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INT. COMM. HEAT MASS TRANSFER 0735-1933/88 $3.00 + .00 Vol. 15, pp. 571-580, 1988 ©Pergamon Press plc Printed in the United States RESEARCH INTO THE ORIGINS OF ENGINEERING THERMODYNAMICS Adrian Bejan Department of Mechanical Engineering and Materials Science Duke University Durham, NC 27706, USA (Ccmmunicated by J.P. Hartnett and W.J. Minkowycz) ABSTRACT This paper draws attention to a series of misconceptions and misstatements regarding the origin and meaning of some of the most basic concepts of engineering thermodynamics. The six examples exhibited in the paper relate to the concepts of reversibility, entropy, mechanical equivalent of the calorie, the first law of thermodynamics for open systems, enthalpy and the Diesel cycle. A complete list of the pioneering references concludes the paper. Obiective The discipline of Engineering Thermodynamics revolves around a relatively large number of good introductory treatments, which - in my view - are all very similar except for certain variations in writing style and graphics quality. It would seem that for generation after generation Engineering Thermodynamics has flowed from one book into the next, essentially unchanged. Today the textbooks describe a seemingly moribund engineering discipline, that is, a subject void of controversy and, most regrettably, references. As students, we are brought in contact with a discipline whose step-by-step innovations seem to have been long forgotten. Traveling back in time to "rediscover" the origins of the discipline is a task tackled only by a curious few. This situation presents a tremendous opportunity for the researcher. I recognized this opportunity four years ago when I began work on a graduate treatise on engineering thermodynamics [1]. In the course of that work I made numerous trips to the Library of Congress, in Washington, DC, where many of the original writings can be located. The many facts and references I discovered are 571

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Page 1: Research into the origins of engineering thermodynamics

INT. COMM. HEAT MASS TRANSFER 0735-1933/88 $3.00 + .00 Vol. 15, pp. 571-580, 1988 ©Pergamon Press plc Printed in the United States

RESEARCH INTO THE ORIGINS OF ENGINEERING THERMODYNAMICS

Adrian Bejan Department of Mechanical Engineering

and Materials Science Duke University

Durham, NC 27706, USA

(Ccmmunicated by J.P. Hartnett and W.J. Minkowycz)

ABSTRACT This paper draws attention to a series of misconceptions and misstatements regarding the origin and meaning of some of the most basic concepts of engineering thermodynamics. The six examples exhibited in the paper relate to the concepts of reversibility, entropy, mechanical equivalent of the calorie, the first law of thermodynamics for open systems, enthalpy and the Diesel cycle. A complete list of the pioneering references concludes the paper.

Obiective

The discipline of Engineering Thermodynamics revolves around a relatively large number of good introductory treatments, which - in my view - are all very similar except for certain variations in writing style and graphics quality. It would seem that for

generation after generation Engineering Thermodynamics has flowed from one book into the next, essentially unchanged. Today the textbooks describe a seemingly

moribund engineering discipline, that is, a subject void of controversy and, most regrettably, references. As students, we are brought in contact with a discipline whose

step-by-step innovations seem to have been long forgotten.

Traveling back in time to "rediscover" the origins of the discipline is a task tackled only by a curious few. This situation presents a tremendous opportunity for the researcher. I recognized this opportunity four years ago when I began work on a graduate treatise on engineering thermodynamics [1]. In the course of that work I made numerous trips to the Library of Congress, in Washington, DC, where many of the original writings can be located. The many facts and references I discovered are

571

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572 A. Bejan Vol. 15, No. 5

now blended with the more recent and more controversial thermodynamics ideas in the final version of my book [1].

In this article I use six examples to draw attention to one class of discoveries

that contradict some of the "historical notes" sprinkled throughout a number of today's

introductory books. At first, I found this string of contradictions surprising, because I

learned the subject by reading (and later teaching from!) the same introductory texts.

In retrospect, what I found supports the point made by Truesdell [2], namely, that it is

much easier (and potentially inaccurate) to quote from a certain piece of work third-

hand, than to go to the trouble of digging up the original (usually, one hundred year

old) ,paper or book. It is certainly easier to quote or, worse, copy from a book

published in English five or ten years ago, than to read the French, German, Italian,

Latin and Russian in which some of the pioneering work was written.

But why else might one worry about setting the record straight and attempting to

assign credit where due, when those involved are long dead? There are a number of

reasons. First, the theory of engineering thermodynamics is a precious and colorful

one. Why rob the field of its fascinating past when therein lies much of its appeal?

Second, the pioneers of the field deserve credit. And they can provide powerful role

models for all of us, if we make an effort to understand them (their personality,

research methodology, fights, disappointments and victories en route to "making it").

In addition, the pioneers are often the best teachers when it comes to explaining the

exotic language of energy, enthalpy, entropy and exergy. Third, an understanding of

the origins of our research fields is necessary for good scholarship on our part. And

our exhibiting good scholarship provides our own students with a powerful role model.

Reversibility

Consider as a first example the concept of a reversible cycle. There is little

disagreement on the greatness of Sadi Carnot's intuitive description of a "limiting"

cycle that consists of a succession of equilibrium states, and of his claim that the efficiency of such a cycle depends only on the temperatures of the two heat reservoirs

and not on the choice of working fluid [3]. Unfortunately, Sadi Carnot's premature

dea(h of cholera in the epidemic of 1832 and the belated discovery of his theory left most of us with the impression that his revolutionary ideas materialized out of thin air.

I use this as an opportunity to draw attention to a growing body of literature that paints an entirely different picture [4-7].

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VOI. 15, NO. 5 ORIGINS OF ~ ~ C S 573

The concept of reversibility in cyclical operation was formulated first by Sa~li's father, Lazare Nicolas Marguerite Cat'not (1753-1823), as an essential condition for maximizing the efficiency of purely mechanical energy converters (mechanisms). in his treatise on engineering mechanics [8,9], Lazare Camot argued thatthe efficiency of a "machine" is maximum when violent effects such as percussion and turbulence (when fluid machinery is involved) are avoided. Lazare Cmnot referred to this limiting and most efficient regime of operation as "geometric motion'.

It is also true that with so little material evidence left after Sadi's death and the atmosphere of political disrepute that surrounded Lazare'S final years, much of the apparently "filial" relationship between Sadi's heat-engine theory and Lazare's theory of mechanisms can only form the subject of educated Speculation. Interesting reading in this direction is provided by Refs. [5,6], which focus on Sadi's adolescence and engineering studies, when Lazare's occupation was that of recording secretary for the Institul; de France. In that capacity Lazare Camot had to examine first-hand and comment on a number of inventions that dealt with heat engines. At the end of such reading Sadi Carnot's analogy between the fall of a water stceam through a work- producing water wheel and the fall of caloric through a work-producing heat engine emerges as an understandable product of the intellectua4 environment in which he was raised. His vision that the temperature differences between the heat engine end the heat reservoirs must be avoided, emerges as a very powerfu! generalization of Lazare Carnot's principle of avoiding the free-fall of water upstream and downstream of the waterwheel.

The thermodynamic property entropy, S, is introduced by writing

~ r e v dS = - - (1) T

in which ~lrev is the infinitesimal heat transfer interaction during a reversible process and T the absolute (thermodynamic) temperature of the closed system that is being considered. Credit for its discovery is given usually to Clausius, who - it is true - invented the name "entropy" in 1865:

"...I have felt it more suitable to take the names of important scientific quantities from the ancient languages in order that they may appear unchanged in all contemporary languages. Hence ! propose that we call S the entroDv of the body after the Greek word '1] Cpo~q', meaning "transformation'.

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574 A. Bejan Vol. 15, No. 5

I have intentionally formed the word entropy to be as similar as possible to the

word energy, since the two quantities that are given these names are so

closely related in their physical significance that a certain likeness in their

names has seemed appropriate" [10].

In fact, the same property was discovered and used as early as 1855 by Rankine

[2,11]. He called it "thermodynamic function" (which it certainly is), labeled it ~ instead

of S, and regarded equation (1) as "the general equation of thermodynamics".

Th~ Mechanical Eeuivalent of the Calorie

An important development that led to the formulation of the first law in classical

thermodynamics was the idea that "heat" and "work" are equivalent, i.e. that their

respective units - which historically had been regarded as different - are

interconvertible. In some modern treatments of engineering thermodynamics, Joule's

name alone is attached to this theoretical development. The published record,

however, shows that the idea of the convertibility of heat units into work units was

published independently by Mayer in May 1842 [12] and Joule in August 1843 [13].

This dual approach to such a great step is a perfect example of how differently two

individuals can think, and a very strong case for the free access to the marketplace of

ideas, as the best recipe for scientific progress. For an important item in the history of

the first law is the fact that both Mayer and Joule had difficulty in getting their papers

published and in being taken seriously by their established contemporaries.

Mayer was the theoretician, the man obsessed by the idea: he conceived it in

circumstances that even today appear removed from the thermodynamics scene

(more on this shortly), and then relied on the contemporary state of knowledge in

order to support its validity. Joule, on the other hand, was the ultimate

experimentalist: he first discovered in his measurements that the heat generated by

electrical resistances is proportional to the mechanical power required to generate

the electrical power. He then recognized the importance of this proportionality and

drew the revolutionary conclusion that a universal proportionality must exist between

the two effects (work and heat). Only to polish this idea and to convince the skeptics

(e.g. the Royal Society) he produced a series of nakedly simple experiments whose message proved impossible to refute. From the point of view of mechanical

engineers, the most memorable among these experiments was the heating of a pool of water by an array of paddle wheels driven by falling weights.

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Vol. 15, NO. 5 ORIGINS OF ~ G ~ N G THEI~ODYNAMICS 575

Mayer was very clear about the meaning of his theory: "We must find out how

high a particular weight must be raised above the surface of the earth in order that its

falling power may be equivalent to the heating of an equal weight of water from 0 ° to

1°C" (Ref. [12], p. 240). He reasoned that an amount of gas needs to be heated more

at constant pressure than at constant volume, because at constant pressure it is free

to dilate and do work against the atmosphere; in today's notation we would write

mcp&T- mcvAT = Patm&V (2)

Using the (Cp) and (Cp/Cv) constants that were known in his time he estimated the left-

hand-side of the equation in calories, while the right-hand-side was known in

mechanical units. He established the equivalence between these units numerically

by listing "365m" as the answer to the question quoted earlier in this paragraph.

Worth noting is that if we use

Pv = RT (3)

Mayer's argument (2) reduces to

cp - Cv = R (4)

This classical relation between the specific heats of an ideal gas used to be

called Maver's eauation. Forgotten seems also the fact that the ideal gas equation of state (3) was first written down by Clapeyron [14], which is why it used to be called

Qlaoeyron's 0ouation.

Th0 First L~,w for Ooen (or Flow~ Systems

When one hears of the history of classical thermodynamics one thinks of the

closed-system formulations that were debated by the pioneers (Rankine, Clausius

and Kelvin). Yet, in engineering thermodynamics we use primarily the open-system

formulations: it is then reasonable to ask who was the first to extend the closed-

system laws of classical thermodynamics to the class of open systems.

The first law for open systems was first stated by Gustav Zeuner as part of the

analysis of flow systems that operate in the steady state. He made this result known

primarily through his technical thermodynamics treatise whose first German edition

was published in 1859 [15]. Equally impressive is that Zeuner saw and stressed the

important role played by the first law in fluid mechanics next to the other equations

that in his time were recognized as the pillars of fluid and gas dynamics [16].

Zeuner's name never made it into the fluid mechanics vocabulary; more surprising is

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576 A. Bejan Vol. 15, No. 5

that it disappeared from engineering thermodynamics beginning with the turn of the century.

The most recent reference I can find in connection with "Zeuner's formula" is in Stodala's treatise on steam turbines, first published in German in 1903 [17]. In our notation, Zeuner's formula for the heat transfer rate to a stream rn in steady flow and without shaft work is

V 2 d(~ = d(u + Pv + y + gz) (5)

The argument on which the derivation of this formula was based is present in virtually every engineering thermodynamics treatise of this century,

Emtu =

Another noteworthy example of death and forgetting in engineering thermodynamics has to do with the invention of the word "enthalpy'. First, it is interesting that the widespread use of the term in engineering was tdggersd by the work of another professor from the old University of Dresden, Richard Motlier (the other influential Dresden figure had been Gustav Zeuner), Mollier recognized the importance of the group (u + Pv) in the first-law analysis of steam turbines, next to entropy (s) in second-law analysis. He presented graphically and in tabular form the properties of steam as the now famous enthalpy-entropy chart (the MoUier chart, h-s) [18].

Mollier referred to the group (u + Pv) as "heat contents" and "total heat" and labeled it "i". G.A. Goodenough, famous professor of thermodynamics at the University of Illinois, called i "thermal potential" and "thermal head" [19]. The symbol i was used until about twenty years ago in the engineering thermodynamics taught in German, Russian and in the languages of Central Europe. Mollier's contdbution is not the discovery of the group (u + Pv) - this group was known already as Gibbs' "heat function for constant pressure" (symbol Z, Ref. [20]) - rather, it is the invention of an important graphical tool whose impact on the efficiency of slide-rule calculations in thermal design is beyond question.

From the point of view of North American engineers, Moilier's "total heat" appears to have been replaced spontaneously by the term "enthalpy" somewhere in the 1930's. Some authors explain the correct pronunciation of enthalpy (e.g. Ref. [21]), however, the originator of this terminology is not mentioned. The name

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Vol. 15, No. 5 ORIGINS OF ]~qGIN]~RIh~ THEI~MODYNAMICS 577

"enthalpy" was coined by Kamerlingh-Onnes [22], professor at the University of

Leiden, otherwise famous for having been the first to liquefy helium and to discover the phenomena of superconductivity and superfluidity. Onnes invented also the names "superconductivity" and "superfluidity". Part of the mystery that persists in the

wake of Kamerlingh-Onnes' innovations is due to the limited circulation enjoyed by

his original writings, for which he used Dutch as language and the bulletin of his own low temperature laboratory as journal [23].

The Diesel CVCI~

We have all been taught that one of the breakthroughs made possible by the invention of the Diesel cycle was the elimination of the need to use spark plugs in

order to achieve ignition. A reading of Rudolf Diesel's original writings shows that this popular view is wrong both historically and thermodynamically. In fact, this view was so shallow that it angered Diesel, forcing him to continue to explain his invention three decades after the fact [24,25]:

"It is often asserted without hesitation by the laity even in scientific circles that the important point of the Diesel process is the self-ignition of the fuel; and

that the object of the high compression is that the fuel, injected at the dead

center, shall ignite itself, the high degree of compression being demanded by this self ignition.

Nothing is more incorrect than this superficial view, which is directly contrary to the facts and especially to the historical development of the idea.

Motors with self-ignition of the fuel had existed before. Neither in my patents nor in my writings did I mention self-ignition as a goal to be sought. I was

seeking a process with the highest heat efficiency, and as it turned out, self- ignition was naturally involved in this."

Conclusions

Much more can be written about the origins of engineering thermodynamics and how the pioneering work of the 1800s has produced our modern discipline and

language [1]. And, certainly, some of the facts debated in the above examples can be found in the better researched engineering textbooks of our time. The benefits of

presenting an accurate history of a subject along with the subject itself go well beyond the making of an abstract course more human and meaningful to an engineer. This balanced approach represents an elegant and erudite way of tempering the fads of

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578 A. Bejan Vol. 15, No. 5

the engineering profession, for example, the shaping of all engineering into analysis

and "science" in the 1960s, and how the computerization of everything in the 1980s.

A careful study of the original sources can teach us a great deal about being

successful as researchers ourselves. To illustrate this point, the best I can do in such

a short space is quote Cardwell [26] who, while commenting on Count Rumford's

career, wrote:

"A successful scientist would appear to need four particular gifts:

- a minimum of technical competence, or ability to use the tools of the

trade, whether laboratory equipment or pencil-and-paper,

- a flair for detecting possibilities not recognized by his colleagues - to recognize, that is, the "growth points" before others do,

- the courage to continue working even though results are slow in

coming, and lastly,

- the ability to convince others of the significance and validity of what he

has done.

...It is not worth possessing the first unless one possesses the other three in

some measure. However, modern educational and institutional arrangements

seem to emphasize the importance of the first to the almost total exclusion of

the others."

,

2.

.

4.

5.

.

Rgfi~rences

A. Bejan, Advanced Enaineedng Thermodynamics, Wiley, New York (1988).

C. Truesdell, Rational Thermodynamics, second edition, Springer-Verlag, 1-3 (1984).

S. Carnot, Relfections on the Motive Power of Fire. and on Machine~ Fitted tO Develoo that Power, Bachelier, Paris (i824); also as ReflectJons on the Motiv~ Power ¢)f Fire and Other Papers, E. Mendoza, ed., Dover, New York (1960).

E. Mendoza, Contributions to the study of Sadi Carnot and his work, Arch. Int. ~ , 377-396 (1959).

M. J. Klein, Carnot's contribution to thermodynamics, Phys, Today, 23-28 (August 1974).

T. S. Kuhn, Sadi Carnot and the Cagnard engine, ~ , 567-574 (1961).

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VOI. 15, NO. 5 ORIGINS OF ]~GINE~RING THEIqM3DYNAMICS 579

.

.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

M. V. Sussman, Availability {Exergy) Analysis, Mulliken House, Lexington, MA (1981 ).

L. Carnot, I~ssai sur les Machines en G(m~ral. Dijon (1783).

C. C, Gillispie, Lazare Carnot Savant. Princeton University Press, Princeton, NJ (1971).

R. Clausius, On different forms of the fundamental equations of the mechanical theory of heat and their convenience for application, first presented to the ZOricher naturforschende Gesellschaft on April 24, 1865, printed in Quarterlv Journal of the Gesellschaft 10, 1, and in Poaoendorfs Annalen 125. 313 (1865); an English translation by R. B. Lindsay can be found in The Second Law of Thermodvnamics. J. Kestin, ed., Dowden, Hutchinson & Ross, Stroudsburg, PA, 162-193 (1976).

W. J. M. Rankine, On the hypothesis of molecular vortices, or centrifugal theory of elasticity, and its connexion with the theory of heat, Phil. Maa., ser. 4, no. 67, 354-363 (Nov. 1855) and no. 68, 411-420 (Dec. 1855); also, (gn the thermal energy of molecular vortices, Trans. Rov. Soc. Edinburah 25, 557-566 (1869).

J. R. Mayer, Remarks on the forces of inorganic nature, Annalen der Chemie and Pharmacie 42, 233-240 (May 1842).

J. P. Joule, On the calorific effects of magneto-electricity, and on the mechanical value of heat, ~ (1843).

I~ Clapeyron, Memoir on the motive power of heat, Polvtechniaue 14 (1834); translated in Reflection~ on the Motive Power of Fire and Other Paoers. E. Mendoza, ed., Dover, New York (1960), and in The Second Law of Thermodvnamics. J. Kestin, ed., Dowden, Hutchinson & Ross, Stroudsburg, PA, 36-51 i1976).

G. Zeuner, Technical Thermodvnamics. first English edition, translated by J. F. Klein, Van Nostrand, New Yo~, 225-231 (1907).

G. Zeuner, D as Locomotiven-Blasrohr, Mayer & Zeller, Zurich (1863).

A. Stodola, Steam Turbines (with an Appendix on Gas Turbines and the Future of Heat Engines), translated by L. C. Loewenstein, Van Nostrand, New York (1905).

R. Mollier, The Mollier Steam Tables and Diaarams (Extended to the Critical Pressure), translated by H. Moss, Pitman, Lor/don (1927); the first German edition appeared in 1906.

G. A. Goodenough, Princioles of Thermodynamics, third edition, Holt, New York, 85 (1932); first published in 1911.

J. W. Gibbs, The Collected Works of J. Willard Gibbs 1, Longmans, Green & Co., New York 51 (1928).

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580 A. Bejan Vol. 15, No. 5

21. P.J. Kiefer and M. J. Stuart, Pripci~:)les of Engineering Thermodynamics, Wiley, New York, 52 (1930).

22. A.W. Potter, The generation and utilization of cold. A general discussion - general introduction, Tr~,n$. Faraday Soc. 18. 139-143 (1922-1923).

23. F.A. Freeth, "H. Kamerlingh Onnes, 1853-1926," Nature 117, no. 2940, March 6 (1926); also Annual Reoort of the Smithsonian Institution, 533-535 (1926).

24. R. Diesel, Die Entstehune des Dieselmotors, Berlin (1913).

25. F. Klemm, A History of Western Technology. MIT Press, Cambridge, MA (1964).

26. D.S.L. Cardwell, From Watt to Clausius. Cornell University Press, Ithaca, NY, 310 (1971).