
  and Potential Energy
• The work potential or exergy of the kinetic
  energy of a system is equal to the kinetic energy
  itself regardless of the temperature and pressure
  of the environment.
• The exergy of the potential energy of a system is
  equal to the potential energy itself regardless
  of the temperature and pressure of the
  environment.

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

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• The work done by work-producing devices is not
  always entirely in a usable form.
• For example, when a gas in a piston-cylinder
  device expands, part of the work done by the gas
  is used to push the atmospheric air out of the
  way of the piston.

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• The difference between the actual work W and the
  surroundings work Wsurr is called useful work Wu
• The work done Wsurr by or against the atmospheric
  pressure has significance only for systems whose
  volume changes during the process (i.e., systems
  that involve moving boundary work.)

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

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• Reversible work Wrev. is defined as the maximum
  amount of useful work that can be produced as a
  system undergoes a process between the specified
  initial and final states.
• The useful work output obtained when the process
  between the initial and final states is executed
  in a totally reversible manner.

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• The difference between the reversible work Wrev
  and the useful work Wu is due to the
  irreversibilities present during the process and
  is called irreversibility I.
• It is equivalent to the exergy destroyed and is
  expressed as
• Where Sgen is the entropy generated during the
  process.

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• For a totally reversible process, the useful and
  reversible work terms are identical and thus
  exergy destruction is zero.
• Irreverisbility can be viewed as the wasted work
  potential or the lost opportunity to do work.
• The smaller the irreversibility associated with a
  process, the greater the work that will be
  produced.
• The performance of a system can be improved by
  minimizing the irreversibility associated with it.

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

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

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• Second-Law Efficiency
• The second-law efficiency is a measure of the
  performance under reversible conditions for the
  same end states and is given by
• For Heat engines and the work-producing devices

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• For refrigerators, heat pumps and other
  work-consuming devices. The second law efficiency
  is expressed as
• In general, the second law efficiency is
  expressed as

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• Example A dealer advertises that he has just
  received a shipment of electric resistance
  heaters for residential buildings that have an
  efficiency of 100, as shown in fig. Assuming an
  indoor temperature of 21OC and outdoor
  temperature of 10OC, determine the second law
  efficiency of the heaters

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

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

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• Example A 200m3 rigid tank contains compressed
  air at 1 MPa and 300K. Determine how much work
  can be obtained from this air if the environment
  conditions are 100 kPa and 300 K.
• The mass of air in the tank is
• The exergy content of the compressed air

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

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• The exergy change of the refrigerant during this
  compression process is determined as
• Therefore, the exergy of the refrigerant will
  increase during compression by 37.9kJ/kg

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• Exergy can be transferred by heat, work and mass
  flow
• Exergy transfer accompanied by heat, work and
  mass transfer are given as
• Exergy transfer by heat

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• Exergy transfer by work
• Exergy transfer by mass

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Decrease of Exergy Principle

• The exergy of an isolated system during a process
  always decreases or in the limiting cases of a
  reversible process, remains constant.
• This is known as the decrease of exergy
  principle and is expressed as

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Exergy Destruction

• Irreversibilites always generate entropy, and
  anything that generates entropy always destroys
  exergy.
• The exergy destroyed is proportional to the
  entropy generated and is expressed as
• Exergy destroyed is a positive quantity for any
  actual process and becomes zero for a reversible
  process.
• Exergy destroyed represents the lost work
  potential.

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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.
• General form
• Rate form

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Exergy Balance Control Volume

• 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
• or