1. Availability (or Exergy) Dr
Availability (or Exergy) Dr. Om Prakash Singh Associate Professor, IIT (BHU), Varanasi
Availability of money reduces drastically due to corruption (irreversibility) in the system

2. Introducing Exergy with a Thought Experiment
When you fill an automobile’s fuel tank with gasoline, it is the exergy of the gasoline you seek and for which you pay.
Exergy is not just another aspect of energy. Exergy and energy are related but distinctly different quantities.
These differences are explored with the figure at right, which shows an isolated system consisting initially of a small container of fuel surrounded by air in abundance.

3. Introducing Exergy with a Thought Experiment
Suppose the fuel burns so finally there is a slightly warm mixture of air and the combustion products formed.
Since air is abundantly present, the temperature of the final mixture is nearly the same as the initial air temperature.
The total quantity of energy associated with the system is constant because no energy transfers take place across the boundary of an isolated system and, by the first law of thermodynamics, energy is conserved.

4. Introducing Exergy with a Thought Experiment
The initial fuel-air combination has a much greater potential for use than the final warm mixture.
For instance, the fuel might be used to generate electricity, produce steam, or power a car whereas the final warm mixture is clearly unsuited for such applications.
Actually, during the process shown in the figures the initial potential for use is predominately destroyed owing to the irreversible nature of that process.

5. Introducing Exergy with a Thought Experiment
The fuel present initially also has economic value, but economic value diminishes as fuel is consumed. The final warm mixture has negligible economic value.
Exergy is the property that quantifies the potential for use and it is exergy that has economic value.

6. Conceptualizing Exergy
Consider a body at temperature Ti placed in contact with the atmosphere at temperature T0. If Ti > T0, the body cools spontaneously until it is in thermal equilibrium with the atmosphere.
However, by controlling the cooling, work can be developed as shown.
Instead of the body cooling spontaneously, heat transfer Q passes to a power cycle that develops work Wc. The work is fully available for lifting a weight, developing shaft work, or generating electricity.

7. Conceptualizing Exergy
Since the power cycle undergoes no net change in state, the potential for developing work Wc arises solely because the initial state of the body differs from that of the atmosphere – namely, Ti > T0.
The body eventually achieves thermal equilibrium with the atmosphere. At equilibrium, the body and atmosphere each possess energy, but there is no longer any potential for developing work from the two because no further interaction can occur between them.
Exergy is the maximum theoretical value for the work Wc. Maximum work is realized only when there are no irreversibilities as the body cools to equilibrium with the atmosphere.

8. Conceptualizing Exergy
In spontaneous cooling to T0, no work is obtained and so the initial potential to develop work, exergy, is destroyed.
Work Wc also can be developed when Ti < T0. In that case, the heat transfers shown on the figure reverse direction and work is developed as the body warms to equilibrium with the atmosphere.
Ti < T0
As before, the potential for developing work arises solely because the initial state of the body differs from that of the atmosphere – namely Ti < T0.

9. Defining Exergy
The term environment – refers to a model for the Earth’s atmosphere: a simple compressible system that is large in extent and uniform in pressure, p0, and temperature, T0. The values of p0 and T0 are normally taken as typical ambient values, such as 1 atm and 25oC (77oF).
Exergy is the maximum theoretical work obtainable from an overall system consisting of a system and the environment as the system comes into equilibrium with the environment (passes to the dead state).
The term dead state refers to when a system of interest is at T0 and p0 and at rest relative to the environment.
At the dead state there can be no interaction between system and environment, and thus there is no potential for developing work.

10. Defining Exergy
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.
It is important to realize that exergy does not represent the amount of work that a work-producing device will actually deliver upon installation.
Rather, it represents the upper limit on the amount of work a device can deliver without violating any thermodynamic laws.
There will always be a difference, large or small, between exergy and the actual work delivered by a device. This difference represents the room engineers have for improvement.

11. Why Exergy Analysis?
Exergy analysis contributes to the goal of making more effective use of nonrenewable energy resources: natural gas, coal, and oil, by determining the locations, types, and true magnitudes of waste and loss in systems fueled by such resources.
Exergy analysis is also relevant for designing more effective thermal systems of all types, guiding efforts to reduce inefficiencies in such systems, and evaluating system economics.

12. Exergy (Work Potential) Associated with Kinetic and Potential Energy
Kinetic energy is a form of mechanical energy, and thus it can be converted to work entirely.
Therefore, 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. That is,
Exergy of kinetic energy:
𝑥𝑘𝑒= 1 2 𝑚𝑉2

13. Exergy (Work Potential) Associated with Kinetic and Potential Energy
Potential energy is also a form of mechanical energy, and thus it can be converted to work entirely.
Therefore, 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
Exergy of potential energy:
𝑥𝑝𝑒=𝑚𝑔ℎ
where g is the gravitational acceleration and z is the elevation of the system relative to a reference level in the environment.
Therefore, the exergies of kinetic and potential energies are equal to themselves, and they are entirely available for work.
However, the internal energy u and enthalpy h of a system are not entirely available for work

14. Surroundings work 𝑊𝑠𝑢𝑟𝑟=𝑃0(𝑉2−𝑉1)
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 This work, which cannot be recovered and utilized for any useful purpose, is equal to the atmospheric pressure P0 times the volume change of the system,
As a closed system expands, some
work needs to be done to push the
atmospheric air out of the way (Wsurr)
𝑊𝑠𝑢𝑟𝑟=𝑃0(𝑉2−𝑉1)
When a system is expanding and doing work, part of the work done is used to overcome the atmospheric pressure, and thus Wsurr represents a loss.
When a system is compressed, however, the atmospheric pressure helps the compression process, and thus Wsurr represents a gain.

15. Reversible work
Reversible work Wrev is defined as 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.
This is the useful work output (or input) obtained (or expended) when the process between the initial and final states is executed in a totally reversible manner.
When the final state is the dead state, the reversible work equals exergy.
For processes that require work, reversible work represents the minimum amount of work necessary to carry out that process.

16. Irreversibility (or Exergy destroyed)
Any difference between the reversible work Wrev and the useful work Wuseful is due to the irreversibilities present during the process, and this difference is called irreversibility, I
𝐼=𝑊𝑟𝑒𝑣,𝑜𝑢𝑡−𝑊𝑢𝑠𝑒𝑓𝑢𝑙,𝑜𝑢𝑡
𝐼=𝑊𝑟𝑒𝑣,𝑖𝑛−𝑊𝑢𝑠𝑒𝑓𝑢𝑙,𝑖𝑛
For a totally reversible process, the actual and reversible work terms are identical, and thus the irreversibility is zero.
This is expected since totally reversible processes generate no entropy.
Irreversibility is a positive quantity for all actual (irreversible) processes since Wrev  Wuseful for work producing devices and Wrev  Wuseful for work-consuming devices.
Irreversibility can be viewed as the wasted work potential or the lost opportunity to do work. It represents the energy that could have been converted to work but was not.

17. Problem The Rate of Irreversibility of a Heat Engine
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
Answers: 375 kW, 195 kW

18. Solution → 𝑊 𝑟𝑒𝑣=𝜂𝑡ℎ,𝑟𝑒𝑣 ×𝑄𝑖𝑛
The reversible power for this process is the amount of power that a reversible heat engine, such as a Carnot heat engine, would produce when operating between the same temperature limits, and is determined to be:
𝜂𝑡ℎ,𝑟𝑒𝑣= 𝑊 𝑟𝑒𝑣 𝑄𝑖𝑛
→ 𝑊 𝑟𝑒𝑣=𝜂𝑡ℎ,𝑟𝑒𝑣 ×𝑄𝑖𝑛
= 1− 𝑇𝑠𝑖𝑛𝑘 𝑇𝑠𝑜𝑢𝑟𝑐𝑒 𝑄𝑖𝑛
= 1− 𝑘𝑊 =375 𝑘𝑊
This is the maximum power that can be produced by a heat engine operating between the specified temperature limits and receiving heat at the specified rate. This would also represent the available power if 300 K were the lowest temperature available for heat rejection.

19. Solution…
The irreversibility rate is the difference between the reversible power (maximum power that could have been produced) and the useful power output:
𝐼=375−180=195 𝑘𝑤
Note:
195 kW of power potential is wasted during this process as a result of irreversibilities.
Also, the 500 – 375 = 125 kW of heat rejected to the sink is not available for converting to work and thus is not part of the irreversibility.

20. Exergy transfer by heat
Heat is a form of disorganized energy, and thus only a portion of it can be converted to work, which is a form of organized energy (the second law). We can always produce work from heat at a temperature above the environment temperature by transferring it to a heat engine that rejects the waste heat to the environment. Therefore, heat transfer is always accompanied by exergy transfer. Heat transfer Q at a location at thermodynamic temperature T is always accompanied by exergy transfer Xℎ𝑒𝑎𝑡 in the amount of
𝑋ℎ𝑒𝑎𝑡= 1− 𝑇0 𝑇 𝑄
When the temperature T at the location where heat transfer is taking place is not constant, the exergy transfer accompanying heat transfer is determined by integration to be
𝑋ℎ𝑒𝑎𝑡= 1− 𝑇0 𝑇 𝛿𝑄

21. Thermoeconomics
The term thermoeconomics is employed for methodologies that combine exergy analysis and other aspects of engineering thermodynamics with engineering economics for:
Optimization studies during design of new thermal systems, and
Process improvements of existing thermal systems.

22. Exergy Costing of Heat Loss
An exergy loss accompanying heat transfer not only has thermodynamic value but also economic value. Consider again the system at the right where fuel is consumed to provide heating.
The rate of exergy loss accompanying heat loss at the rate Ql is ∙

23. Exergy Costing of Heat Loss
Since the source of the exergy lost is the exergy entering with the fuel, the economic value of the loss can be accounted for in terms of the unit cost of the fuel based on exergy, cF (in Rs per kW∙h of exergy, for example), as
Cost rate of heat loss
Q1 at temperature T1 ∙
= cF(1 – T0/T1)Q1
Accordingly, the cost of a heat loss is greater at higher temperatures than at lower temperatures. This outcome can be invoked to guide decisions about whether or not spending money on insulation to reduce heat loss is cost-effective.

24. Exergy of a Fixed Mass: Nonflow (or Closed System) Exergy
Using first law of thermodynamics
−𝛿𝑄=𝑑𝑈+𝛿𝑊, 𝛿𝑊=𝑃𝑑𝑉
−𝛿𝑄 is heat taken away from the system. The pressure P in the P dV expression is the absolute pressure, which is measured from absolute zero. Any useful work delivered by a piston–cylinder device is due to the pressure above the atmospheric level.
Therefore,
The exergy of a specified mass at a
specified state is the useful work that
can be produced as the mass
undergoes a reversible process to the
state of the environment.
𝛿𝑊=𝑃𝑑𝑉= 𝑃−𝑃0 𝑑𝑉+𝑃0𝑑𝑉
𝛿𝑊=𝛿𝑊𝑏,𝑢𝑠𝑒𝑓𝑢𝑙+𝑃0𝑑𝑉

25. Exergy of a Fixed Mass: Nonflow (or Closed System) Exergy…
A reversible process cannot involve any heat transfer through a finite temperature difference, and thus any heat transfer between the system at temperature T and its surroundings at T0 must occur through a reversible heat engine.
Noting that dS = dQ/T for a reversible process, and the thermal efficiency of a reversible heat engine operating between the temperatures of T and T0 is th = 1 - T0/T, the differential work produced by the engine as a result of this heat transfer is
𝛿𝑊𝐻𝐸= 1− 𝑇0 𝑇 𝛿𝑄=𝛿𝑄−𝑇0 𝛿𝑄 𝑇 =𝛿𝑄−(𝑇0𝑑𝑆)
𝛿𝑄=𝛿𝑊𝐻𝐸−𝑇0𝑑𝑆
Substituting the W and Q expressions above into the fist law energy balance relation gives, after rearranging,
𝑊𝑡𝑜𝑡𝑎𝑙, 𝑢𝑠𝑒𝑓𝑢𝑙=𝛿𝑊𝐻𝐸+𝛿𝑊𝑏,𝑢𝑠𝑒𝑓𝑢𝑙=−𝑑𝑈−𝑃0𝑑𝑉+𝑇𝑑𝑠

26. Exergy of a Fixed Mass: Nonflow (or Closed System) Exergy…
𝑊𝑡𝑜𝑡𝑎𝑙 𝑢𝑠𝑒𝑓𝑢𝑙=𝛿𝑊𝐻𝐸+𝛿𝑊𝑏,𝑢𝑠𝑒𝑓𝑢𝑙=−𝑑𝑈−𝑃0𝑑𝑉+𝑇𝑑𝑠
Integrating from the given state (no subscript) to the dead state (0 subscript) we obtain
𝑊𝑡𝑜𝑡𝑎𝑙 𝑢𝑠𝑒𝑓𝑢𝑙= 𝑈−𝑈0 +𝑃0 𝑉−𝑉0 −𝑇0 𝑆−𝑆0 =Exergy
where Wtotal useful is the total useful work delivered as the system undergoes a reversible process from the given state to the dead state, which is exergy by definition.
A closed system, in general, may possess kinetic and potential energies, and the total energy of a closed system is equal to the sum of its internal, kinetic, and potential energies. Noting that kinetic and potential energies themselves are forms of exergy, the exergy of a closed system of mass m is
𝑊𝑡𝑜𝑡𝑎𝑙 𝑢𝑠𝑒𝑓𝑢𝑙= 𝑈−𝑈0 +𝑃0 𝑉−𝑉0 −𝑇0 𝑆−𝑆 𝑚𝑉2+𝑚𝑔𝑧

27. Exergy of a Flow Stream: Flow (or Stream) Exergy
The flow work is essentially the boundary work done by a fluid on the fluid downstream, and thus the exergy associated with flow work is equivalent to the exergy associated with the boundary work, which is the boundary work in excess of the work done against the atmospheric air at P0 to displace it by a volume v
𝑥𝑓𝑙𝑜𝑤=𝑃𝑣−𝑃0𝑣= 𝑃−𝑃0 𝑣=− 𝑃 𝑝0 𝑣𝑑𝑃
Therefore, the exergy associated with flow energy is obtained by replacing the pressure P in the flow work relation by the pressure in excess of the atmospheric pressure, P - P0.
Then the exergy of a flow stream is determined by simply adding the flow exergy relation above to the exergy relation for a nonflowing fluid,
𝑥𝑓𝑙𝑜𝑤𝑖𝑛𝑔 𝑓𝑙𝑢𝑖𝑑=𝑥𝑛𝑜𝑛𝑓𝑙𝑜𝑤𝑖𝑛𝑔 𝑓𝑙𝑢𝑖𝑑+𝑥𝑓𝑙𝑜𝑤
𝑥𝑓𝑙𝑜𝑤𝑖𝑛𝑔 𝑓𝑙𝑢𝑖𝑑= 𝑈−𝑈0 +𝑃0 𝑉−𝑉0 −𝑇0 𝑆−𝑆 𝑚𝑉2+𝑚𝑔𝑧+ 𝑃−𝑃0 𝑣
𝑥𝑓𝑙𝑜𝑤𝑖𝑛𝑔 𝑓𝑙𝑢𝑖𝑑=(ℎ2−ℎ1)−𝑇0 𝑆−𝑆 𝑚𝑉2+𝑚𝑔𝑧

28. Exergy Transfer by Work, W
Exergy is the useful work potential, and the exergy transfer by work can
simply be expressed as
where Wsurr = P0(V2 - V1), P0 is atmospheric pressure, and V1 and V2 are the initial and final volumes of the system.

29. Exergy Destruction
Irreversibilities such as friction, mixing, chemical reactions, heat transfer through a finite temperature difference, unrestrained expansion, non-quasiequilibrium compression or expansion always generate entropy, and anything that generates entropy always destroys exergy.
The exergy destroyed is proportional to the entropy generated, and is expressed as
Note that 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.

30. Exergy Destruction
The decrease of exergy principle can be summarized as follows:
This relation serves as an alternative criterion to determine whether a process is reversible, irreversible, or impossible.

31. EXERGY BALANCE: CLOSED SYSTEMS

32. Problem
A mass of 8 kg of helium undergoes a process from an initial state of 3 m3/kg and 15°C to a final state of 0.5 m3/kg and 80°C. Assuming the surroundings to be at 25°C and 100 kPa, determine the increase in the useful work potential of the helium during this process (or increase in exergy)
The gas constant of helium is R = kJ/kg.K. The constant volume specific heat of helium is cv = kJ/kg.K

33. Solution From the ideal-gas entropy change relation,
The increase in the useful potential of helium during this process is simply the increase in exergy,

34. Problem
An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 3 kg of argon gas at 300 kPa and 70°C, and the other side is evacuated. The partition is now removed, and the gas fills the entire tank. Assuming the surroundings to be at 25°C, determine the exergy destroyed during this process.
The gas constant of argon is R = kJ/kg.K

35. Solution
Taking the entire rigid tank as the system, the energy balance can be expressed as
since u = u(T) for an ideal gas.
The exergy destruction (or irreversibility) associated with this process can be determined from its definition Xdestroyed = T0Sgen where the entropy generation is determined from an entropy balance on the entire tank, which is an insulated closed system,

37. End