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DEPARTMENTOF MECHANICAL ENGINERING

AVAILABILITY (EXERGY)

BASIC THERMODYNAMICS

Name: ANKUR DIMRI

Class Roll No.: 18

Faculty teaching: Mr Suraj Chand

Date: 9th

Dec, 2013


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Certificate

This is certificate that, the candidate has completed the course Work of,

SEMINAR

on topic :-AVAILABILITY , in the subject :- Basic thermodynamic, Code

No:-TME304,with satisfactory performance level and as per the

requirement and direction.

Name: ANKUR DIMRI ,S/o Mr : Vinod Kumar Dimri

Class: B.Tech, Mechanical Engineering, Section: A

Class Roll No: 18, Date of submission: 9thDec 2013


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ACKNOWLEDGEMENT :

I would like to express my gratitude and appreciation to all those who gave me the

possibility to complete this report. My sincere thanks to Mr Suraj Chand sir, whose help,

stimulating suggestions and encouragement, helped me to writing this report. I also want to

thank some of my classmate those help me in making this report.


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ABSTRACT

This report was on AVAILABILITY (EXERGY) . The main finding of this report is available

energy, law of degradation of energy , useful work, availability, exergy analysis, dead state,

availability in steady flow, effectiveness, second law efficiencies.

The sources of energy can be divided into two groups namely, high-grade energy and low

grade energy. The conversion of high-grade energy to shaft work is exempt from the

limitations of the second law, while conversion of low grade energy is subjected to them.

The availability of a given system is defined as the maximum useful work (total work pdV

work) that is obtainable in a process in which the system comes to equilibrium with its

surroundings. Availability is thus a composite property depending on the state of the system

and surroundings.

Dead state which is also important in completing our understanding of the property Exergy.

This also deals with the second law efficiencies.


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TABLE OF CONTENTS

Availability Decrease in available energy when the heat is transferred through a finite

temperature difference

Decrease in available energy when the heat is transferred through a finitetemperature difference

Availability in steady flow Reversible work in a non-flow process Irreversibility Exergy (Availability) analysis Dead state Effectiveness


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LIST OF FIGURES

Fig 1: Heat transfer from a constant temperature energy source.

Fig 2: T-S Diagram for a constant temperature energy source.

Fig 3: Changing temperature energy source.

Fig 4: Increase in unavailable energy due to heat transfer through a finite

temperature difference.

Fig 5: Constant Temperature energy source.


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Available Energy:

The sources of energy can be divided into two groups namely, high-grade energy and low

grade energy. The conversion of high-grade energy to shaft work is exempt from the

limitations of the second law, while conversion of low grade energy is subjected to them.

Example:

High grade energy:

1) Mechanical work

2) electrical energy

3) water power

4) wind power

5) kinetic energy of a jet

6) tidal power.

Low grade energy:

1) Heat or thermal energy

2) heat derived from nuclear fission or fusion

3) Heat derived from combustion of fossil fuels

4) Solar energy.

The high-grade energy in the form of mechanical work or electrical energy is obtained from

sources of low-grade energy. The complete conversion of low grade energy, heat in to high-

grade energy, shaft work is impossible. That part of low-grade energy which is available for

conversion is refered to as available energy, while the part which according to the second

law must be rejected is known as unavailable energy.


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Decrease in available energy when the heat is transferred

through a finite temperature difference:

Whenever heat id transferred through a finite temperature difference there is a decrease in

the availability of the energy so transferred. Let us consider a reversible heat engine

operating between T1and Toas shown in the figure.

Fig 1: Heat transfer from a constant temperature energy source.

Consider the simple situation shown in fig1 in which there is an energy source Q in the form

of heat transfer from a very large source and therefore constant temperature reservoir at

temperature T.

We imagine that a cyclic heat engine is available as shown in figure (b) to convert the

maximum fraction of Q requires that the engine be completely reversible, i.e. a Carnot cycle,

and that the lower temperature reservoir be at the lowest temperature possible, often but

not necessarily at the ambient temperature. From the first and second laws for the Carnot

cycle and the usual consideration of all the Qs as positive quantities weFind,


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W rev HE = QQo Q / T = Qo / To

W rev HE = Q {1-( To / T ) }The fraction of Q given by the right side of the equation is the available portion of

the total energy quantity Q.

Consider the situation shown on the T-S Diagram.

The total shaded diagram is Q.

The portion of Q that is below To, the environment temperature, cannot be

converted into work by the heat engine and must instead be thrown away. This

portion is therefore the unavailable portion of the energy Q, and the portion lying

between the two temperatures T and To is the available energy.

Fig 2: T-S Diagram for a constant temperature energy source.


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Let us consider the same situation except that the heat transfer Q is available from a

constant pressure source, for ex, a simple heat exchanger as shown in the figure. The

Carnot cycle must now be replaced by a sequence of such engines, with the result shown inthe figure B the only difference between the first and the second example is that the second

includes an integral, which corresponds toS,

S =(Q rev / T ) = Qo /To

W rev = QTo * S

Note that this S quantity does not include the standard sign convention. It corresponds to

the change of entropy. The equation specifies the available portion of the quantity Q. the

portion unavailable for producing work in this circumstance lies below to.

Thus the unavailable energy is the product of lowest temperature of heat rejection ends the

change of entropy of the system during the process of supplying heat.

Fig 3: Changing temperature energy source.


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Decrease in available energy when the heat is transferredthrough a

finite temperature difference:

Whenever heat id transferred through a finite temperature difference there is a

decrease in the availability of the energy so transferred. let us consider a

reversible heat engine operating between T1 and Toas shown in the figure

Fig 4: Increase in unavailable energy due to heat transfer through a finitetemperature difference

Then we have Q1 = T1 * SQ2 = To *SW = AE = (T1To) S

Let us now assume that q1 is transferred through a finite temperature difference

from the reservoir or source at T1 to the engine absorbing heat at T1 lower than

T1 as shown in the figure.


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Fig 5: Constant Temperature energy source.The availability of Q1 as received by the engine at T1 and to receiving Q1 and

rejecting Q2.

Q1 = T1 S = T 1 S

T1 > T 1, Hence S >S

Q2 = TcS and Q2 = ToS

Since S >S hence Q2 > Q2

And hence W = Q1- Q2 = T1S - ToS

And W = Q1Q2 = T1STo S

Hence W < W since Q2 > Q2

Available energy lost due to irreversible heat transfer through finite temperature

difference between source and working fluid during heat addition process is

given by

W- W = Q2 - Q2 = To(S - S)

Or decrease in AE = To (S - S)


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Thus the decrease in available energy is the product of the lowest feasible

temperature of heat rejection and the additional entropy change in the system

while receiving heat irreversibly compared to the case of reversible heat transferfrom the same source. The greater is the temperature difference (T1T1) the

greater is the heat rejection Q2 and greater will be the unavailable part of the

energy supplied. Energy is said to be degraded each time when it flows through

a finite temperature difference. Thats why the second law is sometimes called

the law of degradation of energy and the energy is said to run down hill.

Availability:

The availability of a given system is defined as the maximum useful work (total workpdV

work) that is obtainable in a process in which the system comes to equilibrium with its

surroundings. Availability is thus a composite property depending on the state of the system

and surroundings.

Let U,S and V be the initial energy, entropy and volume of a system and Uo So,Vo their final

values when the system has come to equilibrium with its environment. The system

exchanges heat only with the environment. The process may be either reversible or

irreversible. The useful work obtained in the process in the form of equation

W


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The availability A of a given system in a given environment is the maximum useful work

obtainable in reversible process.

A = W max = - o .This work is obtained in part from a decrease in the internal energy of the system and in

part from the heat withdrawn from the environment.

Let a system be taken from an equilibrium state 1, in which its availability is A1 to a second

equilibrium state 2 in which its availability is A2. The end state 2 is not in equilibrium with

the environment. The maximum useful work that could be obtained in the process,

W max = A1A2 = (1 - o )(2 - o )

W max = (1 - 2)

Availability in steady flow:

The steady stet steady flow equation is given by,

H1 + (mv12 ) + mgz1 + Q = H2 + (mv22 ) + mgz2 + W

The subscript 1 and 2 refer to the entrance and exit respectively. At the exit let the system

be in equilibrium with the environment at pressure Po and temperature to. Let symbol

without subscripts refers to the entrance condition of the system and changes in KE and PE

are negligible. Then useful work is given by,

W = (H-Ho) + Q.

The greater the value of Q larger will be the useful work. Thus W will be maximum when Q

is a maximum.

Let S and So be the entropies of the systems at the entrance and exit of the

device then,

(S) system = SoS. and (S)surr = - (Q / To)

From the entropy principle ( SoS )(Q - To) > = 0.

Therefore Q


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For entrance and exit condition the useful work is maximum when the heat absorbed is a

maximum i.e when the internal irreversibility is zero.

The maximum work obtainable from a system at the entrance of a device when the pressureand temperature at the exit are those of the environment is called the available of the

system in steady flow and is given by,

A = W max = B- Bo.

The alternative names for availability and for unavailable quantity ToS are Exergy and

Anergy respectively.

Useful Work:

The work done by work producing devices is not always entirely in a useable form. Consider

the piston-cylinder device shown in the following figure,

The work done by the gas expanding in the piston-cylinder device is the boundary work and

can be written as ,

0 0

b, useful 0

( )W P dV P P dV P dV

W P dV


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The actual work done by the gas is ,

The word done on the surroundings is ,

Any useful work delivered by a piston-cylinder device is due to the pressure above the

atmospheric level,

Reversible work in a non-flow process:

In a non-flow process dm1 = dm2 =0

The entropy equation for flow process reduces to

(dW)rev = - d (U1- ToS + (mv12) + mgZ)

Between two equilibrium end states 1 and 2

(W) rev1-2 = U1-U2To(S1-S2) + m( V12-V22)/2 + mg(Z1-Z2)

If the system doesnt possesses any KE and PE

(W) rev1-2 = U1-U2To(S1-S2)

Irreversibility:

The actual work done by a system is always less than the idealized reversible work, and the

difference between the two is called the irreversibility of the process.

I = W maxW

This is also some time referred to as degradation or dissipation. For a non flow process

between the equilibrium states, when the system exchanges heat only with the

environment.

b, useful 0

b, useful 0 2 1( )

W W P dV

W P V V

surr 0 0 2 1( )W P dV P V V

u surr W W W


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I = {(U1-U2)To(S1-S2) }{(U1-U2) + Q} = To (S2-S1)Q

= To (S) system + To (S)surr

= To[ (S)system + (S)surr ] Hence I > 0.

Similarly for the steady flow process I = WmaxW

= To (S2-S1)Q

= To (S) system + To (S)surr

= To[ (S)system + (S)surr ]

Thus same expression for irreversibility applies to both flow and non-flow process. The

quantity To[ (S)system + (S)surr ] represents an increase in unavailable energy or Anergy.

Exergy (Availability) analysis:

This introduces a method that uses the conservation of mass and energy principles together

with the second law of thermodynamics for the design and analysis of thermal systems. It isalso called as availability analysis. The main importance of developing thermal systems that

make effective use of non-renewable energy resources such as oil, natural gas and coal is

apparent. This analysis is suited for the goal of more efficient energy resource use since it

enables the location, types and true magnitude of waste and loss to be determined.

Finally this information can be used to design thermal systems, guide efforts to reduce

sources of inefficiency in existing systems and evaluate system economics.

Energy is conserved in every device. It cant be destroyed. Energy entering with fuel,

electricity, flowing streams of matter and so on can be accounted for the products and by

products. The basis for the Exergy concept is present in the introduction to the second law

of thermodynamics. An opportunity exists for doing work whatever to systems at different

states are brought into communication and finally they come to equilibrium. When


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one of the two systems is a suitably idealized system called an Exergy reference

environment and the other is some system of interest, Exergy is the maximum theoretical

work obtainable as any interact to equilibrium. The definition of Exergy will not be completehowever, until we define the reference environment and show how numerical values for

Exergy can be determined. These tasks are closely related because the numerical value of

Exergy depends on the state of a system of interest as well as the condition of the

environment.

Dead state:

Dead state which is also important in completing our understanding of the property Exergy.

If the state of a fixed quantity of matter, a closed system departs from that of the

environment, an opportunity exists for developing work. However as the system changes

state towards that of the environment new opportunity diminishes ceasing to exist when

the two are in equilibrium with one another. This state is called Dead state. At the dead

state, the fixed quantity of matter under considerations is imagined to be sealed in an

envelope impervious to mass flow at rest relative to the environment and internally

equilibrium at the temperature and pressure of the environment.

At the dead state both the system and environment possesses energy, but the value of

Exergy is zero because there is no possibility of a spontaneous changes within the system or

the environment, nor can there be an interaction between them.

Energy is said to be degraded each time it flows through a finite temperature difference.

That is why the second law of thermodynamics is sometimes called the law of degradation

of energy and energy is said to run downhill.


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Effectiveness:

Effectiveness is defined as the ratio of actual useful work to the maximum useful work. The

useful output of a system is given by the increase of the availability of the surroundings. The

effectiveness of an actual process is always less than unity. Thus effectiveness of a process is

the measure of the extent to which advantage has been taken of an opportunity to obtain

useful work.


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REFERENCES :

1. P.k. Nag,Tata Mcgraw hill,3rdedi 2002.2. Yunus A.cenegal and Michael A.Boles Tata McGraw hill pub.2002


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