tsatsaronis2007

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Energy 32 (2007) 249–253

Definitions and nomenclature in exergy analysis and exergoeconomics

George Tsatsaronis

Technische Universitat Berlin, Institute for Energy Engineering, Marchstr. 18, 10587 Berlin, Germany

Abstract

This paper presents the definitions of some terms used in exergy analysis and exergy costing, discusses options for the symbols to be

used for exergy and some exergoeconomic variables, and presents the nomenclature for the remaining terms.

r 2006 Published by Elsevier Ltd.

Keywords: Total energy; Exergy; Physical; Chemical; Kinetic; Potential; Thermal; Mechanical; Reactive and nonreactive exergy; Symbols for exergy;

Exergoeconomics

1. Introduction

The number of publications dealing with exergy analysis

and exergoeconomics has been increasing continuously in

the past years. The symbols used in these publications and

in textbooks (see Table 1) cover a rather large spectrum of

the Latin and Greek alphabets. There is an urgent need for

some consensus on the symbols to be used in the future.

This will facilitate both the communication among practi-

tioners and the further development of the disciplines of

exergy analysis and exergoeconomics. The symbols used in

Sections 2 and 3 are suggested for publications in journals

and conference proceedings. In Section 4, some alternatives

are presented for use in textbooks.

2. Exergy

Exergy of a thermodynamic system is the maximum

theoretical useful work (shaft work or electrical work)

obtainable as the system is brought into complete thermo-dynamic equilibrium with the thermodynamic environment

while the system interacts with this environment only. The

total exergy of a system consists of:

physical exergy (due to the deviation of the temperature

and pressure of the system from those of the environ-

ment),

chemical exergy (due to the deviation of the chemical

composition of the system from that of the environ-

ment),

kinetic exergy (due to the system velocity measured

relative to the environment), and

potential exergy (due to the system height measured

relative to the environment).

The physical exergy consists of:

mechanical exergy (associated with the system pressure),

and

thermal exergy (associated with the system tempera-

ture).

For a given thermodynamic state at a temperature T and

pressure p, the thermal exergy should be calculated along

the isobaric line at p (from state [T , p] to state [T 0, p]),

whereas the mechanical exergy should be calculated alongthe isothermal line at T 0 (from state [T 0, p] to state [T 0, p0]).

The chemical exergy of a system can be split into:

reactive exergy (associated in its calculation with

chemical reactions), and

nonreactive exergy (associated in its calculation with

nonreactive processes such as expansion, compression,

mixing and separation).

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An option for splitting the chemical exergy into reactive

and nonreactive exergy is presented in Ref. [1]. Thesplitting of physical and chemical exergy into their

components might be useful for defining more accurate

exergetic efficiencies and for improving the costing

approach.

The symbol for exergy has been the subject of a lot of

controversy in the past. The exergy symbol should be easy

to use and recognize. We should not use two letters for this

symbol (e.g., Ex) because (a) this is not common for

important variables in thermodynamics, and (b) there is a

potential for missinterpretations when this symbol is used

with superscripts and subscripts.

With exergy we mean the potential to generate work

regardless of the cases, systems, or exergy components

being actually considered. Therefore, it is logical to use

only one and the same symbol for all cases, systems and

exergy components, as well as for exergy destruction and

exergy loss. The fact that in energy analysis we use

traditionally different symbols for total energy, internal

energy and enthalpy should not lead us to use different

symbols for the physical exergy of a system and the

physical exergy of a material stream simply because the

equations used to calculate each of these physical exergies

are different. If we would follow this way, we should use

different symbols also for the exergy associated with both

heat transfer and work, and we would soon arrive at a

completely unacceptable situation regarding symbols for

exergy.If we now agree that a one-letter symbol should be used

in all cases in conjunction with exergy, the question arises

what letter should this be. The easiest and more natural

approach for publications in journals and conference

proceedings would be to use the letter E for exergy, as it

has been used in Germany and some other countries from

the very moment the exergy concept was introduced.

It should be taken into account that the vast majority of

publications involving exergy refer usually to control

volumes at steady state. In these applications the relevant

energy terms are only enthalpy, heat and work. Therefore,

there is no danger of confusing total energy, which is also

denoted by E , with any form of exergy. In cases where both

exergy and total energy appear in the same publication,

a slightly different font can be employed for total

energy, unless energy is mainly used and exergy is

mentioned only in passing. In the last case, a slightly

different symbol (for example, the roman font) can be used

for exergy. This should not result in confusion because it is

always clear from the context whether exergy or total

energy is meant.

Thus, for publications in journals and conference

proceedings, where a simple approach is very important,

the following equations should be employed in exergy

analysis. Alternatives are presented in Section 4.

ARTICLE IN PRESS

Nomenclature

c average cost per exergy unit

C cost associated with an exergy stream

e specific exergy

E exergyE sys total exergy of a system

E PH sys physical exergy of a system

E c exergetic cost

h specific enthalpy

H enthalpy

k c unit of exergetic cost

p pressure

s specific entropy

S entropy

T temperature

u specific internal energy

U internal energy

v specific volumeV volume

~v velocity relative to the environment

z height relative to the environment

Z cost associated with equipment

Greek letters

e exergetic efficiency

Z energetic (or thermal) efficiency

Zs isentropic efficiency

k inverse of the exergetic efficiency

l marginal cost (optional)

Subscripts

D exergy destruction

F fuel exergy

L exergy loss

P product exergy

sys system

0 conditions of the thermodynamic environment

Superscripts

c exergetic cost

CH chemical exergy

KN kinetic exergy or energyM mechanical exergy

N nonreactive exergy

PH physical exergy

PT potential exergy or energy

R reactive exergy

T thermal exergy

G. Tsatsaronis / Energy 32 (2007) 249–253250



Total exergy of a system:

E sys ¼ E PH sys þ E KN þ E PT þ E CH , (1)

esys ¼ ePH sys þ eKN þ ePT þ eCH . (1a)

To distinguish the physical exergy and the total exergy of

a system from the same exergies associated with a stream of

matter, a subscript ‘‘sys’’ is used here for the exergies of the

system.

Physical exergy of a system:

E PH sys ¼ ðU U 0Þ þ p0ðV V 0Þ T 0ðS S 0Þ, (2)

ePH sys ¼ ðu u0Þ þ p0ðv v0Þ T 0ðs s0Þ. (2a)

Mechanical and thermal exergy of a system:

E PH sys ¼ E T

sys þ E M sys, (3)

ePH sys ¼ eT

sys þ eM sys. (3a)

Reactive and nonreactive exergy:

E CH ¼ E R þ E N , (4)

eCH ¼ eR þ eN . (4a)

In applications of the exergy concept, the subscript ‘‘sys’’

will be replaced by the abbreviation used for the

component being considered (e.g., ac for air compressor,

hrsg for heat-recovery steam generator, and sr for storage

vessel).Total exergy of a material stream:

E ¼ E PH þ E KN þ E PT þ E CH , (5)

e ¼ ePH þ eKN þ ePT þ eCH . (5a)

Physical exergy of a material stream:

E PH ¼ ðH H 0Þ T 0ðS S 0Þ, (6)

ePH ¼ ðh h0Þ T 0ðs s0Þ. (6a)

Mechanical and thermal exergy of a material stream:

E PH

¼ E T

þ E M

, (7)

ePH ¼ eT þ eM . (7a)

The terms E KN and E PT (eKN and ePT ) in Eqs. (1) and (5)

are calculated by

E KN ¼ 1

2 m~v2, (8)

eKN ¼ 1

2~v2 (8a)

and

E PT

¼ mgz, (9)

ARTICLE IN PRESS

Table 1

Symbols for exergy and exergetic efficiency used in textbooks [initially compiled by Noam Lior]

Specific exergy

(kJ/kg) or (J/

mol)

Ex ergy (J) The sp ecifi c

exergy function

(J/kg)

The exergy

function (J)

Specific energy

(kJ/kg)

Energy (J) Exergy

destruction

Exergetic

efficiency

Textbook reference

Db — b e E Irreversibility e Keenan

L F, b e E I Hatsopoulos andKeenan (1965)

c Kotas (1985)

e Moran

e E e E E d e Moran and Shapiro

ex for open

systems, x for

closed

E x for open

systems, X for

closed

b for open

systems, a for

closed

B for open

systems, A for

closed

e E Wlost ZII Bejan

e E e E E D e Bejan, Tsatsaronis,

and Moran

B db ZB , Z p Szargut et al.

c for open

systems,

X e E I, X destroyed ZII Cengel and Boles

j for closed

c for open

systems,

c, ~ e E Z 2nd Anderson

j for closed

c, O E e Gyftopoulos and

Beretta

E z Bosnjakovic

~ ZII Sussman

c for open

systems,

~ e E I Z 2nd law Sontag, Borgnakke,

van Wylen

j for closed

e _E (only for

streams)

e E Baehr

G. Tsatsaronis / Energy 32 (2007) 249–253 251



ePT ¼ gz. (9a)

Here, ~v is the system velocity measured relative to the

environment and z represents the system height also

measured relative to the environment.

3. Other exergetic variables

3.1 The product exergy represents the desired result

(expressed in terms of exergy) generated by the system

being considered. The product exergy is denoted by E P .

3.2 The fuel exergy represents the resources (expressed in

terms of exergy) expended to provide the product

exergy. The fuel exergy is denoted by E F . The term

‘‘fuel exergy’’ here is not limited to fossil fuels but

represents in general the exergetic resources used to

drive (to ‘‘fuel’’) the process being considered.

3.3 The exergetic efficiency is the ratio between product

exergy and fuel exergy and is denoted by e (Greek

epsilon). The inverse of the exergetic efficiency isdenoted by the symbol k (Greek kappa). The terms

second-law efficiency and rational efficiency are not

precise and should be avoided when an exergetic

efficiency is implied by them.

3.4 The energetic (or thermal) efficiency, defined in a

similar way as the exergetic efficiency but using only

energy terms, is denoted by Z (Greek eta).

3.5 The thermodynamic inefficiencies of a system consist of

exergy destruction (E D) associated with the irreversi-

bilities (entropy generation) within the system bound-

aries and of exergy losses (E L) associated with the

transfer of exergy (through material and energystreams) to the surroundings. The uses of the term

irreversibility (instead of exergy destruction) and of the

symbol I should be avoided. The term irreversibility

does not imply that the exergy concept is used because

the exergy destruction can be calculated with the aid of

only entropy values.

4. Alternatives in the nomenclature

The suggestions made above refer to publications in

journals and conference proceedings when exergy is mainly

used and total energy is mentioned, if at all, in passing. For

such applications addressed mainly to exergy practitioners,

the letter E can be used for exergy without creating

confusion.

The situation might be different if we deal with students

who might be easily confused by differences in notations.

For textbooks an E should be used for total energy. This is

in accord with current use in most textbooks.

Then we have the following options for the exergy

symbol. The options presented in order of decreasing

simplicity and degree of preference.

Option 1: Use the letter E in a different font, for example

the roman font E (instead of an italic E).

Experience with textbooks using this option (e.g.,

[2]) shows that this seldom results in confusion.

Texts and instructors simply need to point out the

different fonts being used.

Option 2: Use a Greek epsilon (e, e). This option requires

that a letter different than e (for example, Greek

zeta z) is used for the exergetic efficiency since nowe represents the specific exergy.

Option 3: Use the letter X (x) which is the second one in

the word exergy. This letter is used, however, to

denote an unknown variable in mathematics.

Option 4: Use a Greek epsilon (e, e) for the exergy

associated with material and energy streams and

a Greek psi (C, c) for the exergy associated with a

system, to avoid the use of subscript ‘‘sys’’.

Option 5: Use the two letters Ex (ex).

It is apparent that several more options exist for exergy

and also for the other variables associated with exergycosting. Authors should consider that simplicity and ease

of use are two very important factors in selecting the

symbol for exergy.

5. Exergoeconomics: exergy costing

Exergoeconomics is the branch of engineering that

appropriately combines, at the level of system components,

thermodynamic evaluations based on an exergy analysis

with economic principles, in order to provide the designer

or operator of a system with information that is useful to

the design and operation of a cost-effective system, but notobtainable by regular energy or exergy analysis and

economic analysis. Exergoeconomics rests on the notion

that exergy is the only rational basis for assigning

monetary costs to the interactions that a system experi-

ences with its surroundings and to the sources of

thermodynamic inefficiencies within it. We call this

approach exergy costing. When exergy costing is not

applied, authors should use a different term (e.g., thermo-

economics). Thermoeconomics, being a more general term

and characterizing any combination of a thermodynamic

analysis with an economic one, might also be used instead

of the term exergoeconomics (but not vice versa). The

following definitions and symbols are recommended in

publications dealing with exergoeconomics:

5.1 The cost associated with a material or energy stream

(that means with an exergy stream) in exergoeconomics

is denoted by the symbol C . The average unit cost

(usually a cost per unit of exergy) is denoted by c.

5.2 The cost associated with an equipment item is denoted

by Z .

5.3 The exergetic cost of a stream represents the fuel exergy

that needs to be supplied to the overall system to

generate the exergy associated with that stream. The

exergetic cost is denoted by E c. The product and fuel

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G. Tsatsaronis / Energy 32 (2007) 249–253252



exergetic costs are denoted by E P c and E F

c, respec-

tively. The unit of exergetic cost is the ratio between

exergetic cost and corresponding exergy and is denoted

by the symbol k c.

5.4 When marginal costs are used, these must be explicitly

defined. A l (Greek lambda) may be used for this

purpose.

Acknowledgment

This project was initiated by Noam Lior. Input was also

provided by many exergy practitioners including the

following:

Cai Ruixian

Michel Feidt

Christos Frangopoulos

Richard Gaggioli

Ben Hua

Signe Kjelstrup

Andrea Lazzaretto

Giampaolo Manfrida

Alberto Mirandola

Michael Moran

Silvia Azucena Nebra

Gordon Reistadt

Ricardo Rivero

Enrico SciubbaJan Szargut

Antonio Valero

Michael von Spakovsky

Andrej Ziebik

It should be mentioned that not all of the above listed

practitioners agree with every single suggestion made here.

References

[1] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization.New York: Wiley; 1996.

[2] Moran M, Shapiro. Fundamentals of engineering thermodynamics,

5th ed. New York: Wiley; 2004.

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G. Tsatsaronis / Energy 32 (2007) 249–253 253

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