A brief Commented History of Exergy From the Beginnings to 2004

A brief Commented History of Exergy From the Beginnings to 2004
Int. J. of Thermodynamics
Vol. 10 (No. 1), pp. 1-26, March 2007
ISSN 1301-9724
A brief Commented History of Exergy
From the Beginnings to 2004
Enrico Sciubba*
Dept. of Mechanical & Aeronautical Engineering
University of Roma 1 “La Sapienza”
Roma, Italy
[email protected]
Göran Wall
Independent Researcher
Mölndal, Sweden
[email protected]
This paper presents a brief critical and analytical account of the development of the concept
of exergy and of its applications. It is based on a careful and extended (in time)
consultation of a very large body of published references taken from archival journals,
textbooks and other monographic works, conference proceedings, technical reports and
lecture series. We have tried to identify the common thread that runs through all of the
references, to put different issues into perspective, to clarify dubious points, to suggest
logical and scientific connections and priorities. It was impossible to eliminate our
respective biases that still affect the “style” of the present paper: luckily, some of our
individual biases “cancelled out” at the time of writing, and some were corrected by our
Reviewers (to whom we owe sincere thanks for the numerous and very relevant corrections
and suggestions).
The article is organized chronologically and epistemologically: it turns out that the two
criteria allow for a quite clear systematization of the subject matter, because the
development of the exergy concept was rather “linear”.
This work is addressed to our Colleagues who are involved in theoretical research,
industrial development, and societal applications of exergy concepts: if they extract from
this article the idea of an extraordinary epistemological uniformity in the development of
the concept of exergy, our goal will be achieved. The other addressees of this paper are
Graduate Students taking their first steps in this field: in their case, we hope that
consultation of our paper will prompt them to adopt and maintain throughout their career a
scholarly valid method of research, which implies studying and respecting our scientific
roots (the sources) but venturing freely and creatively into unknown territory.
In the Conclusions we try to forecast future developments: this is the only part of the paper
that is an intentional expression of our own views: the previous historical-scientific
exposition is instead based on verifiable facts and accepted opinions.
Keywords: Exergy, maximum work, thermo-economics, cumulative exergy cost, history of
*Author to whom correspondence should be
Int. J. of Thermodynamics, Vol. 10 (No. 1)
1. Introduction
1.1 Why this paper
This paper originates from a very
simple reflection: in the year 1970, about 50
articles on exergy (then called “Available
Energy” in the US and “Arbeitsfähigkeit” or
“Exergie” in Germany) were published in
archival journals or presented at workshops
and conferences; in 2004, this number by far
exceeded 500. All major current Energy
Engineering Journals publish on the average
1 or 2 articles on exergy-related concepts in
each issue: since 2000 there is an
International Journal of Exergy, which
enjoys even in front of stronger competitors
a satisfactory number of subscribers and
authors. More and more graduate students
use exergy analysis in their works, and
classical exergy methods evolve very
creatively. Every serious Thermodynamics
textbook devotes at least one entire chapter
to this topic, and Thermo-Economics (so
strongly linked to exergy to be sometimes
called “Exergo-Economics”) is a topic for
monographs of its own. Finally, and most
importantly from an engineering viewpoint,
industrial and institutional policymakers
have started adopting exergy as the basis for
their energy planning.
It occurred to us that there was no
comprehensive historical account of the
development of this very important concept
and of its applications: most modern
Thermodynamics books contain brief
sketches of the line of thought that led to the
introduction of the concept of “available
energy” or “maximum potential work”, but
these notes are indeed too brief to provide
the interested scholar with a complete
impression of the very instructive sequence
of individual steps that led from the
recognition that “the generation of motive
power requires not a consumption of
caloric, but rather its transportation from a
hot to a cold body” (Carnot, 1824) to the
statement “living systems thrive on exergy”
(Wall, 1997). A recent paper by Rezac &
Metgalchi (2004), after giving a detailed
analysis of the emergence of the term
“exergy”, concentrates on some present
controversial issues in the attempt of
resolving them, and thus does not provide a
discussion of the extremely important and
Int. J. of Thermodynamics, Vol. 10 (No. 1)
interesting series of debates that led from the
“seminal years” (basically, and rather
schematically, those before 1960) to the
remarkable maturity of the exergy concept
(roughly speaking, the beginning of the
In this “brief commented history” our
primary goal is to provide readers with a
clear idea of the importance of the individual
contributions to the path that led from the
theory of caloric to the present day exergy
applications in the fields of energy
diagnostics and management, analysis of
Very Large Complex Systems (VLCS),
information technology and sustainability
analysis. We try to do this by two means: a
very accurate bibliographic research that
does not neglect any of the major
contributions to the field; and a critical
review of each source, in a consistent
attempt to put things in the correct
perspective, to describe this development as
the evolutionistic combination of several
“threads” that join into a well organized
systematic theory for a while, then branch in
different directions, sometimes converging
again at a later stage.
1.2 Contents and limitations of this
This work is based on the references
listed in the Extended Bibliography, which
includes archival works and proceedings of
major Conferences published before
December 31, 20041. In all instances in
which a paper was published first in the
Proceedings of a Conference, and then
-under the same title- in a Journal, we quote
here the Journal reference. Though every
effort has been made to include original
quotations, in some of the “classical”
references (e.g., Carnot, Gibbs, Maxwell)
we had to base our work on revised editions
or/and translations. Also, all works
originally published in languages other than
English, French, German, Italian and
Swedish were accessible to us only through
English translations. Whenever possible,
obscure or controversial points of all
With only two exceptions: a book by Szargut,
published in 2005, the proofs of which were available
to us in 2004, and a paper by Sciubba & Ulgiati,
submitted in 2004 and published in 2005.
publications that appeared between 1950 and
2004 have been discussed with the authors:
obviously, the responsibility of having
gathered the correct interpretation rests
entirely with us. The Bibliography may
appear slightly biased towards publications
in the fields of Mechanical Engineering,
Energy Conversion Systems, and Resource
Management: it is indeed so, because our
familiarity with other fields where Exergy
analysis is also applied (like Chemistry,
Applied Physics, and Biochemistry for
instance) is -unfortunately- rather limited.
The enormous extent of the list of exergy
references makes it unsuitable for direct
inclusion in a paper like this: therefore, we
have adopted a different, though less userfriendly, approach: the complete reference
list is contained in a .pdf file available online
under www.icatweb.org/vol10/10.1/Sciubba
many forms in which energy flows present
themselves in nature, there are several
corresponding forms of exergy. The most
commonly used are listed in Table I.
The physical significance of the belov
“equivalence table” is clear:
• The kinetic energy of a system
traveling at a speed V with respect to a
Galilean frame of reference can be -in
principle- entirely recovered into any other
form: potential (the ideal pendulum); heat
(friction brake); mechanical (impulse
turbine); electrical (piezoelectric effect).
• The same applies to gravitational
potential energy and to all energy forms
related to motion in a conservative force
• Mechanical work and electrical
energy can also be freely converted into
each other.
• Chemical energy cannot be entirely
transformed into -say- mechanical work: the
maximum “work” that we can extract from a
system composed of a single pure substance
depends not only on the chemical enthalpy
of formation of that substance, but also on
the difference between its concentration in
the system and in the reference environment.
1.3 The modern definition of exergy
Exergy is defined as the maximum
theoretical useful work obtained if a system
S is brought into thermodynamic equilibrium
with the environment by means of processes
in which the S interacts only with this
This is a rephrasing of a concept that
was clear from the very beginning: already
Gibbs’ “availability function” (see Section
2) had the peculiar property of representing
the “freely available work”. Since there are
• Heat is the “least available” form of
energy flow: the portion that can be
converted into work depends on both the
system (Tq) and reference (T0) temperatures.
Type of
energy flow
J/kg; follows from definition
J/kg; follows from definition
 T 
q 1 − 0 
 T 
q 
J/kg; follows from definition
J/kg; follows from definition
J; follows from definition
 c0 
µ − µ 0 = ∆g G = g G − g G , 0
4T 3T0 T04 
3 
W/m2; for black body
µ − µ 0 + RT0 ln
σ  T 4 −
Notice that for electrical energy and for radiation the notion of “exergy per unit mass” makes little sense. The correct
extension of the definition is clear though in the context of every single application
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Therefore, neglecting for the moment
electrical energy3, for an open system S
identified by the thermodynamic parameters
T1, p1, µ1, V1, z1 that can interact only with a
reference environment B at T0, p0, V0, z0,
and in which the concentration of substance
1 is c0, the specific exergy content, in J/kg, is
a state function given by:
V12 − V02
+ g ( z1 − z 0 ) +
 c1 
+ RT0 ln
 − T0 ( s1 − s0 )
 c1, 0 
e1 = h1 − h0 +
consequences of the above definition:
a) If the system S is in state “0” (i.e.,
all of its relevant parameters take the same
value as those of the reference environment
B), its exergy is equal to zero: exergy is a
thermodynamic potential, a general measure
of “difference”, and requires two different
states for its definition.
b) There
combinations of the values of the
thermodynamic parameters such that e1 < 0:
the physical significance is that in this case,
to bring the system in equilibrium with the
reference environment, work must be done
on the system by the environment;
c) If S proceeds from state 1 to state 2,
its exergy variation in this process is also a
function of state:
V12 − V22
e1 − e2 = h1 − h2 +
+ g ( z1 − z 2 ) +
c 
∆g1,0 − ∆g 2, 0 + RT0 ln 1  − T0 ( s1 − s 2 )
 c2 
d) If in the transformation 1→2 some
heat Q flows under whatever small but finite
temperature differences) into S, the exergy
of the state 2 is smaller than that of state 1
augmented of the quantity of energy Q:
exergy has been destroyed in the process
(namely, in the transfer of heat from higher
to lower temperatures);
For the sake of simplicity, and in line with current
use, we do not include in Eqn. 1) other contributions,
that may become important in specific applications:
nuclear, magnetic, molecular vibration exergy, etc.
Int. J. of Thermodynamics, Vol. 10 (No. 1)
e) Any irreversibility in the process is
reflected in a further decrease of exergy
between the initial and the final state:
denoting by ∆sirr,1→2 the irreversible entropy
generation, we have:
∆e1→2 =T0∆sirr,1→2
f) The reference state B (T0, p0, V0, z0,
c0) is necessary to the definition of exergy:
for an isolated homogeneous system that
cannot exchange either mass or energy with
any other system, exergy is not defined;
g) If we consider processes that take
place in finite times (always maintaining the
assumption that they can be represented by a
proper succession of quasi-equilibrium
states), equations 1, 2 and 3 maintain their
significance, if all the terms therein are
substituted by their time derivatives;
h) If a system evolves in the presence
of a varying environment (long geological
timescales, or time- or site dependent
external conditions), its exergy level varies
accordingly, even if its state does not: this
means, quite simply, that the maximum
work we can extract from the system varies
as well.
1.4 A word about notation
Different Authors have adopted wildly
different notations: we shall uniformly refer
to the notation provided in the Symbols list
above. Where a different significance has
been used, we shall identify it case by case.
2. The Early Beginnings: Carnot & Gibbs
It is widely recognized today that the
exergy concept has its roots in the early
work of what would later become “Classical
Thermodynamics”. If an “exact starting
date” must be found, this can only be 1824,
when Carnot (1824) stated that “the work
that can be extracted of a heat engine is
proportional to the temperature difference
between the hot and the cold reservoir”.4 It
is correct to say that this simple statement
led, 30 years later and after much labouring
by Clapeyron (1832,1834), Rankine (1851)
and Thomson (1852) to the position of the
It is still a matter of debate whether Carnot’s
“caloric” ought to be interpreted as “heat flux” or
“entropy”. The context he uses the word in is often
(and clearly unintentionally) ambiguous.
second law of thermodynamics by Clausius
(1850,1867). However, Gibbs (1873) who
had earlier defined the thermodynamic
function “available energy”, was the first to
explicitly introduce the notion of available
work, including the diffusion term. He
stated: “We will first observe that an
expression of the form
-ε + Tη - Pv + M1m1 + M2m2 … + Mnmn
denotes the work obtainable by the
formation (by a reversible process) of a
body of which ε,η,v,m1,m2,…mn are the
energy, entropy, volume, and the quantities
of the components, within a medium having
the pressure P, the temperature T, and the
potentials M1,M2,… Mn. (The medium is
taken to be so large that its properties are
not sensibly altered in any part by the
formation of the body.)”
Equation 4 (n.54 in Gibbs’ work), is in
exact correspondence with the present
definition of exergy, equation 1 above.
Tait (1868), and Lord Kelvin as well,
had also defined in his lectures something
similar to Gibbs availability, but offered no
extended discussion of the concept. Also
Duhem (1904) in France and Caratheodory
(1909) in Germany elaborated on Gibbs’
With no direct reference to Gibbs’
work, the Frenchman L.G. Gouy (1889) and
the Slovak A. Stodola (1898)6 independently
derived an expression for “useful energy”
(in French énergie utilisable) as the
diffeence between the enthalpy and the
product of a reference temperature (which
they specifically stated to be the ambient, or
environment in modern terms, temperature)
and the change in entropy, To∆S7.
Maxwell (1871) and Lorenz (1894)
presented some applications to the
evaluation of thermal processes on the basis
Gibbs’ original notation has been maintained here
Aurel Stodola lived and worked in Switzerland,
where he was a professor in the ETH- Zürich
It is interesting that a paper by Gouy (1889b) was
criticized by Duhem (1889), who claimed priority in
the “discovery” of available energy (energìe
utilizable). Gouy rebutted (1889c), but the issue was
not conceded by Duhem. In modern terms, Duhem
was referring to the Gibbs free energy function (u-Ts),
and Gouy to exergy (u-T0s): thus, Gouy was right!
of entropy, and though neither of them
explicitly mentions an availability function,
it appears that they make a “mental use” of
the concept.
Some reflections on Gouy’s work
appeared in France due to Jouget, who in a
series of works (1906, 1907, 1909), applied
the “dissipated work” concept (exergy
destruction in modern terms) to thermal
machines. Similar considerations, that imply
a critique of the “first law” efficiency for
thermal-to-mechanical conversion processes,
were developed in the US by Goodenough
(1911) and de Baufre (1925), in Germany by
Born (1921) and in France by Darrieus
(1930, 1931) and Lerberghe & Glansdorff
In the same years, J. H. Keenan in a
series of fundamental works expanded and
clarified the concept of exergy (in his
notation, “availability”). His publication “A
steam-chart for second-law analysis”
(Keenan 1932) included explicit references
to most of the earlier work. His textbook on
thermodynamics (Keenan 1941) has exerted
contributed to a more widespread knowledge
about second law analysis in general and
about the availability concept in particular.
Contemporary to Keenan, Fran
Bošnjakovic (1935, 1938), a Croatian who
taught in Dresden, Zagreb, Braunschweig
and Stuttgart, laid the foundation of the
German school of applied and theoretical
Thermodynamicists, that were to further
develop the concept of exergy two decades
contributions to the identification of
irreversibilities by a proper Second Law
analysis, and stressed the importance of
Gibbs’ availability, that he called Work
Potential (Arbeitsfähigkeit). In the same
years, additional fundamental contributions
were published by Rosin & Fehling (1929),
who calculated the exergy of fuels, Emden
(1938), and Rant (1947) who provided one
of the first exergy analyses of a chemical
process (soda production). Some interesting
applications of the “available energy”
concept to the analysis of heat exchangers
were published in Russia (Gochstein 1939,
Kirpitschev 1949) and in Germany (Glaser
Int. J. of Thermodynamics, Vol. 10 (No. 1)
In the US, Obert & Birnie (1949),
published a seminal paper dealing with the
assessment of the losses in a fossil fuelled
power plant: the novelty was the use of
availability to locate the most critical
processes, a theme that will be tackled again
about two decades later.
The legacy of those early years is too
often forgotten: to a modern reader, it is
apparent that in all the works quoted above,
the concept of what we now call exergy
analysis was entirely clear to all Authors
(except perhaps for the very early ones:
Carnot, Clapeyron and Clausius). The
problem of the reference state had already
been posed, but was not investigated at all in
its implications; the possible effects of a
Second Law analysis on the then scarcely
available cost-efficiency correlations was
also well understood; but the emphasis was
generally placed on the possibility of
irreversibilities and improve the “real
efficiency” of the processes under
3. The Definition of the Concept and of Its
Fields of Application: 1950-1970
At a scientific meeting in 1953, the
Slovenian Zoran Rant suggested that the
term exergy (in German Exergie) should be
used to denote “technical working capacity”
(Bošnjakovic’s technische Arbeitsfähigkeit).
This was the proposal of a cultivated man:
energy literally means “internal work” (from
the Greek en [εν] and ergon [εργον]), and
the prefix ex [εξ] implies instead an
“external” quantity. Rant even published
(1956) a linguistic essay to discuss
international equivalent names for this
quantity (he proposed exergie in French,
exergia in Spanish, essergia in Italian and
eksergija in Slavic languages). By adopting
this name, all previous expressions, such as
available energy, availability, available
work, potential work, useful energy,
potential entropy, etc. and later introduced
terms such as essergy could in principle be
abandoned. In practice, it took 50 years for
Rant’s denomination to become accepted
worldwide: even at present, some US
Authors still use the obsolete “availability”
Int. J. of Thermodynamics, Vol. 10 (No. 1)
As stated above, the modern definition
of exergy is a rephrasing of Gibbs’ original
statement: The exergy of a thermodynamic
system S in a certain state SA is the
maximum theoretical useful work obtained if
S is brought into thermodynamic equilibrium
with the environment by means of ideal
processes in which the system interacts only
with this environment.
Baehr gave in 1962 another definition,
which is still widely used especially in
energy conversion applications: Exergy is
the portion of energy that is entirely
convertible into all other forms of energy.
(in German, die Exergie ist der
unbeschränkt, d.h. in jede andere
Energieform umwandelbare Teil der
Energie). This definition is though
misleading, because it implies that the “total
energy” of a system is composed of two
additive parts, one “convertible” (exergy)
and one non-convertible (anergy)8. But there
are several examples of systems with a
negative anergy (solids below T0, gases in
certain ranges of T<T0 and p<p0, etc.), and
this makes the use of Baehr’s definition
The mature definition provided above
had its roots in fifteen years of intense
debate about the exergy concept: this debate
took place mostly in Germany, with only
marginal contributions from France,
Switzerland, Italy and Sweden. It turns out,
that in the same years (1950-1965) some
prominent scientists from Russia and
Eastern Europe (Martinowsky 1950,
Gochstein 1951, 1962, 1963, Martinowsky
& Alexejev 1955, Brodyanski & Meerzon
1960, Brodyanski & Ishkin 1962,
Brodyanski 1963, 1964, 1965, 1967,
Andreev & Kostenko 1965, Chernyshevsky
contributions to the field: but their works
were not directly available to the larger
scientific body of the world, and therefore
the two developments remained somewhat
independent for years (the only link being
Baehr (1965) also discussed the function anergy,
which we shall not consider here, since it is redundant
(anergy=energy–exergy in his definition): but several
Authors published on anergy to a large extent until
recently (Erdelyi 1952, Almqvist 1964, Szargut 1966,
Geisler 1969, Kalitzin 1969, Kurt 1969, Tuma 1971,
Wachter 1977, Muschik 1978, Alefeld 1988a).
provided by Eastern European scholars who
had direct access to the Russian sources).
At first, there was an effort to
reformulate the thermodynamic problemsolving procedures in terms of entropy or
exergy: thus, Gourdet & Proust (1950),
Glaser (1953), and Rosin & Fehling (1929),
among others, published enthalpy/exergy or
enthalpy/lost work diagrams and developed
process analysis procedures on these bases.
Then, a major problem that was the matter
of heated debates was the proper definition
of the “efficiency” of a thermal process: in
the works of Darrieus (1931), Hauser
(1950), Hegelmann (1950), Grassmann
(1950)9, Frieder (1952), Lange (1953),
Schmidt (1953), Grassmann & Kammerer
(1954), Kammerer (1954), Nesselmann
(1955), Bock (1956) and Mattarolo (1956) a
critical review of “first law” efficiency
definitions leads, on the basis of theoretical
justifications, to a proposed “new definition”
of a Second Law based performance
parameter. It is noteworthy that this debate
continued in the 1960s’, and led to the
modern efficiency definitions we are using
today (see the books by Kotas 1985, Moran
1986, Bejan, Tsatsaronis & Moran 1996,
Szargut 2005). In general, the goal of these
Authors is to show that the thermodynamic
performance of any process in which energy
is converted from one form into another
cannot be measured properly by First Law
considerations, and that the energy in- and
outflows ought therefore to be expressed in
exergy terms.
In the same years, other Authors were
involved in a theoretical debate about the
foundation, the formulation and the
applicability of exergy: the list includes
among others Keenan (1951), Nesselmann
(1952, 1953), Heller (1954), Marchal
(1956), Denbigh (1956), Elsner & Fratzscher
(1957, 1959), Evans (1958), Fratzscher
(1959), Ackeret (1959), Bruges (1959), who
all published original contributions to the
field, and developed applications mostly in
the field of energy conversion, heat
exchangers and chemical processes.
Robert B. Evans (1961) showed that
exergy (which he called “essergy”) in itself
In recognition of Grassmann’s fundamental
contributions to the field, the exergy flow diagrams of
a process are called today “Grassmann diagrams”
incorporates other thermodynamic concepts
such as Gibbs free energy, Helmholtz free
energy, enthalpy, as well as the
“availability” introduced by Keenan. In
Evans’ mind, even Gibbs free energy,
Helmholtz free energy and enthalpy could
easily -albeit with due attention- be replaced
by exergy. The theoretical value of the
concept of exergy (in his notation, still
“availability”) was addressed by Myron
Tribus in his 1961 MIT course on
Thermodynamics: his goal was to unify
“classical” thermodynamics originating from
the work of Carnot with statistical
mechanics and information theory that had
evolved from the atomic model to the new
concept of quanta, and to reconcile the
definitions of entropy. But Tribus’ major
accomplishment today is considered to be
the “invention” of Thermo-Economics10, see
below, Section 7.
aimed at a systematic analysis of the
efficiency concept, were coupled with
practical and often very innovative
applications to the exergetic assessment of
both existing cycles and processes in the
works of Almqvist (1964) in Sweden, of
Andreev & Kostenko (1965) and Brodyanski
(1964, 1968) in Russia, of Fratzscher (1961),
Gašperšič (1961), Rant (1961), Gasparovic
(1962), Baehr (1962, 1963, 1965, 1968),
Bošnjakovic (1963, 1965), Giesen (1965),
and Heller (1968) in Germany, of Borel
(1965) and Berchtold (1970) in Switzerland,
of Chambadal (1965a) in France, of Medici
(1966) and Codegone (1967) in Italy, of
Gaggioli (1961) and Evans (1969) in the US,
of Szargut (1954, 1956, 1957) and Petela
(1963) in Poland. These works led not only
to a more thorough understanding of the
intrinsic loss mechanisms of engineering
processes, but at times to quantum advances
in cycle configurations, obtained by the
more accurate analysis of the irreversibilities
allowed by the exergy approach.
Bošnjakovic (1961) edited a Special Issue of
In spite of lack of formal acknowledgement on the
part of Tribus, it is clear in hindsight that he ought at
least to share this credit with El-Sayed and Evans, who
were working in his group at the time. Both made
fundamental contributions to the field (Evans in the
years 1960-1980; El-Sayed is still active at the time of
this writing). By contrast, Tribus did not publish any
further on this topic.
Int. J. of Thermodynamics, Vol. 10 (No. 1)
the BWK, and Baehr (1965) edited another
monography for the German Engineering
Society (Verein Deutsche Ingenieure, VDI):
both works contain several interesting and
seminal papers on exergy analysis.
A mature topic requires a standard
notation system: Szargut (1962, 1964) and
later Weingaertner (1969) suggested two
(different!) notational systems. As we shall
see, this problem with notation was at least
formally solved only much later (Kotas et al.
1987), but these early attempts were
thermodynamic function (exergy) was
referred to under different names (available
energy, exergy, maximum potential work,
work capacity), but there were almost as
many definitions of “exergy efficiency” as
there were Authors in the field. The dispute
about the correct name to attribute to the
function “h-Tos” went on for years, but the
definitions of efficiency that emerged from
the debate of the 1960s’ converged to three
fundamental ones:
a) the “Second Law” or “exergy”
useful exergy output
used exergy input
exergy of " products"
∑ (exergy inputs)
c) the
annihilated exergy
total exergy input
TO ∆sirr
∑ (exergy inputs)
This debate about the correct efficiency
definition was very relevant in the European
literature (Grassmann 1950a,b, Kammerer
1954, Nesselman 1953, 1955, Bock 1956,
1957, Fratzscher 1961, Gasparovic 1962,
Nitsch 1964, Borel 1965, Baehr 1968), much
less in the US, where the definitions
proposed by Keenan (1941), Obert
(1948,1960) and Obert & Gaggioli (1963)
were later refined and completed by
Gaggioli (1961a, 1968), and almost
uniformly accepted in the English literature.
The development in Russia was parallel to
Int. J. of Thermodynamics, Vol. 10 (No. 1)
that in Germany, due to the free exchange of
information within the then Eastern Block.
At the end of the 1960s’, thus, the
theory of exergy was more or less
completed, but only a small number of
practical applications had been discussed
(mostly to chemical systems and to energy
conversion plants): in retrospect, we can say
that in general the intellectual fallout of the
exergy theory to industrial applications was
slight if not absent at all.
4. The Mature Exergy Theory: After 1970
In our view, the extraordinary
development and expansion of the exergy
theory in the 1970s’ and the exponential
growth of its applications were due to two
very different but equally influential causes:
one is the concise, clear and stimulating
discussion offered by some textbooks of the
Hatsoupoulos & Keenan), that prompted
generations of graduate students in
Engineering Thermodynamics to enter the
field; and the other is the so-called “oil
crisis” of 1973, that forced Governmental
Agencies and industries in industrial
Countries to concentrate on “energy
savings”. Increasing the “efficiency” of the
chain of transformations that lead from raw
resources to commercial products requires a
thorough understanding of the location and
of the relative importance of irreversible
losses, and this is where, of course, exergy
analysis comes to use.
In fact, most of the theoretical
publications produced from the beginning of
the 1970s’ to the end of the 1990s’ (with the
exception of Thermoeconomics, see Section
7 below) deal with optimization procedures:
the goal becomes that of defining the most
maximizes the exergetic yield of a process
for a given resource input. Thus, the
problem of correctly identifying the proper
performance indicator for each elementary
transformation or for an entire process is
discussed in an extremely large number of
publications worldwide. In this period, the
first international workgroups are organized
to facilitate the exchange of information by
forcing different schools of thought to
confront each other, and this results at once
in an extraordinary
deepening of the field.
There is no univocal way to summarize
the enormous amount of work done in these
years in the field of exergy: we chose here to
separately consider theoretical developments
(4.1); theoretical applications to energy
improvements (4.3); theoretical progress in
chemical processes (4.4); the development
of design tools (4.5); the study of material
properties and of standard reference states
(4.6); and more tutorial divulgatory works
(4.7). Applications proper (i.e., procedures
applied to practical cases) are examined in
Section 5 below. It must be recognized,
though, that a substantial degree of
overlapping exists in most of the references
quoted here.
4.1 Theoretical developments
development of the exergy concept
proceeded at a constant pace in these last 35
years. More and more scholars became
involved in Exergy Analysis, and there is no
Country which can be regarded as “leading
the field”: though the vast majority of the
works listed here were authored by US or
German researchers, numerous fundamental
contributions came from Russia and in
general from the then Eastern Block, from
Japan and from western Europe.
One of the most debated topics is of
course the definition of all the implications
of the exergy function and of its theoretical
applications: Reistad (1970), Ussar (1970),
Vlnas (1970), Weingaertner (1970),
Wissmann (1970), Thoernqvist (1971),
Bojadzev (1972), Keller (1972, 1982),
Chernyshevskyi (1974), Fratzscher (1974),
Haywood (1974, 1979), Kalz (1974, 1975,
1976), Medici (1974), Naylor (1974),
Andryuschenko (1975), Mayer (1975),
Sawada (1975), Tribus (1975), Yasnikov
(1975), Roegener (1976), Vivarelli et al.
(1976), Yasnikov & Belousov (1976,
1977a,b), Berchtold (1977), Soerensen
(1977a,b), Wachter (1977), Brzustowsky &
Golem (1978), Kestin (1978, 1979), Klenke
(1978, 1991a,b), Muschik (1978), van Lier
(1978), Voigt (1978), Andresen & Rubin
(1979), Borel (1979c), Kameyana &
Yoshida (1979, 1980), Martinowsky (1979),
de Nevers & Seader (1979a,b), Sussmann
(1979a,b, 1980), Wepfer (1979), Woollert
(1979), Yamauchi (1979, 1981), Andrews
(1980), Ahern (1980b), Gaggioli (1980,
1983), Penner (1980), Silver (1981),
Zschernig & Dittmann (1981), Enchelmayer
(1982), Sato (1982, 1983, 1985, 1986a,b,c),
Wall (1986), Gyftopoulos & Beretta (1987),
Alefeld (1988b,c), Wang & Zhu (1988),
Zilberberg (1988), von Spakowsky & Evans
(1989a, 1990a,b), O’Toole & McGovern
(1990), Lucca (1991), Dunbar et al. (1992),
and Moran & Sciubba (1994), in their works
made fundamental advances in the
understanding of the thermodynamic
meaning of exergy, contributed to a clearer
definition of its derivation from prime
advantages in the analysis of energy
transformations, analyzed its correlation
with irreversible losses and with the
construction of a measure of an “energy
quality scale”. Hatsopoulos & Gyftopoulos
(1976a,b,c,d) provided, within a larger
theoretical framework, a rational derivation
of the "available energy" that is in essence
equivalent to Baehr's maximum work
concept, but avoids the introduction of an
"anergy" function and extends Baehr's
maximum work concept, i.e. the “exergy”,
to any system (large or small; macroscopic
or microscopic, including one-particle
systems) and to any state (stable or not
stable equilibrium).
Ageev & Martynov (1970), Opreschnik
(1970), Baehr (1971), Brodyansky (1971),
Alexiev (1973), Martinowsky & Meltser
(1973), Martinowsky & Brodyanskyi
(1974), Meltser et al. (1975), Ahern (1980a),
Szargut & Maczek (1983) studied the
implications of the exergy analysis on
cooling and (Reinke 1971b, Adebiyi &
Russell 1986) air conditioning processes.
Press (1976), Marshall & Adams
(1978), Parrot (1978), Karlsson (1982),
Haught (1984), Kutomi & Nobusawa
(1984), Scholten (1984), Kar (1985), Altfeld
et al. (1988), Suzuki (1988a,c), Badescu
(1992), Svirezhev & Steinborn (2001),
Wright et al. (2002) studied the exergy of
solar radiation and/or its implications in the
theory of solar collectors.
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Glansdorff et al. (1955, 1956), Bauer
(1970), Maltry (1971), Clarke & Horlock
(1975), Lewis (1976), Li & Qiu (1992),
applied the exergy concept to the analysis of
aeronautic propulsive systems: this area is
still under development today, with
enormous implications for advanced flying
vehicles, see Section 5.1 below.
Heat transfer is another field that did
benefit from the introduction of exergy
analysis: Harrison & Dean (1978), Evans &
von Spakovsky (1980), Bejan (1982c), Boyd
et al. (1982), Tapia & Moran (1986),
Aceves-Saborio et al. (1989), Bejan &
Sciubba (1992), Carrington & Sun (1992),
Mereu et al. (1993), demonstrated that the
optimal design point of a heat exchanger can
be calculated only by taking into proper
account entropic losses, i.e., exergy
destruction. In a closely related field, Heat
Exchangers Networks design and synthesis,
exergy methods were developed by
Fratzscher (1973, 1982), Berg (1979),
Umeda et al. (1979), Vukovic & Nikulshin
(1980), Pehler & Liu (1981), Ishida (1983),
Vinograd et al. (1983), Chato & Damianides
(1986), Gaggioli et al. (1991), Hale (1991),
Maiorano & Sciubba (2000): all of these
studies showed that the original Hohmann
(1971) analysis could be extended to
considerations, resulting in faster procedures
for optimal networks designs.
Heat- and work integration is also a
field in which an exergy analysis leads to
better thermodynamic optima: Beyer (1970),
Gruhn et al. (1972), King et al. (1972), Berg
(1974c), Khlebanin & Ten’kaev (1974),
Yoon (1974) Rokstroh & Hartmann (1975),
Sweeney et al. (1975), Edgerton (1979),
Nishio et al. (1979), Umeda et al. (1979),
Liu (1980, 1982a,b, 1983), Sophos et al.
(1980a), Takamatsu & Naka (1982), Sciubba
et al. (1984a,b, 1985a,b), von Spakovsky &
Evans (1984), Nikulshin (1985), El-Sayed &
Gaggioli (1988), Evans & von Spakovsky
(1988, 1990), von Spakovsky & Geskin
(1989), Tomlinson et al. (1990), Safonov et
al. (1991), Streich et al. (1991) demonstrated
that from a theoretical point of view exergy
leads to better process integration, and
therefore to more efficient resource use.
Buergel (1974) proposed to found the
diagnosis of an industrial process on its
Int. J. of Thermodynamics, Vol. 10 (No. 1)
exergy analysis: his work had no application
until much later, see also Sections 5.6 and
8.3 for some recent applications.
Chimeck & Chandrasekhar (1984a,b)
devised a model of Large Energy Systems
and proposed to analyze them by means of
exergy methods; earlier, Chlebanin &
Nikolaev (1977) had produced a model of a
supply-consumer system. Both works, which
have some similarity with Szargut’s method
of Cumulative Exergy Content (see Section
8), went unnoticed for years, until the most
recent developments published by Le Goff
(1977), Wall (1983,1987,1988) Ayres
(1998,2003), Azzarone & Sciubba (1995),
Sciubba (1995), that led to a general method
of Large Complex System Analysis.
Dehlin (1979) proposed to study the
energy crisis of the 70’es by means of an
exergy analysis: this seminal idea, also
neglected at that time, resulted in later work
in closely related fields by several authors
(Wall 1981,1987a,b, Sciubba 1995, Ayres
4.2 Energy conservation
A closely related field to process
integration is of course energy conservation:
actually, it is difficult to separate the
contributions in these two fields. With this
caveat, mention must here be made of the
most important works in this topic, where
Ross & Socolow (1974), Grassmann (1975),
Hall (1975), Zlatopolskji & Zavadskji
(1975), Gyftopoulos & Widmer (1977),
Sussmann (1977), O’Callahan & Probert
(1977), Graichen et al. (1978), Hanna &
Frederick (1978), Michaelides (1979), van
Gool (1979, 1980, 1992), Didion et al.
(1980), Leidenfrost et al. (1980),
Timmerhaus & Flynn (1980), Gaggioli &
Wepfer (1981), Grant & Anozie (1981),
Novusawa (1981), Soerensen (1981),
Paolino & Burghardt (1982), Shinskey
(1982), Kenney (1983, 1984), Rotstein
(1983, 1988), Reay (ed., 1984), Alavarado &
Iribarne (1990), gave a major impetus to the
idea that energy “savings“ in all processes
can be attained only by judicious use of an
exergy analysis.
Gaggioli (1977), Roberts (1982) and
Stepanov (1984) introduced -though in a
preliminary and still rather sketchy form- the
related concept of exergy audit as a
necessary substitute for the current energy
audits. The concept was a fruitful one, was
developed into an application by Valero et
al. (1986), and gave origin to a series of
publications in this area (Boyle & Lang
1990, Frangopoulos 1992, Özdogan &
Arikol 1995, Nokicenovic et al. 1996,
Cornelissen 1997, Belli & Sciubba 2001,
Cornelissen & Hirs 2002, Dewulf &
Langehove 2002a,b, Dincer 2002). Notice
that all “national budget analysis methods”
discussed in Section 9.5.3 below are also a
direct application of this method.
Peters et al. (1977), Roth & Miley
(1979), Petit & Gaggioli (1980), Rothstein
& Stephanopoulos (1980) and Primus et al.
(1984) proposed that exergy analysis be
used in determining the future needs for
research in the field of energy systems: this
idea was also fruitful, and actually their
works sparkled a series of proposals of new
cycles and processes that stemmed from a
basic exergy analysis of the drawbacks and
of the limitations of “standard” processes.
4.3 Efficiency improvements
Another closely related field is that of
improvement: Munser & Dittmann (1971),
Reistad & Ileri (1973), Zlatopolskji (1973),
Bandura (1974), Bidard (1974), Hamel &
Brown (1976), Slabikov (1976), Hevert
(1979), Kaloferov (1979), Hussein et al.
(1980), Kotas (1980), Khalifa (1981),
Mansoori & Gomez (1981), Gerz (1982),
Szafran (1982), Knoche et al. (1984),
Horlock & Haywood (1985), Baines &
Carrington (1986), Alefeld (1987), Tobias
(1991), presented proposals for the
improvement of process- and component
efficiencies founded on an underlying
exergy analysis. The definitions of the
“second Law efficiency” they use are based
on the studies conducted in the 1950s’ and
1960s’ mentioned above (Section 3).
4.4 Theoretical progress in chemical
Though the general trend that emerges
from an analysis of the chemical engineering
literature is that of directly applying the
exergy concepts to process analysis, some
noteworthy theoretical developments also
took place: Streich (1975), Nishimoto
(1976), Abrams (1978), Krishna (1978),
Sakuma (1978), Hohmann & Sander (1980),
Platonov & Zhvanetskji (1980), Henley &
Seader (1981), Fonyo (1982), Andrecovich
& Westerberg (1983), Al-Ahmad & Darwish
(1991) studied separation, rectification,
distillation and desalination processes, and
Reinke (1971a), Standart & Lockett (1971),
Szargut (1973), Ahrendt (1974, 1977),
Riekert (1974, 1976a,b,c, 1979, 1980, 1981),
Moran (1975), Semeniuk (1976), Vakil
(1980), Teja & Roach (1981) Moore &
Wepfer (1983), Richter & Knoche (1983),
Rabinovitsch et al. (1984) and Siemons
(1986) published contributions to several
topics in chemical engineering, from
reacting flows to combustion.
In the related field of Material Science,
Shieh & Fan (1981, 1982) published a list of
calculated exergies of materials with a
complex physical structure.
4.5 Development of design tools
As industrial researchers became more
accustomed to exergy analysis, a trend
began to emerge towards the search for
“standard” analysis and design procedures.
Process analyses were published by
Rademacher (1974), Rochelle & Andejewski
(1974), Semenov et al. (1975), Urdaneta &
Schmidt (1977), Hedman et al. (1979),
Stepanov (1984), Hua (1986), until Kotas
(1986) published the first systematic set of
“exergy analysis procedures”.
produced to be used as design aid tools by
Tuma (1961), Glaser (1972), Reistad (1972),
Baloh (1974), Daly & Harris (1979), Ishida
& Oaki (1981), Oaki et al. (1981), Tapia &
Moran (1981), Ishida & Ohno (1983), Zhu et
al. (1988), Yantowsky & Lukina (1990),
and. Ishida & Taprap (1992)
These developments were paralleled by
extensive work directed to the determination
of material properties, see Section 4.6
In more recent years, the original
“design procedures” developed into
computer codes. It is impossible to provide a
complete list of the computational
procedures published in the last ten/fifteen
Engineering, and we report here only the
ones that can be considered “fundamental”
Int. J. of Thermodynamics, Vol. 10 (No. 1)
on a time priority basis, with the obvious
applications have remarkably improved on
the quality of the few pioneering ones:
Gaggioli et al. (1964), Gruhn et al. (1976),
Johnson (1980), Krumm et al. (1984),
Abtahi et al. (1986), Rosen & Scott (1986),
Tapia & Moran (1986), Tsatsaronis et al.
(1986), Valero et al. (1987), Melli &
Sciubba (1987), Alconchel et al. (1989),
Bidini & Stecco (1991), Wimmert et al.
(1991), Ngaw (1998), Maiorano et al.
4.6 Material properties and standard
reference states
As the application of exergy analysis to
different processes and cycles developed,
the need arose for a standard data base of
material properties. The problem is that the
calculation of the exergy of a material
system on the basis of Eqns. (1) and (2) does
not make much sense: it depends not only on
the composition of the particular material,
but also on the “reference state” that one
takes for its components. Since it is
obviously not possible to measure the
concentration of each chemical constituent
in the environment, the solution (first
proposed by Szargut in 1957 but published
in German in 1965 and in English only in
1980) is that of selecting a set of “reference
substances” and determining their average
concentration in the Earth’s crust. These
reference substances are the basis for the
calculation of the exergy of the individual
chemicals. The problem becomes of course
that of defining a “standard reference
environment”. This is still an open issue
today, and we shall examine the historical
developments that led to the present
situation. The basic problem is to define a
congruent list of “fundamental chemical
compounds” and their average concentration
in a model of the Biosphere (the Earth’s
hydrosphere). For instance, once the
“fundamental state” of the water in the
reference environment (which has by
convention zero exergy) is taken to be that
of the sea at Tref = 298 and at a conventional
salinity of 45‰, pure water at Tref = 298 will
have a positive exergy, equal to the negative
of the desalination chemical potential. This
is only an example: the problem of course
Int. J. of Thermodynamics, Vol. 10 (No. 1)
does not lie with the reference state of water
or air, but with that of some of the most
common ores present in the earth crust,
mainly silicates, carbonates, nitrates and
oxides. Already in the 1960s’, the problem
was tackled by Bošnjakovic (1963),
Fratzscher & Gruhn (1965), and Szargut &
Styrylska (1965). In the following years, the
problem of how to identify a convenient
“average composition” of the lito-, hydro-,
and lower atmosphere, was debated among
others by Brodyanskyi et al. (1971),
Kostenko et al. (1975), Ahrendts (1979,
1980), Ahern (1980), Gaggioli & Wepfer
(1980), Sussmann (1981), Sorin (1984),
Kotas (1985), Sorin & Brodyanskyi (1985),
Szargut & Morris (1985), Morris & Szargut
(1986), Szargut (1987), Fratzscher &
Michalek (1989), Diederichsen (1991), Ranz
et al. (1998), van Gool (1998): these Authors
gave solutions that differ little from one
another (the list of reference substances is
almost the same), but even small differences
in the reference elements produce substantial
differences in the exergy values for most
practical metals, fuels and construction
materials. Valero et al. (2003) proposed an
original method, based (partially) on
substitution, in which the exergy content of
an element is computed as the amount of
exergy that would be expended to “replace”
it in the mine. At present, in practice all
exergy calculations are based on the
“reference environment” published by
Szargut et al. (1988), with some corrections
due to Valero et al. (2002), Valero & Botero
(2003) and Rivero & Garfias (2004),: notice
that also Gaggioli et al. (2002) and Gaggioli
& Paulus (2002) explored the theoretical
implications of the exergy concept by
“revisiting” the original Gibbs’ works, and
their findings have had some influence on
the debate about the proper reference state.
Several Authors published their
calculations of the exergy of different
working media: we provide here a list of
their works, with the warning that the
reference states are not the same for all
calculations. Rosin & Fehling (1929- oils &
coal), Bock (1958 -oil and coal), Buimovici
(1958- liquid fuels), Rant (1960a,d -gaseous
& liquid fuels), Baehr & Schmidt (1963- oil
and gas), Pruschek (1970- nuclear),
Zakharov (1970- organic fuels), Valent et al.
(1977- gas), Baehr (1979, 1986 -coal and
oil), Cheng et al. (1980-coal), Srivastan
(1988- coal), Stepanov (1995 - liquid &
gaseous fuels) and Rivero (2002 - oil). The
most general result was that -except for
nuclear fuels- the exergies are approximately
equal (within 2-5%) to the respective lower
heating value. Gasperšič (1961), Baehr &
Schmidt (1964), Knoche (1967), Rant &
Gasperšič (1972) and Abu-Arabi & Tamimi
(1995) computed the exergy of combustion
Harmens (1975), Doering (1977a,b)
and Ahern (1980) calculated the exergy of
several refrigerants; Kabo et al. (1998) that
of alkanes; Liley (2002) and Marquet (1993)
that of moist air; Magaeva & Radnai (1986)
that of non-electrolytes; Marin & Turegano
(1986) that of electrolytical solutions;
Poersch & Neef (1971) that of vapour/gas
mixtures; Rao & Srinasavan (1997) that of
Nitrogen; Runge (1968) that of Neon;
Wandrasz (1968) that of a series of Fe-C
Opreshnik (1970), Eckert & Fratzscher
(1987), Rosen & Scott (1988), Fratzscher &
Michalek (1989), Etele & Rosen (2000),
Paulus & Gaggioli (2001), Serova &
Brodyansky (2002) provided methods for
accounting for a changing environment: this
can be of importance in the case of process
calculations in the presence of seasonal
temperature or concentration variations, or
of pressure, temperature and composition
variations with altitude.
4.7 Tutorial divulgation works
Though less important from a scientific
standpoint, an extensive literature exists of a
more tutorial and divulgatory character. We
are not referring to monographic books
(which are listed separately in Section 9),
but to articles in archival and non-archival
journals that contributed to propagate the
idea that exergy analysis was a “better” tool
for engineering design and analysis
purposes. Examples are the archival articles
by Alexander (1977), Fratzscher & Beyer
(1981) on the status and trends of exergy
analysis, of Tsatsaronis & Valero (1989) on
divulgative ones by Wertan (1972),
Townsend (1980), Vrugging & Collins
(1982), Mc Cauley (1982, 1983), Soma
(1982, 1983, 1985a,b) and Spreng (1991).
There are also “state-of-the-art” papers (in
encyclopaedias) that have played a nonnegligible role in bringing up the subject
among academic and non-academic
(1955,1957), Tribus (1958), Keenan et al.
(1974), Schipper (1976), Tsatsaronis &
Cziesla (2002a,b), Serra & Torres (2003),
Valero (2003), Valero & Torres (2003),
Valero et al. (2003).
5. Engineering Applications: 1950-2003
Applications of exergy methods to the
analysis of energy-conversion and chemical
processes are very abundant in the archival
literature: the list provided here is only
indicative. The subdivision by topic is also
somewhat arbitrary, and interested readers
are encouraged to consult the original papers
for better reference.
5.1 Power cycles and components
5.1.1 Steam power cycles: In this area,
after the very fundamental works of the
early years (Birnie & Obert 1949, Roegener
1961, Salisbury 1969), and after the later
papers by Keller (1959), Danila & Leca
(1966), Gaggioli et al. (1975), Sciubba & Su
(1986), Lozano & Valero (1987), Alconchel
et al (1989), Acar (1997), Rosen (2001),
Espirito Santo (2003) no relevant studies
have been published. The reason is
obviously the exceptional maturity of this
type of plants: it is likely that a renewed
interest in these studies will be prompted by
the recent emphasis on “zero CO2” cycles
for the production of hydrogen, see Fiaschi
& Tapinassi (2002), Zhang & Lior (2003),
Soufi et al. (2004). However, most processes
proposed to date are of the cogenerating type
(electricity + H2, or gas/steam/CO2 cycles)
and fall under point 5.1.4 here below.
Daniel (1996) presented an interesting
study of a reciprocating steam engine.
5.1.2 Gas turbine cycles: The gas
turbine cycle is still a preferred topic for
exergy analysis. Several papers continue to
appear in archival publications, confirming
the idea that the Brayton cycle (especially
with the most recent advances in materials
and blade cooling technology) will see some
breakthrough in the near future. Chambadal
Int. J. of Thermodynamics, Vol. 10 (No. 1)
(1965a,b), Gasparovic & Stapersma (1973),
Bandura (1974), Vivarelli et al. (1976a,b),
Harvey & Richter (1994), Pak & Suzuki
(1997), Fiaschi & Manfrida (1998a,b),
Abdallah et al. (1999), Di Maria &
Mastroianni (1999), Falcetta & Sciubba
(1999), Lombardi (2001), Zheng et al.
(2001), Alves & Nebra (2002), Jin et al.
(2002), Song et al. (2002), Aronis &
Leithner (2003), Ishida (2003), Kopac &
Zemher (2004) (steam-injected GT), Sue &
Chuang (2004) all dealt with both global and
local aspects of the problem, and some of
the works explicitly addressed transient
operation regimes.
5.1.3 Renewable energy cycles: The
most suitable candidate for an exergy
analysis is of course solar technology (both
for low and high temperatures). Works in
this area were published by Bejan (1982),
Edgerton (1981) (solar energy systems),
Çomakli & Yüksel (1994), Luminosu &
Fara (2004) (solar collectors). Photovoltaics
(especially the new ones, which combine
heat and power production) were also
explored, for instance by Ahmad &
Mohamad (2000).
5.1.4 Other Energy conversion
cycles: The combined and the cogenerating
cycle are the most frequently studied
processes, as testified by the works of
Andryushenko (1963), Avgousti et al.
(1989), Bilgen (2000), van Poppel et al.
(2003), Rosen et al. (2004), (cogeneration);
Bejan (1984), Bram & De Ruyck (1995)
(CO2 combined cycle); Chlebanin &
Nikolaev (1977), Brzustowski & Golem
(1978), Didion et al. (1980), Bitterlich et al.
(1982), Sciubba et al. (1984 a,b), Gaggioli
ed. (1985), Yantowsky et al. (1992)
Sawillion & Thöne (1994), Tuma (1995),
Sahin et al. (1997), Torres & Gallo (1998),
Cownden et al. (2001), (combined cycles
and other energy systems); Reistad &
Gaggioli (1970), Pak & Suzuki (1997) (total
energy systems). Some trigeneration
examples are studied in Sciubba & Guerrero
(1985), Gao et al. (2002) (poly-generation),
Marrero et al. (2002).
Fuel cells are also a system often
subject to an exergy analysis: Dunbar et al.
Douvartzides et al. (2004) (fuel cells
combined cycle); Kazim (2004).
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Buchet (1973), Dunbar et al. (1995),
Lior (1997a,b) presented exergy analyses of
nuclear cycles; Rakopoulos & Giakoumis
(1997,2004) and Caton (2000) studied
reciprocating internal combustion engines;
Hepbasli & Akdemir (2004), Koroneos et al.
(2004) and Yildirim & Gokcen (2004)
analysed a geothermal energy conversion
process; Kalina & Brodiansky (1997)
analysed the so-called ammonia-based
Kalina cycle.
Glansdorff et al. (1956) were the first to
publish an exergy analysis of a jet engine.
Only much later Bauer (1970), Clarke &
Horlock (1975), Lewis (1976), Malinowsky
(1984) produced complete system analyses.
And it took another 20 years before Bejan &
Sims (2001), Etele & Rosen (2003), and
Rosen & Etele (2004) presented exergy
analyses of flying vehicles, considered as
“energy conversion systems”. Cszys &
Murthy (1991), Brilliant (1995) and Bottini
et al. (2003, 2004) developed specific
applications to scramjets.
5.2 Heat
Exergy is well suited to perform a
systematic study of heat exchange processes,
and the book by Bejan (1982) provides
several examples of what he calls an
“entropy generation rate” analysis aimed at
the identification of optimal designs. This
proved to be a very productive field: heat
exchangers proper were analysed by Elsner
(1960), Chambadal (1965a), Bejan (1977),
Petela (1984), Aceves-Saborio et al. (1989),
Hale (1991), Lampinen & Heikkinen (1995),
Bejan et al. (1998), Bisio (1998),
Cornelissen (1999), Sorin et al. (2000),
Abbassi & Aliehyahei (2004) (evaporation
District heating was analysed by
Cornelissen et al. (1996), Cornelissen &
Hirs (1997), , Skorek & Kruppa (2003)
(low-T heating) and Ozgener et al. (2004).
An exergy-based method for the
optimal synthesis of heat exchanger
networks was originally proposed by Pehler
(1983), but was later developed into a
systematic method by Sama (1983), and
further by Gaggioli et al. (1991), Sama
(1995a,b), Maiorano & Sciubba (2000),
Maiorano et al. (2002).
Other applications in the field were
published by Beyer (1970, 1972, 1978)
(sugar production), Ramayya & Ramesh
(1998) (latent heat storage), Errera et al.
(2000) (bulk cooling), d’Accadia et al.
(2003) (vapour compression heat pump),
Gomri & Boumaza (2003) (solar heat
pump), Ionita (2003) (apartment heating),
Mahmud & Fraser (2004) (porous stack),.
5.3 Cryogenics
Since the exergy content of a stream
temperature, cryogenics is yet another field
in which an exergy analysis can provide new
and original design insight. The first papers
in this topic were published by Nesselmann
(1938), Martinowsky (1950) (whose book
inspired many later German textbooks on
the subject), Grassmann (1952) and Bock
(1956). In the 1960s’, Fratzscher (1964),
Grassmann (1964), Peculea (1964) and
Szargut & Maczek (1964) published
interesting contributions.
Among the more recent papers, we like
to quote here those by Ahern (1980),
Benelmir et al. (1991) and Wall (1991)
(optimisation), Srinivasan et al. (1995),
Adewusi & Zubair (1997), Cornelissen &
Hirs (1997,1998), Fartaj et al. (1997),
Ahmed et al. (1998), Lu et al. (1998), Torres
et al. (1998), Liu & You (1999), Rosen
(1999), Rosen et al. (1999,2000) (cold
thermal storage), Chen et al. (2001), Aprea
& Greco (2002) (R-22 substitution),
Badescu (2002) (solar heat pump), Bilgen &
Takahashi (2002), Szargut (2002), ,
Yumrutas et al. (2002), Rakhesh et al.
(2003), Varani et al. (2003) (Li-Br
absorption cycle), Kilicaslanb et al. (2004)
(vapour compression cycle), Sahoo et al.
(2004) (absorption cycle), Snoussi & Bellagi
(2004) (heat driven cooling system),
Somasundaram et al. (2004).
5.4 Chemical processes
The conversion of chemical exergy into
thermal exergy, and vice versa the injection
of thermal exergy to promote and maintain a
chemical conversion is of great importance
for industrial and power conversion
applications. Already Rant (1947) in his
doctoral dissertation discussed a Second
Law analysis of a soda plant. An influential
work was that of Denbigh (1956), in which
the concept of “chemical reaction
efficiency” was discussed. Bock (1959),
Rant (1960), Fratzscher & Nitsch (1961) and
Fratzscher & Schmidt (1961) expanded the
exergy analysis to homogeneous and
heterogeneous reactions. Gašperšič (1961)
computed then the exergy of combustion
gases, useful for gas turbine applications and
for many industrial processes.
Fundamental papers were published by
Zakharov (1970), Ahrendts (1974, 1977),
Nydick et al. (1976), Eckert et al. (1987),
Futterer et al. (1991), Guoxing & Zijung
(1997). Combustion was also extensively
studied: Knoche (1967), Rosen (1996),
Szwast & Sieniutycz (1997), Anheden &
Svedberg (1998), Sorin et al. (1998),
Rasheva & Atanasova (2002), Woudstra &
Stelt (2003).
In the most recent years, the emphasis
is being shifted towards an exergetic or
thermo-economic analysis of specific
applications: Gaggioli & Petit (1977),
Gaggioli & Rodriguez (1980, Gaggioli &
Wepfer (1980) (coal gasification); Ishida
(1983) (coal liquefaction); Ishida & Taprap
Kirova-Yordanova et al. (1994,1997,2003),
synthesis); de Oliveira & van Hombeeck
(1997) (petroleum separation); Tober et al.
(1999) (aniline process); Sorin et al. (2000)
(multi-step processes); delle Site & Sciubba
(2001) (ethanol production); Okazaki et al.
(2002), Akiyama & Maruoka (2003)
(methane conversion); Syahrul et al. (2002)
and Poswiata & Swast (2003) (drying);
Atanasova & Lasheva (2003) (precipitate
production); Geuzebroek et al. (2004) (CO2
5.5 Distillation and desalination
Since desalination processes convert
thermal or mechanical exergy into chemical
exergy (they increase the exergy content of
salty water to make it “fresh” or potable),
this is also a field of extensive investigation.
The first paper in the field is that by
Freshwater (1951), but the later monographs
by Spiegler & Laird (1966) and El-Sayed
(1970) have exerted an important influence
on designers of desalination plants.
On the general topic of “desalination”,
we can quote here the papers by Abrams
Int. J. of Thermodynamics, Vol. 10 (No. 1)
(1978), Umeda et al. (1979), Henley &
Sieder (1980), Andrecovich & Westerberg
(1983), al-Ahmad & Darwish (1991), alSulaiman et al. (1995), Hamed et al. (1996),
Sauar et al. (1997), El-Nashar et al. (1998),
El-Nashar (1999), Garcia-Rodriguez &
Gomez-Camacho (2001), Slesarenko (2001),
Cerci (2002), Bona et al. (2003) and
Darwish (2004).
The important issue of the optimal
integration of desalination processes with
topping thermo-mechanical ones was
studied among others by Gaggioli et al.
(1989) and Sommariva & al. (1997).
The contributions by El-Sayed, Evans
and Tribus that led to the development of
Thermo-Economics are discussed in Section
7 here below.
Kaiser & Gurlia (1985) introduced the
concept of “ideal column” to apply exergy
Cornelisson et al. (1995), Rivero (2001,
2002) and Husain et al. (2003) studied crude
oil distillation, while Fitzmorris & Mah
(1979), Naka et al. (1982), Fonyo & Rev
(1981,1982), and Ishida & Ohno (1983)
analysed chemical distillation processes.
5.6 Industrial & agricultural systems
There are several application studies in
the literature, most of them presented at
Conferences and only few published in
archival journals. The first paper (Elsner &
Fratzscher, 1957) dealt with a boiler, a
thermo-mechanical conversion plant, and a
steam locomotive! Bosnjakovic (1959) was
a good second with his exergy analysis of an
industrial oven. Due to the very extensive
range of studied applications, a complete list
is difficult to compile, but the following one
gives an idea of the breadth of the field:
Akpinar & Sarsilmaz (2004) analyzed the
solar drying of apricots; Aoki (1992), Fan et
al. (1985) agricultural systems; Auerswald
(1980), Baloh (1981) and Guallar & Valero
(1988) a sugar factory; Çamdali et al. (2004)
the cement production process; Akiyama et
al. (1991), Çamdali & Tunc (2003),
Chinneck (1983), Costa et al. (2001),
Keenan et al. (1974), Masini et al. (2001),
Michaelis et al. (1998), Morris et al. (1983),
Szargut (1961), Ziebik & Stanek (1997)
metallurgical processes; Barclay (1981) and
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Brodyansky & Ishkin (1962) the liquefaction
of gases ; de Lieto et al. (1983) and Gaggioli
& Wepfer (1981) building systems; De
Lucia & Manfrida (1990) and Sun & Xie
(1991) glass production; Dinale et al.,
(1992), Eskin & Kilic (1996), Ghamarian &
Cambel (1982), Segovia et al. (2003) and
Sieniutycz (1990) fluidised beds; Dincer
(2002), Kato (1981) and Szwast (1990) the
drying of solids; Gemici & Öztürk (1998),
Gong & Karlsson (2004), Helik (1972) and
Wall (1987) pulp paper processes; delle Site
& Sciubba (2001), Midilli & Kucuk (2003),
Sama (1989) biomass; Mozes et al. (1998),
Öztürk (2004) solar cooker; Petela (1984)
the grinding of solids, Saidi & Allaf (1999)
the vortex tube, Taprap & Phutthame (2003)
and Trägårdh (1981) the food industry;
Abbakumov (1975) and Brauer & Jeschar
(1963) industrial ovens.
6. Environmental Applications
Due to its very definition, it is intuitive
that exergy can be regarded as some sort of
environmental impact of a process:
unfortunately, the simple equivalence
“exergy discharge into the environment =
pollution” (Crane & al. 1990, 1992, Masini
et al. 2001), though -albeit only in partqualitatively correct, is incorrect from a
quantitative point of view.
The first papers approaching this
problem are those by Kraft (1974) and
Szargut (1974), in which an attempt is made
to assess the global impact of “energy
systems” on the environment, with specific
regard to the problem of the so-called
“global warming”. Mejer & Jørgensen
(1979), Jørgensen & Mejer (1981) and
Eriksson (1984) tried to explicitly apply the
thermodynamic function “exergy” to the
modelling of ecological systems: this line of
research was later developed to full potential
by Jørgensen (1992).
The problem has two facets, because
the “ecological cost” of what we generally
call “pollution”11 can be computed in
exergetic or in monetary terms: accordingly,
some Authors (Eriksson et al., 1976, Wall
1977, 1978, Szargut 1978, 1986, Valero &
For an important reflection on the difference
between what “pollution” represents for humans and
for Nature, see (Wall 1997)
Arauzo 1991, Ayres et al. 1998,
Makaritchev 1998, Zaleta et al. 1998, Zhang
& Reistad 1998, Rosen & Dincer 1999) have
computed the amount of exergetic
“consumption” that “makes up” for the
pollution, while others (Frangopoulos 1992,
von Spakovsky & Frangopoulos 1994) have
attempted to calculate the amount of
monetary expenses for remediation. This
second line of thinking leads directly to a
Thermo-economic treatment, developed in
fact by Valero (1998).
Resource recovery and recycling (to
minimize discharge into the environment) is
another closely related issue: papers on this
topic have been published by Otoma & Goto
(1979), De Lucia & Lanfranchi (1991),
Ayres et al. (1998), Connelly & Koshland
(2001), Dewulf & van Langehove (2002a),
Lattouf & De Oliveira (2003), Sciubba
A life-cycle analysis for the correct
treatment of the problem of the effluents has
been proposed by Finnveden & Östlund
(1997), Ayres et al. (1998), Cornelissen &
Hirs (2002) and Dewulf & van Langehove
The “environmental issue” is connected
to the concept of “sustainability”: the
problem is particularly complicated, because
sustainability is not a thermodynamic
concept (Second Law denies “strong”
sustainability!), and the issue is often marred
by a commixture of technical and nontechnical considerations. Papers on this topic
have been published by Jørgensen (1992),
Sciubba (1995a,b), Cornelissen (1997),
Rosen & Dincer (2001), Wall & Gong
(2001), and Dewulf & van Langehove
(2002b): most present research in this area is
aimed at finding an implicit or explicit
functional use of exergy in the analysis of
environmental issues.
Valero and coworkers (Valero &
Botero 2002, Valero et al. 2002) coined the
word “Exergo-ecology” to denote the
analysis of environmental effects performed
by means of exergy costing methods (see
Section 7 below).
7. The Exergy Cost (“k”) or Cumulative
Exergy Content (“CEC”)
Szargut (1978, 1987) must be credited
as the originator of this method: actually,
there is a long history of his previous littleknown publications in Polish journals
(starting already in the early 70’es) that
build up to the final concept. Michalek &
Stritzel (1990) applied the CEC method to
some process industries, and Szargut et al.
(2002) made further extensions. The central
idea is that, since exergy is additive, any
production chain may be seen as a series of
elemental processes, each one of which adds
some exergy to its inputs, destroys some
exergy in its internal irreversibilities, and
delivers a product endowed with some
“added exergy value”. The “final” product,
i.e., the one that is generated at the end of
the chain, has therefore a Cumulative
Exergy Content (expressed in kJ/unit) that
can be exactly computed once the
production process is known. Recursive
application of this technique leads to the
calculation of one (or more, if the same
product is generated by different production
lines) exergy cost (“k”12) or cumulative
exergy content (“CEC”) for each commodity
that we use in our society, including
dematerialized ones like power, electricity
etc. In Valero’s formalization, the theory of
the exergy cost asserts that it is possible to
express the exergy of the products as a
process-dependent function of the exergy of
the inputs:
EO = Π ( Ei )
Where the matrix Π is called the
transfer function of the process, and depends
on the process configuration, i.e., on the
connectivity of the system. Π is easily
obtained by properly assembling the exergy
destructions) of the individual components
(Valero et al. 1986, Sciubba 1995c). It must
be remarked that the “Cumulative Exergy
Consumption” and the “Exergy Cost” are,
by definition, exactly the same: in spite of
their rather different formalization, Szargut’s
and Valero’s methods are indeed equivalent.
8. Thermo-Economics
The idea of linking Thermodynamics
and costing considerations was explored first
by Lotka (1921), Keenan (1932), Benedict
In Valero’s original works, the exergy cost is
denoted by a capital B. We had to change the symbol
here, because “B” in this paper denotes the reference
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Gyftopoulos in 1980) and Gilbert (1956):
the clear concept that emerged from their
very general papers was that entropic
considerations ought to be somehow
accounted for in monetary cost calculations.
Beckmann (1953), Henatsch (1957) and
Szargut (1957) explicitly addressed the
problem of the correct cost allocation
between co-generated products (steam and
At the beginning of the 60’es that,
almost simultaneously and by independent
investigators, the joint application of exergy
analysis and engineering economics was
proposed, under the name of ExergoEconomics (in Europe, Rabek 1964, Szargut
& Petela 1964, Baehr et al. 1965,
Brodyanski 1965, Fratzscher 1965, Elsner
1965, Nitsch 1965, Bergmann & Schmidt
1967) and Thermo-Economics (in the US,
Evans 1961, Tribus 1961, Tribus & Evans
1962, Evans & Tribus 1965, El-Sayed
1970). The basic idea of this method is to
apply the usual procedures of Engineering
Accounting, linking the prices of
components to their operating parameters
and to their exergetic efficiency, and pricing
not the unit mass, but the specific exergy
content of a stream (material or energy).
If we attribute a monetary cost to the
exergetic inputs, this cost will be
incrementally increased in the various steps
of the process, due to the hardware and
operating costs that “add to the value” of the
successive production steps. Since in general
the production chain is not strictly linear,
some outputs from a certain component may
be split and constitute the inputs for two or
more of the remaining components;
conversely, two or more outputs may
constitute the input to a different component.
Therefore, to compute the cost of the final
outputs (the product streams) we need to
properly allocate the hardware costs (capital
& maintenance, for instance) among the
various outputs of each component: this can
be done mathematically (as shown by
Valero et al. 1986) by augmenting the
matrix Π with a proper set of auxiliary “cost
allocation equations”. The result is again a
matricial function in the form
CO = B( Ei , Ci )
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Since both Ei and Ci are in turn
functions of thermodynamic parameters xj,
material properties πk, hardware design
variables di and allocation criteria am (where
each suffix varies in its proper range), the
cost function CO can be rewritten formally
CO = Φ ( x j , π k , d i , a m )
Notice that Thermo-Economics can be
used in two different ways:
a) For a given configuration, one can
use Eqn. 10 to find the specific cost cO,n (€/J)
of the unit of exergy of each product. The
extensive cost CO,n (€/kg, €/J, €/unit) is then
found by multiplying cO,n by the proper flux
of that product (kg/s, J/s, units/s). This is the
original Tribus-Evans-El Sayed formulation,
and constitutes a noticeable improvement
with respect to the usual engineering
accounting procedures, that do not take into
account the exergy destructions in each
component. The method is especially useful
when more than one product is co-generated
by the same production line;
b) If the configuration can be changed
(by inserting additional components,
eliminating others or simply varying the
connectivity of the process), or if some of
the process parameters or design variables
can be changed, one can find the “optimal”
design point by means of a constrained
optimization procedure, in which the “fixed”
arguments in Eqn. 10 act as constraints, and
the parameters that can vary are the
independent variables of the optimization.
Lagrange multipliers were used by the first
Authors (see for instance Kotas 1985, Evans
1988, Gaggioli et al. 1988): the multipliers λ
turn out to be the marginal costs of the
respective products. Later, more general,
powerful and effective multi-variable
optimization techniques have been applied
(Fietzel et al. 1985, Frangopoulos 1992,
Sorin et al. 1992, Uche et al. 2003).
The word Thermo-Economics (TE) was
first used by Myron Tribus in his MIT
lectures, and the original developments are
due mainly to El-Sayed & Evans, and
independently to Elsner & Fratzscher. A
substantial contribution was provided by
Gaggioli, Reistad and Wepfer in the US,
who had to struggle at the time to find
access to archival energy journals for TErelated topics.
(1980, 1985) are the most relevant papers in
this field.
A more modern approach, based on an
elegant and very general matricial notation,
was developed only much later, by (Valero
et al. 1986 a,b,c; Valero et al. 1992 a,b,c),
and goes under the name of Structural
Thermo-Economics. It is based on the
construction of an “exergetic cost matrix”
assembled on the basis of the process
connectivity and of the rules of exergy
costing, and is formally entirely equivalent
to Eqn. 9 above. The present formalization
of the theory and applications of TE is due
entirely to Valero and coworkers, who in the
above quoted publications provided not only
a solid theoretical foundation, but also
opened the way to a series of important
applications to process and system analysis.
A formally slightly different method was
proposed by Szargut (1971, 1986),
Tsatsaronis (1990), Tsatsaronis & Krane
(1992), but in essence their approach is
embedded in Valero’s formulation.
Of importance is also the more
industry-oriented approach proposed by
Tsatsaronis et al. (2003), Cziesla &
Tsatsaronis (2003), as well as the efforts by
Szargut (1987) to include taxation effects
into the pricing structure.
After the publication of Valero’s works
in 1986, the interest in TE increased
steadily, and today most energy journals
offer at least 2 or 3 papers on TE in each
issue. A remarkable example of critical
comparison of contrasting theories and
concepts in thermoeconomics is provided by
the so-called “CGAM” project (Valero et al.
1994) that gave origin to four papers by
different Authors who tested their respective
approaches on the analysis of a Combined
Powerplant benchmark (Frangopoulos 1994,
Tsatsaronis 1994, Valero et al. 1994, von
Spakovsky 1994).
An extension to explicitly include into
the accounting a modelled set of
environmental externalities has been later
proposed by Szargut (1987) and,
independently, by Frangopoulos & von
Spakowski (1993). Further extensions, to
account for unsteady operating conditions
and to include life-cycle effects have been
proposed by Frangopoulos & von Spakovski
(1993) and Tober et al. (1999) respectively.
The early papers on this topic constitute
a difficult reading, because of the
determination of the exergy unit costs, the
different and often contrasting terminology
employed, and the not always crisply
defined general framework of the analysis.
Szargut (1957, 1969), Gruhn (1965), Panzer
(1965), Bergmann & Schmidt (1967),
Ponyatov (1968), El-Sayed (1970), El-Sayed
& Evans (1969a,b), Fratzscher (1973),
Kalinina & Brodyanskyi (1973, 1974), Borel
(1974), Beyer (1978, 1979a,b), Grubbstroem
Subsequent applications are very
diverse in scope, breadth and depth: Alvarez
et al. (2003) (fuel cell GT cycle), Avgousti
et al. (1989), Ben et al. (1989), Borgert &
Velasquez (2003, 2004) (Kalina cycle),
Frangopoulos & Nakos (2003), Kakaras et
al. (2003) (fuel cells), Jassim & Khir (2004)
(rotary air regenerator), Modesto et al.
(2003) (industrial cogeneration), Nikulshin
et al. (2003) (energy supply networks),
Gallo & Gomes (2003) and Rivero et al.
(2003) (combined cycles), Sahoo et al.
(2004) (absorption systems), Torres et al.
(1989), De Oliveira et al. (2003)
(trigeneration systems), Rücker & Bazzo
(2003), Silva et al. (2003) (cogeneration),
Velasquez & Sandrini (2003) (steam from
9. The Extension of the Concept and the
Inclusion of Externalities: 1980-2003
A concise modernization of the exergy
theory, with a strong emphasis on possible
applications to the analysis of complex
systems was presented by Göran Wall
(1977), who called exergy “a useful concept
in resource management”, to meet the
increasing needs of a sustainable
development (though the word “sustainable”
had not yet been coined at that time).
In Wall’s paradigm, the concepts of
human and industrial ecology are the only
tools capable of modeling the social
metabolism, i.e. the use of natural resources
as carriers of exergy in the society. Exergy
(destruction) can be seen as the driving force
of the evolution of all systems, from the
smallest living cell to the largest cosmic
Int. J. of Thermodynamics, Vol. 10 (No. 1)
object, and it is of the utmost importance
that its supply, distribution and use, for all
purposes, are performed in such a way that
its destruction be minimized. Through the
work of Wall, exergy applications have been
extended to include problems such as
“natural resource accounting” considering
both energy and material resources, life
cycle exergy analysis, environmental
environmental taxation that encourages
sustainable development.
Customarily, the production cost of a
commodity is expressed by a “Production
Function” f whose operands are the products
of the unit costs of each production factor by
an intensive measure of the factor itself (J
for energy, kg for materials, € for capital and
environmental cost, work-hours for Labour):
cj = f(C, M, E, L,O)
It has been shown (Fratzscher 1965 &
1967, Szargut 1978, Wall 1978c,
Grubbström 1980 & 1985, Momdjan &
Sciubba 1993) that it is possible to construct
a physical costing paradigm in which the
energy-, material and Environmental costrelated “Production Factors” are represented
in terms of exergy.
It is clear that once the three factors E,
M and O, which are per se incommensurable
with each other, are made homogeneous by
adopting exergy as the common quantifier
for all streams that flow “in” and “out of”
the process, the irreversibilities in the
production chain are better accounted for:
this is the basis of the Extended Exergy
Accounting (Sciubba 2000, see below).
There is no problem in expressing Energyand Material inputs and outputs in terms of
exergy: how to assign a proper exergy cost
to Environmental effects is still the topic of
some fundamental debate (Szargut 1973 &
1974, Frangopoulos & von Spakovsky 1993,
von Spakovsky & Frangopoulos 1993,
Valero 1995a & 1998, Sciubba 1999).
9.1 Process conversion efficiency
Aoki (1992) studied the behaviour of
complex processes at steady state; Lior
(2002) studied the implications of exergy
analysis on some possible trends in the
energy conversion systems; Michalek &
Stritzel (1990) analysed some materialprocessing technologies; Sciubba & Ulgiati
(2005), in a much broader context, provided
an exergy analysis of a corn-to-ethanol
distillation process. Tekin & Bayramoglu
(2001) provided an analysis of the sugar
production process; Wang et al. (2003),
Chen et al. (2003a,b) studied the exergy
destruction of a class of turbulent flows in a
Capital Production Factor
Material Production Factor M=
Energy Production Factor
Labour Production Factor
“Production Factor”
fK = unit cost of Capital
K = Capital (in monetary units)
fMi = unit cost of the i-th material
mi = mass flow rate of the i-th material (kg/s)
fEk = unit cost of the k-th energy flow
enk = energy content of the k-th stream (kJ/s)
fj = unit cost of the j-th Labour input
Wj = Labour (in workhours)
fj = unit environmental cost of the p-th
mp = mass flow rate of the p-th effluent (kg/s)
The symbol “O” here denotes the initial letter of the Greek word ’όικος (=home) whence all the “eco-” prefixes have
20 Int. J. of Thermodynamics, Vol. 10 (No. 1)
9.2 Process structure optimization
Aceves-Saborio et al. (1989) studied
the design optimization of heat exchangers;
Aglieri-Rinella et al. (1991) provided an
exergy-based optimization of a steam
generator for industrial applications; Bejan
& Siems (2001) applied exergy destruction
minimization to the identification of the
quasi-optimal design of an aircraft,
considered as an energy conversion system;
Chinneck (1983) applied a sort of exergyenhanced network theory to devise the
optimal structure of some thermal processes;
Dekhtyarev (1978) and El-Sayed (2002)
used an exergy analysis as a guide to
preliminary design optimization of cyclic
processes, while Doldersum (1998) applied
the same approach to identify the optimal
process modifications (revamping) of
thermal processes. The important problem of
optimal synthesis had been discussed
previously already by El-Sayed & Gaggioli
(1988), Evans et al. (1981), Gaggioli et al.
(1991) and Sama (1995a,b): notice however
that an exergy-based approach to the optimal
design of a HEN had been previously
proposed by Pehler (1983). Based on these
two latter works, Maiorano & Sciubba
(2000) and Maiorano et al. (2002) proposed
an exergy-guided intelligent design assistant
for Heat Exchanger Networks (HEN). In the
same line, Monanteras & Frangopoulos
(1999) devised an optimal design procedure
for a fuel cell-based powerplant. Szargut
(2002c) presented a slightly more general
formulation for optimal design, which can
be in principle applied to any process.
9.3 Exergy-based diagnostics
In two seminal works, Torres et al.
(2002) and Valero et al. (2002) elaborated
on an original proposal previously made by
Buergel (1974), and developed a method to
identify malfunctions in a component of a
process by studying their impact on the
exergy efficiency of other connected
components. Further work in this area was
published by Carraretto et al. (2003). A
similar method has been also distilled into
an Artificial Intelligence procedure by
Biagetti & Sciubba (2002, 2004). Lazzaretto
& Toffolo (2003), Verda (2003), Verda et al.
(2003), Zaleta et al. (2003) developed a TEbased diagnostic method, in which the fault
is identified by a “localised” increase in the
thermo-economical cost-formation chain of
the process: this line of work culminated in
the so-called “TADEUS” project (a
complete TE-Diagnostic procedure with an
application), which was published in 2004
byValero et al. Though it is true that the
actual effect of a malfunction can be
corresponding increase in the exergy cost of
the output, in our opinion an exergy-cost or
a TE analysis of a malfunction follows a
diagnostic act, and cannot anticipate it. It
must be remarked though that both Valero
and Verda express in their papers exactly the
opposite opinion.
9.4 Exergy life-cycle assessment
This is a line of research that has had
little momentum since it was proposed by
Cornelissen & Hirs (1997), but appears to
deserve more attention as present resourcemanagement strategies move towards
“sustainability”. In fact, all the most recent
methods of exergy analysis (including
Thermo-Economics, Cumulative Exergy
Accounting) take a life-time perspective,
and -at least in theory- trace the “exergetic
history” of a commodity from well or mine
to final disposal. It is interesting to remark
that the seed of Cornelissen’s work may be
found in earlier work by van Gool (1980,
1987) who started as an energy analyst and
only later (van Gool 1990) became an
exergy practitioner. Cornelissen & van der
Berg (2003) extended this line of research
9.5 Complex system
biological and societal systems
9.5.1 Complex Systems: The analysis
of complex systems by exergetic methods
consists in the adoption of exergy to express
the energy content of each material or
immaterial input- and output stream and of
exergy efficiencies to quantify the system
“performance”. Relevant papers are those of
Radebold (1974), Le Goff (1977), Morf
(1978), Morf (1978), Otoma (1979), Soma
(1983), Corliss (1986), Mansson (1986),
Malaska & Groenfors (1991), Valero &
Arauzo (1991), Rosen (1992), Schaeffer &
Wirtshafter (1992), Özdogan & Arikol
Int. J. of Thermodynamics, Vol. 10 (No. 1)
(1995), Sciubba (1995), Connelly &
Koshland (2001a,b), Nikulshin (2001),
Gogus et al. (2002), .
9.5.2 Biological Systems: The largest
number of publications in this area come
from the “emergy” arena14. The initial idea
can be traced back to the works of
Joergensen & Mejer (1977, 1981), in which
the Authors proposed to employ exergy as
an indicator for biological processes
(emergy had been devised for this purpose a
decade earlier). Further refinements of this
approach were discussed in Joergensen
(1981) and Jizhong et al. (1996).
Joergensen (1992a, 1992b, 2001,
2004)15, Joergensen et al. (1995, 2002a,b),
Salomonsen & Jensen (1996), Bastianoni &
Marchettini (1997), Marques et al. (1997),
Xu (1997), Fonseca et al. (2000), Ray et al.
(2001), Ray et al. (2001), Debeljak (2002),
Demirel (2004), Fabiano et al. (2004), Fath
& Cabezas (2004), developed several
applications of an approximate exergy
analysis of biological systems. Their works
are, in our opinion, characterised by a high
degree of originality and biological insight,
but also by a lack of thermodynamic rigor:
most of their applications rely on
equilibrium principles and are applied to
A discussion of the concept of emergy is beyond the
scope of this paper. Interested readers may consult the
original work by Odum (1970), or the brief and critical
discussion presented in Sciubba & Ulgiati (2005).
In 1948, C.E.Shannon, then at the Bell
Laboratories, published a paper on information theory,
A mathematical theory of communication. This was to
be literally the start of a new science, Information
Theory. In the context of this review paper, the
importance of Shannon’s work resides in his definition
of an “entropy function” that is depending on the
amount of information bits needed to completely
define the “state” of a (not necessarily
thermodynamic) system. The implication is obvious:
an exergy value can be attributed to information, or
putting it in other words, exergy is a measure of
information content. Similar concepts (using a
different definition of entropy) were developed by
L.Brillouin (1953), and in 1957 E.T.Jaynes published
a formal derivation of Gibbs’ results using Shannon’s
entropy as a starting point. Though the matter is far
from being clear in all of its implications, we prefer to
adopt Kline’s point of view here (Kline 1999): he
found some fundamental faults in the extension of
Shannon’s entropy to classical Thermodynamics that
invalidate the equation entropy=information (NOT the
concept: just the dimensional equivalence). There are
other ways to link exergy to information content, as
we shall discuss in Section 11 below.
Int. J. of Thermodynamics, Vol. 10 (No. 1)
living beings, which by definition are
systems far from equilibrium. The original
works from which such lines of research
stemmed are those of Knizia (1986) and of
course the famous book by Schrödinger
(1944), both of which were much more
rigorous and did not make recourse to
somewhat arbitrary “additional principles of
Another line of research was directed to
the definition of the modes and methods of
exergy analysis of complex (networking)
structures, always considered as systems
interacting with the Biosphere: Nielsen
(1995, 1997), Bendoricchio & Joergensen
(1997), Bianciardi & Ulgiati (1998),
Svirezhev (1997, 2000), Szargut (2003)
published relevant works in this field.
9.5.3 Societal Systems: The first author
to explicitly compute the exergy flow
diagram of a Nation was Reistad (1975),
who analysed the US system. The method
was extended and improved about ten years
later in a much-referenced series of works
by Wall (1986, 1990, 2002) and Wall et al.
(1994). Societal sectors have also been
analysed from a 2-nd Law point of view,
both in isolation: Le Goff (1977), Widmer &
Gyftopoulos (1977), Nakicenovic et al.
(1996), Ossebaard et al. (1997), Ptasinski &
Koymans (2004), and as an integral part of a
“societal control volume”: Azzarone &
Sciubba (1995), Ileri & Gürer (1998),
Ertesvag & Mielnik (2000), Ertesvag (2001,
2004), Mei & Wall (2001), Wall & Mei
(2001), Ayres et al. (2003).
The sustainability issue was discussed
on the basis of an exergy approach by
Cornelissen (1997), Kalf et al. (1997),
Cornelissen & Hirs (1999), Cornelissen et
al. (2000) and Cornelissen & Boersma
9.6 Extended exergy accounting
On the basis of a method developed by
Sciubba (1998), which may be traced back
to an idea published much earlier by
Grubbstroem (1985), a new field of exergy
analysis has emerged under the name of
Extended Exergy Accounting (“EEA”). The
method is a standard exergy analysis in
which Szargut’s CEC (see Section 7 above)
is augmented by additional exergy flows that
represent the exergetic equivalents of the
Remediation Production Factors (whence
the name “extended”): the final “balance” is
given by an equation formally identical with
eqtn. 8 above. Both in its method and in its
formalization, EEA is very similar to
Valero’s Structured Cost Theory (Section 8),
though there are some non negligible
differences in the form of the Transfer
Function Matrix Π. Applications have been
published by Milia & Sciubba (2000), Belli
& Sciubba (2001), Sciubba (2001, 2002),
Ertesvag (2003), Ptasinski & al. (2004).
10. Books
There are several books that treat
exergy in a (more or less) monographic
sense. The list provided here is probably the
most complete and updated reference
available today. Exergy researchers are
advised to carefully consult these
monographs, which offer different and often
contrasting definitions and approaches, but
definitely provide an enlightening view of
the development of the exergy concept
through the years.
The old works by Maxwell (1871), Tait
(1868), Jouget (1909) and Goodenough
(1911) are only of historical interest today.
Interesting are the early developments
presented by Bosnjakovic (1935) and
Keenan (1941), this second one with
fundamental applications that are still
relevant after over 60 years. Also
fundamental are the two books (in German)
by Schmidt (1953) and Baehr (1962) that
have influenced two or three generations of
european researchers in the field. Other
books on exergy are those of Martinowsky
(1950), Gourdet & Proust (1950), Marchal
(1956), Bruges (1959) and Ford et al.
More modern approaches are presented
by Ahern (1980), Kotas (1985) (which is a
recommended first lecture for graduate
students in the field), Moran (1982) (very
detailed and tutorial, also a recommended
lecture), and Sussman (1980). The two
works by Bejan (1982, 1988) are less
monographic and contain a substantial
portion of fundamentals, presented and
discussed with a very original approach. The
later monographic work by Bejan et al.
(1996) is presently the most referenced book
on Exergy analysis and Thermo-economics,
and finally, the two books by Szargut
(Szargut et al., 1988, and Szargut, 2005)
constitute essential (albeit advanced) reading
11. Review Papers, Nomenclature
Definitions and Bibliographies
The first review paper on exergy was
published by Gasparovic (1961) and -almost
concurrently- by Bosnjakovic ed. (1961): for
obvious reasons, both included rather few
mentioning are those compiled by Szargut
(1964), which includes several useful and
difficult to find references to works
published by Authors in the then Eastern
Block; by Baehr ed. (1965) and by Soma
(1983), who presented a relatively small list
of references and is rather limited in his
selection criteria. Another useful source was
the ACS Symposium Series 235 edited by
Gaggioli (1983). The most comprehensive
reference list (before the one attached to this
paper) is that compiled by Wall (1987),
which is very extensive even if not always
precise. Other lists were published by Kotas
et al. (1987); by Elsner (1993), which is
more a historical overview of the theory and
concepts than a real review paper; by
Cornelissen (1994) in his Ph.D. dissertation;
by Kay (1989, placed on the web in 1998);
and by Rezac & Metgalchi (2004), who
approached the subject from a more
theoretical viewpoint, privileging concepts
rather than completeness.
12. What Next? A (Biased) Look Into the
To foretell “whereto exergy analysis is
going” is a double-edged argument:
furthermore, the present authors are
obviously rather strongly biased towards
“Complex Systems” issues, and this might
have influenced our conclusions here below.
However, with the obvious caveat that such
a prediction has to be taken with care, we
can conclude that:
1) It is clear that Process Analysis will
see more and more applications of Exergy
methods. The present ever increasing
number of publications in the field of
organic- and inorganic Chemical Processes
is a sure sign that accounting for real process
Int. J. of Thermodynamics, Vol. 10 (No. 1)
irreversibilities provides a better grasp of
even complex processes such as distillation,
petroleum cracking, etc.
In the Energy Conversion arena, there
is today practically no process- or cycle
analysis that does not include exergy
considerations. This can be regarded as a
very mature field, and it seems that the
exergy methods are on their way to being
regarded as standard industrial analysis
procedures. There are still issues that need to
be addressed in more depth and breadth,
even at fundamental level: life-cycle exergy
analysis of real processes, the influence of
dynamic operation, the analysis of Very
Large Complex Systems are examples. But
we cannot detect theoretical hindrances on
the way of constant advances and
refinements of both theoretical and
application-oriented exergy analysis.
Exergy-based optimization procedures
exist, and more will undoubtedly be
developed in the future. A present limit here
is posed by the immense computational
resources required by a complete
optimization of systems with a high number
of relevant parameters (each one of which
constitutes a degree of freedom for the
2) It is also rather clear that ThermoEconomic methods will be more and more
extensively adopted in the assessment of
industrial processes and production cycles.
There are still some issues as to the
inclusion of environmental considerations
into TE, and some major research effort is
needed in this area, because the presently
proposed solutions are not entirely
3) System synthesis is most likely the
“next frontier”: the possibility of
formulating an optimization problem in
which the independent variables are not only
related to process parameters but also to
process configuration is very real already at
present: at least formally, the problem can
be solved by MILP techniques (Muñoz &
von Spakovsky 1999), Genetic Algorithms
(Toffolo & Lazzaretto 2002), and Artificial
Intelligence techniques (Melli et al. 1992,
Sciubba & Melli 1998). Practical
applications to simple systems (i.e., systems
with few independent variables) have
already been published. Large complex
Int. J. of Thermodynamics, Vol. 10 (No. 1)
“optimization”. Notice that since the goal of
system synthesis is the minimization of the
“product cost” (monetary or exergetic), the
costing functions can be conveniently
Thermoeconomics, Cumulative Exergy
Content and Extended Exergy Accounting.
Thermoeconomics seems to be the one that
is more likely to be used in practical
applications in the near future, EEA being a
good but rather distant second. Interesting
are also some attempts based on heuristics
(like the search for an optimal geometry of a
gas turbine blade, or similar CFD-based
exergy destruction calculations, see next
point here below), that show potential of
being transformed into automated -albeit
4) It is possible, and highly desirable,
that the application of exergy methods be
expanded into the realm of thermofluiddynamics applications. Under the
continuum hypothesis, the local entropy
generation rates can be computed by most
present CFD codes, and therefore the exergy
destruction in heat- and fluid flow can be
properly assessed even at local level: this
may lead to the concoction of more effective
design methods for fins, compact heat
exchangers, ailerons, surface treatment
and/or injection/suction, etc. This is an area
in which not much has been published to the
date of this writing (see though Bejan 1982,
Carrington & Sun 1992, Fewell et al. 1981,
Harrison & Dean 1978, Kouremenos 1971,
Natalini & Sciubba 1994 & 1999,
Poulikakos & Bejan 1982, Sciubba 2004),
but which might open up entirely new
perspectives as energy (exergy!) efficiency
becomes a more important issue.
5) The interconnection of the exergy
concept with “environmental issues” (taken
in their broader sense) is also likely to be
explored in more depth. Exergy per se is
NOT a measure of environmental impact,
but in essence at the end of the life cycle of
any device, plant and product, the exergy
“balance” of the extraction-transformationproduction-distribution-use-disposal cycle
shows how many primary exergy resources
have been actually used up (consumed), and
there are already some studies that address
the issue of designing “more exergyconscious” production cycles to attain a
higher degree of sustainability.
6) In a closely related field, namely the
analysis of “living” systems, we are not so
optimistic. Exergy is a thermodynamic
function defined for equilibrium or quasiequilibrium processes, and its extension to
far-from-equilibrium systems (as all living
systems are) is not to be taken for granted.
Thus, unless some breakthroughs in
irreversible thermodynamic are made, we
neither foresee nor favour exergy analyses
of plants, forests, bacterial colonies and the
like, and much less those of human beings.
In some living systems analyses, the
use of an “information exergy” is proposed.
This exergy is considered to correspond to
the genetic “information” contained in the
DNA. We must remark that a) there is no
proven link between exergy and information
except in a strictly physical sense specified
under point 7 here below, and b)
“thermodynamics of life” -if such an object
exists!- goes well beyond the concept of
“transmitting information”.
7) Cumulative Exergy Consumption
methods are likely to see more and more
applications in the near future. They provide
an extremely clear picture of the “resources”
used up (incorporated in) the production of
goods. They can be extended to include
immaterial services, and (like in EEA) they
can account for labour and capital as well,
thus paving the way to the calculation of an
“exergy cost” of commodities measured in
kJ/unit (as in CEC and EEA) instead of €/kJ
(as in Thermo-Economics). An open
problem for CEC is its neglect of Labour
and in general of all immaterial production
factors; but this issue is being already
debated in the literature, and it is likely that
a satisfactory solution can be found. This
would be good news, because there are
numerous proposed applications to the
analysis of societal systems that could
greatly benefit from the existence of an
accepted paradigm.
8) Application of exergy analysis to
microscopical physics appears problematic.
The current paradigm prescribes that, once
either the continuum and/or the equilibrium
hypothesis are abandoned, exergy becomes a
matter of convention. In their 1976 work
(see Section 4.1 above) Hatsopoulos and
Gyftopoulos argue against this view, and
propose an extension of the definition of
exergy that applies also to microscopic nonequilibrium systems. In our opinion, the
issue awaits clarification, and some
additional research is definitely needed in
this field.
9) The few attempts to define “the
exergy content of one bit of information”
(based on mind-experiments performed on
boxes and “pistons” with 1, 2 or 3 atoms)
strongly suffer from a lack of well-founded
theoretical development. Notice that in their
above quoted works, Hatsopoulos and
Gyftopoulos (1976a,b,c,d) argue quite
strongly from a theoretical and mathematical
standpoint that such an informational
framework contains a built-in violation of
the 2nd Law. A more formal critique has
been raised by Kline (1999, see footnote #15
on previous page). We must stress that in
our view the only reasonable way to account
for information is at present a CEC or an
EEA approach, in which the amount of
physical resources expended for the
generation of 1 bit of information can
actually be computed on the basis of an
analysis of the process that generates this
bit: also this view is, of course, in dispute.
10)On the opposite, an application of
exergy analysis to macroscopic physics
(astronomy, for instance) appears possible,
even if no example is known to us as of
2004 except for Jørgensen et al. (1998).
Since exergy includes both gravitational and
radiation effects, it is in principle possible to
perform an exergy “balance” of a galaxy
(the "reference environment" being the 3K
residual radiation field). Far fetched as it
may seem, such an analysis might lead to
interesting finding on the entropy generation
rate of the Universe.
List of Symbols
Reference system, Biosphere
Molar concentration
Specific heat, J/(kg K)
Exergy, J/kg
Gravitational constant, m/s2
Gibbs free enthalpy, J/kg
Enthalpy, J/kg
Electric current, A
Radiative energy flux, W/m2
Int. J. of Thermodynamics, Vol. 10 (No. 1)
Specific thermal energy, J/kg
Gas constant, J/(kg K)
Entropy, J/(kg K)
Time, s
Absolute temperature, K
Internal energy, J/kg
Velocity w.r.t. Galilean frame, m/s
Specific work, J/kg
Elevation, m
Greek symbols
Electrical potential, Volts
Exergy efficiency
Energy efficiency
Chemical potential, J/kg
Stephan-Boltzmann constant, W/(m2K4)
Degree of irreversibility
Coefficient of exergetic destruction
Int. J. of Thermodynamics, Vol. 10 (No. 1)
0 Reference conditions
irr Irreversible
The present paper contains over 2600
references: it was clear from the onset that it
would have been impossible to include a
regular “Reference List”. We decided
instead, with the permission of the IJoT
Editor, to attach here a link to the Journal
web-site where the cited works are properly
listed. We will be grateful to readers who
suggest additions or corrections to this list.
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