im. J. Heat Mass Tramfer.

Vol. 7, pp. 125432.

PergmamonPress 1964.

Printed in Great Britain

THE WORKS OF RICHARD MOLLIER*
L. M. K. BOELTERt
Departmentof Engineering,and ELDON

University of California,

L. KNUTH:
Los Angeles 24, California(RecfGed 1 Ocfober 1963)

at the end of which time he was admitted as
Privatdozent. He was awarded the degree of Doktor der Philosophie three years later, in 1895.
He was called, in the fall of 1896, to theposition of pIanmHssiger ausserordentlicher
Professor fir angewandte Physik und Maschinenlehre at the Universitat Gijttingen; a year later,
at the age of 33, he was called to the position of
BIOGRAPHICALSKETCHordentlicher Professor fiir Technische Thermodynamik
at the Sichsischen
Technischen
Although a biographical sketch of Mollier
is not the primary purpose of this paper, a Hochschule in Dresden, succeeding Professor
brief review is provided in order to place his Gustav Zeuner. Here Mollier taught for 36
works in perspective. More detailed biographicalyears until his retirement at the age of 69. He
passed away two years later, after a very briefi~ormat~on is provided in the one biography,
the three necrologies and the five notices “Zumillness, on 13 March 1935.
70. Geburtstag” listed in Volumes VI and VIIa
As will be brought out in the paragraphsof J. C. Poggendorfls b~ographj~ch-ii?erar~sches which follow, Richard Mollier’s professional
Hanhvorterbuch.
career was motivated largely by a desire toRichard Mollier was born in Triest on 30 provide engineers with aids for the solution ofNovember 1863, the oldest son of Eduard
difficult problems of thermodynamics,
heat
Mollier, director of the Tries& Maschinentransfer and mass transfer; his success was due
fabrik und Schiffswerft. His mother was the largely to his effective use of graphical methods,
daughter of Carl von Dyck, director of the The concern for the engineer’s problems may
Kijniglich Bayerschen Eisenbahn. After passing be traced to his family background; his effectivewith distinction the final examination at the use of graphical methods in thermodynamics
Deutschen Gymnasium in Triest in 1882, appears to have roots in the works of J. Willard
Richard Mollier studied mathematics and Gibbs and Gustav Zeuner. Gibbs’ first two
physics for two years at the Universitit, Graz,
papers, [l, 21, were pubIished originaHy in 1873
and Mechanical Engineering for four years at and translated by W. Ostwald into German in
the Technische Hochschule, Mlinchen. From1892 [3]; Zeuner’s Thermodynamics texts [4]1888 to 1890, he worked as an engineer in his and [Sl appeared respectively in 1860 and infather’s machine factory and shipyard. He 1890. Mollier’s writings indicate a high respect
returned then to Miinchen. where he served for for the effective use of graphical methods
two years as Assistant fir Theoretische
exhibited by these two thermodynamicists.
Maschinenlehre with Professor Moritz Schrater,_-- .-_PUBLISHED WORKS* Prepared as acontribution to the MolliercommemoraA chronological list of the published works oftion issue, accepted after deadline.
Richard Mollier known to the authors is appent Professor and Dean of Engineering.
ded as a Bibliography. Brief scentson these
2 Associate Professor and Head of Chemical, Nuclear
works follow.
and Thermal Division.
FOREWORD

ON the hundredth anniversary of the birth ofRichard Mollier, a brief review of his publishedworks and of the influence of these works upon
the engineering profession is appropriate. We
have attempted, in the paragraphs which follow,
to provide such a review.

125
HM

f

A

126

L. M. K. BOELTER

and ELDON

Mollier’s first paper [Bl], his Habilitationss&rift, clarifies and extends, for the benefit of
the engineer, the use of the temperature-entropy
diagram. Regarding Gibbs’ first paper [I], hewrites in the introduction, “In dieser Arbeit ist
dem Entropie-Temperaturdiagramm
ein eigenes
Kapitel gewidmet und darin sind mit vollster
Klarheit die allgemeinen Eigenschaften desDiagramms entwickelt und dessen grosse Verwendbarkeit such fur technische Zwecke betont”.
Also, commenting on Zuener’s second text [5],he states “Bei weitem ausfuhrlicher als allebisher genannten Schriften beschlftigt sich mit
dem Gegenstande Zeuner’s Technische Thermodynamik, indem hier das Wgirmediagramm fast
durchgehends parallel mit dem Indikatordiagramm zur darstellung allgemeiner und technischer Probleme verwendet ist, und so bildete
denn such das Studium dieses Werkes, neben
dem der friiher genannten Schrift von Gibbs die
hauptslchliche
Gnmdlage zu der folgenden
Arbeit”. As further evidence of his appreciationof the value of graphical representations, wefind the phrase “urn es an zahlreichen Beispielen
vor Augen fuhren”, or its equivalent, used morethan once. In an appendix, we find an interesting
discussion of the use of co-ordinates (such aswork) which are not unique functions of thethermodynamic state of the system; he suggeststhat such co-ordinates might be useful for the
representation of certain processes, but that theuse of state variables is preferred in general.
(Incidentally, contrary to the impression given
by Partington [6, p. 1791, the enthalpy-entropy
diagram is not mentioned in Mollier’s first
paper; the writers find it mentioned first in
Mollier’s 1904 paper). This first paper, written
clearly and illustrated effectively with fourteenline drawings, sets the stage for all of his following technical publications. Although written 70
years ago, students of thermodynamics still
would find this paper stimulating.
In his second publication [B2], graphicalmethods provide a simplified description of therelative motions of the slide valve and the piston
in the steam engine. This paper, as well as nearly
all of the papers which follow, appeared in the
Zeitschrtft des Vereines deutscher Ingenieure, anindication of his effort to reach the practising
engineer.

L. KNUTH

His dissertation [B3], concerning the entropyof vapors, established further his reputation as athermodynamicist.
Unfortunately,
this work
does not appear to have been published in aform which is available readily. The writers
have been unable to locate copies of this work.
Next, beginning with available thermodynamic
data and using the general methods of thermodynamics, he expressed the thermal properties ofCO,, NH, and SO, in forms convenient for
use by refrigeration engineers [B4]. Wheneverpossible, he uses, for COz, the data publishedby Amagat several years earlier. Temperatureentropy relations are presented in equation form
for all three refrigerants, also in tabular form for
COB and NH,, and also in graphical form forCOz. He considered apparently CO, to be themost important and SO, the least important ofthese three refrigerants.
Motivated by the fact that a large portion of
the processes occurring in COz refrigerators
involve superheated COz, and beginning with theexperimental results of Amagat, he extended
these tables and graphs in the following year toinclude superheated CO, [BS]. Numerical examples at the end of this paper illustrate the useof such tables and graphs and show that analyticalresults obtained using the given tables and graphare in better agreement with experimental results
than are analytical results obtained using the
calculation procedures of contemporary
refrigeration engineers.
His review paper on heat transfer and related
experimental results [B6] was prepared at therequest of the Vdl (Vereines deutscher
Ingenieure). The VdI had appropriated, in 1895,
5000 M “fur Arbeiten zur Losung der Aufgabe
betr. den Durchgang der Warme durch Heiz&hen”[7] and asked Mollier to provide astarting point for these studies by clarifying,on the basis of available research results, thestate of understanding of the laws of heattransfer. In the resulting paper, conduction,
convection and radiation (including convection
with boiling and convection and radiation fromflames) are discussed extensively. Most of thereviewed studies appear to have been motivatedby the problems encountered in generating andhandling steam. Although many of the fundamental concepts which are used today in heat

THE

WORKS

OF RICHARD

transfer studies are mentioned in this paper,
quantitive correlations were in the first stages ofdevelopment. E.g. although the variation of theforced-convection unit conductance had been
established as a function of the square root of the
Huid speed (for low fluid speeds), no expression
relating quantitatively the unit conductance withfluid properties and system geometry is given;again, although Stefan’s radiation equation had
been presented 8 years previously. it was not yet
accepted universally. Mollier points out inconsistencies in some of the measurements,suggests possible sources of errors, and emphasizes the need for more extensive and moreaccurate data. He expresses the highest regard
for the manner in which Joule arranged his
experiments and drew his conclusions.
His paper on the evaluation of the steam
engine [B7], in \vhich he advocates comparing
the measured thermal efficiency of the engine
with the efficiency computed neglecting losses
due to irreversible processes, was motivated by
the fact that some engineers, including Zeuner,
made a practice of comparing the measured
thermal efficiencies of all steam engines, regardless of the cycle of operation, with the efficiency
of a Carnot cycle operating between the same
temperature limits. The procedure advocatedby Mollier provided a more meaningful measureof the engine performance as influenced by its
design and construction.
As further evidence of his desire to aid thepracticing engineer. we find that he authored or
co-authoredfor three decades the section“W3rme” in Hutte. tics Irtgenieurs Taschenhuch[B8]. (WC have been able to establish withcertainty that he authored this section in the
18th edition in 1902 and co-authored this sectionin the 26th edition in 1931 with F. Merkel.)
The 2lst (191 I) and succeeding editions are
divided into parts on thermal properties ofmaterials. heat transfer, general laws of thermodynamics, perfect gases. vapors, flows of gases
and vapors, and combustion. Numerous applications (power production, refrigeration. etc.) are
discussed. Combining a sound understanding of
the physical processes, the powerful methods ofthermodynamics. and a desire to aid (rather thanto impress) the engineer, he wrote so clearly that
we find it necessary to remind ourselves that the

MOLLIER127

earlier editions are over a half century old. We
are especially impressed by the clarity of his
discussion, in the earlier editions, of the maximum useful work which can be obtained from aclosed system. The only place in which we would
desire greater clarity is in his use of the word
“adiabatic”; when Mollier writes “adiabatic”,
he means “constant-entropy”,
at variance withcurrent usage. The fact that Mollier authoredthis section in Hiitte explains perhaps why we
do not find a thermodynamics textbook by
Mollier; such a textbook might have duplicatedmuch of the material in Hiitte.
His paper on the gas force required at thepiston head to accelerate the connecting rod [B9]
was motivated by the wide variations in theassumptions made by designers when handling
this problem. Skilfully combining analyticalengineeringgraphical
methods,
methods,
approximations and a survey of typical designs,
he is led to recommend that the designer add
half the mass of the connecting rod to the tnassof the remaining reciprocating parts, a recommendation with simplicity and usefulness typicalof Mollier.
His next paper, on the degree of irregularity
of intermittent-firing internal-combustion
engines with idle-stroke governing [BlO], also waswritten in order to correct false concepts. Typicalof Mollier, a clarifying graphical presentation of
the results of his analysis is included.
His best-known publication is perhaps his
paper on new diagrams for engineering thermodynamics [RI I]. appearing the year following
Gibbs’ death. He presents enthalpy-entropy
diagrams for steam and for carbon dioxide,suggesting that these diagrams might be usefulin studies of steatn engines, steam turbines,
steam jets, throttling processes, and refrigerators. In closing, he presents also an enthalpypressure diagram for carbon dioxide, suggestingthat this diagram might be useful in studies ofprocesses involving fixed pressure levels, suchas occur in refrigerators.
His shortest paper is the two-sentence
description of the geometrical relationshipbetween the mass polygon and the distancediagram for a four-cylinder machine balanced
to first approximation [B12]. It is accompanied,of course, by the appropriate diagram.

128

L. M. K. BOELTER

and ELDON

Mollier, recognizing the value of Callendar’sstate equation for steam, used it as the basis forhis tables and diagrams for steam [B13] whichappeared in 1906. Mollier’s improved version ofCallendar’s equation was used in the later
editions, the seventh edition appearing in 1932.
Both an enthalpy-entropy
diagram and an
enthalpy-pressure diagram are included.
Equations and diagrams applicable to processes occurring in a gas generator are presented
in Mollier’s next paper [B14]. Because information required for the calculation of equilibriumcompositions was not available at that time(1907), he used the first law of thermodynamics
and the appropriate chemical equations to
express, for the reaction of air and H,O withcoal, the H,, CO and N, content of the generator
products as functions of the CO, content of the
products, the 0, content of the incoming air andthe generator efficiency. The fact that the CO,content (a measure of the extent of reaction) isleft undetermined is a consequence of omitting
the conditions for chemical equilibrium. He
emphasizes explicitly the need for equilibriumcomposition data.
The only non-technical writing by Mollier
which we have found is the paper on Zeuner[B15] presented at the general meeting of theVdl in 1908, the year after Zeuner’s death. The
similarities of objectives and thought processes
between Mollier and Zeuner, brought out by
this paper, are remarkable. Mollier writes,
concerning Zeuner’s motivations, “Er hat eine
Lebensaufgabe darin gefunden, die Maschineningenieure die Gesetze der mechanischen
Wgrmetheorie zu lehren” and, with regard to his
methods,* “Zeuner denkt augesprochen geometrisch und erleichtert dem Leser die Auffassung iiberall durch Schaulinien”. Mollier was
truly Zeuner’s successor !
For more than a decade after this paper, wefind no new writings by Mollier. Although thecause for this publishing inactivity is not* Concerning the use of geometrical methods inthermodynamics, compare Mollier’s comment on Zeuner
with Bumstead’s comment on Gibbs [81, “Professor
Gibbs was much inclined to the use of geometricalillustrations, which he employed as symbols and aids tothe imagination. . and this method he used with greatease and power.”

L. KNUTH

apparent at the distance from which we are
examining his career, we suspect that WorldWar I aggravated this inactivity.
His next publication, in 1919, was motivatedonce again by the desire to correct a popular
misconception. During the preceding 15 years,
several cycles in which pistons and rotors are
replaced largely by nozzles had been proposed,
and a Deutsches Reichspatent had been issued
for a refrigerator in which the expansion and a
portion of the compression take place in nozzles.
Moldier examined both power and refrigeration
cycles in which pistons and rotors are replaced,at least in part, by nozzles and showed [B16] thatviscous losses render these cycles impracticable.
The only paper which Mollier published in a
non-engineering journal bears on a graphicalrepresentation of the equation of state [B 171,
appearing in Physikalische Zeitschrift. His
choice of co-ordinates (based upon an examination of van der Waals’ equation of state) reveals,
in graphical form, deviations from the van der
Waais equation and provides, for several
empirical expressions, a better physical understanding.
As a consequence of increasing interest in
combustion processes, his 1907 paper on gas
generation is extended in 1921 in a paper on theequations of the combustion process [B18]. For
the case in which the combustion products
consist only of 0,. N,, CO and CO,, he develops
relationships between the amount and composition of the combustion products, the amountand composition of the fuel (solid, liquid or
gaseous) and the amount of supplied air. As inthe earlier study, the CO, content (a measureof the extent of reaction) is left undetermined.
The paper improves upon an assumption madeearlier by Ostwald regarding the relationshipbetween the amount of excess supply air andthe amounts of 0, and CO, in the combustion
products. This paper is unique among Mollier’s
twenty publicationsin that it contains
nodiagrams.
Mollier’s enthalpy-mass
fraction diagram forbinary mixtures appears first in his paper
presenting a new diagram for vapor-air mixtures [B19]. In this paper he suggests that theenthalpy-mass fraction diagram is more versatile
than the enthalpy-temperature
diagram in use

THE WORKS

OF RICHARD

at that time. Such diagrams are used chiefly forsituations in which one of the components
cannot be treated as a perfect gas; Mollier’s
diagram is convenient especially for processes
in which the composition does not vary. Relative
to the psychrometric chart, his diagram has theadvantage that the end state for mixing processes
may be obtained exactly by simple geometricalconstructions.
Improvements on this diagram are includedin the paper on the &x-diagram for steam-air
mixtures [B20]. He recommends using inclined
co-ordinates and replacing lines of equal relative humidity by lines of equal degree ofsaturation. The last section of this paper (thelast paper published by Mollier) is perhaps his
most controversial publication. He entered into
the discussion of the theory of the psychrometer and assumed (as did Carrier) that the
wet-bulb temperature equals the adiabaticsaturation temperature. Although this assumption is correct numerically, to a good approximation, for water diffusing into air over a wide
range of flow conditions, it is not correct inprinciple; one must take into account, as shown
by Busemann [9], Kirschbaum [lo] and others(see e.g. Matz [l1, p. 1651 and Sherwood andPigford [12, p. 97]), the pertinent transportphenomena. Unfortunately,
many thermodynamics textbooks state, even today, that the
wet-bulb temperature and the adiabatic-saturation temperature are equal.
If one examines the authorships of the twenty
publications listed in the Bibliography, then one
notices that (with the exception of the lastedition of the “Warme” section in Hiitte) all of
the publications were authored by Mollier alone.
As a possible explanation, we note that NHgel
writes [13], on the occasion of Mollier’s 70thbirthday, “Es verdient besonders hervorgehoben
zu werden, dass es Mollier in erster Linie am
Herzen lag, seine erfolgreichsten Probleme durchseine Assistenten bearbeiten zu lassen unddiesen die voile Autorschaft fur die erzielten
Ergebnisse zuzuschreiben”. This procedure wascertainly a most generous policy on the part of agreat engineer and educator!
We notice also that Mollier was, althoughextremely modest, confident of the value of his
works. Nagel writes [14], “Obwohl er sich seines

MOLLIER

129

Kiinnens und seines Wertes wohl bewusst war,
war doch immer die persijnliche Bescheidenheit
der Zug, der seinen Charakter hervorstechendauszeichnete”. This modesty and confidence
reminds us again of Gibbs, of whom Bumstead
writes [8], “His modesty with regard to his work
was proverbial among all who knew him, andit was entirely real and unaffected. There wasnever any doubt in his mind, however, as tothe accuracy of anything which he published,
nor indeed did he underestimate its importance. . . .”PROFESSIONAL CONTRIBUTIONSRECOGNITIONAND

The recognition awarded a man is not always
proportional to his professional contributions;sometimes the recognition is disproportionately
low (specially in the case of pioneers), manytimes it is disproportionately high (specially inthe case of followers). The further we delve into
the professional contributions of Mollier, themore we are convinced that his contributions
are more valuable than is appreciated generally,
especially by the younger engineers in the
United States.
As a lower limit to the value of these contributions, let us summarize briefly the highlightsof the recognitions given Mollier. At the age of33, he was called to the position of ordentlicher
Professor fur Technische Thermodynamik, i.e.
his contributions and potential in the field of
thermodynamics were recognized early. In 1919,
the Technische Hochschule in Braunschweig
conferred upon him the degree Ehrendoktor. In
1928, the VdI awarded him its highest honor,
the Grashof Medal, in recognition of his contributions. as an outstanding teacher and investigator, to the development of engineering
thermodynamics for the purpose of understanding thoroughly the processes in heat-power andrefrigeration machines. His tables and diagramsfor steam [B13] and his last two papers [B19 andB20] were translated and published in the
English language [15-171. At the time of his
70th birthday, he was honored by articles in
Forschung auf dem Gebiete des Ingenieurwesens,
Zeitschrif,fiir die gesamte Ktilte-Industrie,
Forschungen und Fortschritte, and Zeitschrift fiir
angewandte Mathematik und Mechanik ; an130

L. M. K. BOELTERandissue of Fors~h~g auf dem Ge&iete des Ingenieurwesens, as well as Forsch~gshefi 363, preparedby his students and colleagues, was dedicated tohim; Busemann dedicated his volume on Der
Wiirme- und Stoffaustausch dargestellt
imMollierschen Zustandsdiagramm fiir Zweistoflgem&he [9] to Mollier; and a Festschrift was

published, at Karlsruhe, in his honor. At thetime of his death, necrologies appeared in
Zeitschrift des Vereines deutscher Ingenieure (inwhich journal he published nearly all of his
papers), in Zeitsc~~t fik die gesamte Kalte~ndustrie (in which journal he published two of
his earlier papers) and in Sit~gs~ericht
Isis
Dresden. On 26 May 1936, the directorate of the
VdI, at the suggestion of the Ausschusses fur
WHrmeforschung and the Deutschen KPltevereins, resolved that the i,s-, i,p- and i,xdiagrams should henceforth be known as Mollier
diagrams and be identified respectively as the
Mollier-i,s-Diagram,
the Mollier-Q-Diagram
and the Mollier-i,x-Diagram.*
Because his
professional career was motivated largely by adesire to provide engineers with aids for thesolution of difficult problems of thermodynamics, heat transfer and mass transfer, therecognitions by the several engineering societies
are significant indeed; he employed graphicalmethods so effectively that the association of his
name with these three graphs is certainly
appropriate.
The influences of Mollier on current technology, consisting of both tangible and intangible influences, is difficult to evaluate. In theparagraphs which follow, we can hope to touchbriefly upon only a few of the most obvious
cont~butions.
Consider tirst the more tangible influences,
In spite of the fact that the engineering problemsof Mollier’s time have been replaced, to a large
extent, by new engineering problems, the thermo---.~* Sometimes several other thermodynamic-state diagrams either are credited to Mollier or are called Moflier
Diagrams. E.g. BoSnjakoviC credits Mollier with thei-log p diagram [18, p. 1351 and with the i-T diagram[19, p. 151whereas Tribus calls the T-s diagram a Mollier
Diagram ]20, pp. 281 and 2851. However, Callendar
suggested apparently the i-log p diagram [21, p. 3531
whereas Moilier credits 0. H. Mueller with suggesting
the i-T diagram [B19] and Beipaire with suggesting theT-s diagram @l].

ELDON

L. KNUTH

dynamic diagrams and parameters introduced
by Mollier are still in use today. Regarding the
Mollier-i,s-Diagram, Keenan writes [22, p. 881,
“The enthalpy-entropy
chart is probably thechart most commonly employed as an aid inengineering calculations. It is called the Mollier
chart in honor of Richard Mollier, who first
proposed its adoption”. Used primarily forimperfect gases, it has served specially engineers
dealing with processes involving steam andrecently engineers dealing with processes involving relatively high tem~ratures.
For arecent steam application, see the diagram
prepared by Schmidt [23]; as examples of hightemperature applications, see the diagram prepared by Feldman [24] for air up to 13 OOO’X,
for use in hypersonic-flow problems, and the
diagram prepared by Ducati [25] for helium up
to 46OOO”K, for use in plasma-flow problems.
The Mollier-&p-Diagram, used widely in the
refrigeration industry, is used frequently now
also in applications involving cryogenic fluids
and high-temperature gases. For examples ofcryogenic-fluid applications, see, e.g. Scott [26];as an example of high-tem~rature applications,see the diagram prepared by Moeckel andWeston [27] for air up to 15 000°K. The Mollieri,x-Diagram continues to be used widely forhumidifying, evaporative-cooling,
drying andsimilar processes occurring, e.g. in the fields of
air conditioning, chemical engineering andmeteorology; see, e.g. Eckert and Drake 128,
Ch. 151. The gas-generator diagram included,
e.g. by BognjakoviC [18, p. 2251 has its origin
in Mollier’s paper [Bl4], whereas the combustion
parameters used, e.g. by Schmidt 129, p. 2391
come from Mollier’s 1921 paper fBl8f. The
availability~ntropy diagram published by Keenan [30] was derived from the Mollier-i,sDiagram. The writers suggest that a diagram
in which the available-energy function (suggested
by Evans [31] as a generalization of Keenan’s
availability) is displayed as a function ofentropy might prove to be a useful diagram in
the field of thermo-economics.
Consider now the less tangible influences.
Foremost among these contributions is perhaps
his direct influence upon immediate associates
and students-some of whom are still practicing
engineering. Nligel writes [14], “Er wies ihnen

THE

WORKS

OF RICHARD

nicht nur die Bahnen der geda~lichen Farderung schwebender wis~nschaftlicher Probleme,er Iebte ihnen ein Vorbild vor, das einen
Reichtum an wertvollsten Motiven fiir die
Formung des eigenen Lebens darbot”. The
extent to which these associates and students
propagated the values received from theircontacts with Mollier will never be known.
Additional intangible influences derive from his
published works-paragons
of modesty anddirectness, and evidences of powerful thoughtprocesses and benevolent motivations-inspirations for generations to follow.

CLOSING REMARKSThis review was undertaken as a challengeto discover what could be done in a short time
and with materials available in the United Stateslibraries (chiefly in the University of California
libraries) and in our private libraries. We trustthat this brief and incomplete evaluation of
Richard Mollier and his works will emphasize
the human side of en~neering cont~butions, aside which is overshadowed too often by the
inanimate side.

REFERJPXES
1. J. WILLARDGIBBS,Graphical methods in the thermodynamics of fluids, Transactions of the Connecticut
Academy 2,309-342 (April-May 1873).
2. J. WILLARDGIBBS,A method of geometrical representationof the thermodynamic
properties
ofsubstances by means of surfaces, Transactions of theConnecticut Academy 2, 382-404 (December 1873).
W. OSTWALD (translator), Thermodynamjsche Studien
volt W. Gibbs. Veit and Company, Leipzig (1892).
GUSTAV ZEUNER, Grtlndztige der me~hanischen
Wiirmetheorie (1860).
GUSTAVZEUNER,Technische Thermodynamik. Leipzig(1890).
J. R. PARTINGTON,An Advanced Treatise on Physical
Chemistry. Vol. 1. Longmans, Green and Co., London(1949).
7. 2. Ver. dtsch. Zng. 39, 1273 (19 October 1895).
8. H. A. BUMSTEAD,Josiah Willard Gibbs, Amer. J. Sci.
Ser. 4, xvi (September 1903). Reprinted in The
Coffeeted Works of J. Willard Gibbs. Yale University
Press, New Haven (1948).
9. ADOLPH BUSEMANN,Der W&me- und Sto~~ustaus~h~rgesteIit im Mollierschen ~ustandsdiagramm fiir
Zwe~sto~gem~c~. Springer-Verlag,
Berlin (1933).

MOLLIER

10. EMIL TUBAL,

131

W&me- und Stoffaustausc~ im
Forsch. Arb. Zng.Wes. 7,109-l 13 (May/June 1936).
11. WERNER MATZ, Die Thermodyanmik des W&me- undStolyaustausches in der Verfahrenstechnik. Verlag
Dr. Dietrich Steinkopff, Frankfurt (1949).
12. T. K. SHERWOOD
and R. L. PIGFORD,Absorption and
Extraction. McGraw-Hill, New York (1952).
13. A. NAGEL, Richard Molfier zum 70. Geburtstage,
Forsch. Arb. Ing. Wes. 4, 261 (November/December
1933).
14. A. NXG~L, Richard Mollier, Z. Ver. dtsch. Ing. 79,
451-452 (13 Aprit 1935).
15. RICHARD‘MO;LIER, The bossier Steam Tables andDiagrams, extended to the Critical Pressure. (English
edition adapted and ~pl~fi~ from the third German
edition by Dr. H. Moss.) Pitman and Sons, London(1927).
16. RICHARD MOLLIER, A new diagram for water
vapor-airmixtures, Mech. Engng. 45, 703-705(December 1923).
17. RICHARD MOLLIER,The i-x diagram for steam-air
mixtures, Mech. Engng. 51, 769-771 (October 1929);
849-850 (November 1929).
18. FR. BOSNJAKOVI~,Technische Thermodynamik, Erster
Teil. Verlag von Theodor Steinkopff, Dresden (1948).
19. FR. B&NJAKOVI~,Technische Thermodynamik, Zweiter
Teil. Verlag von Theodor
Steinkopff,
Dresden(1951).
2:. MYRONTRIBUS,Thermostutics and Thermodyanamies.
Van Nostrand, Princeton (1961).
and A. R. MILLER,Heat and Thermo21. J. R. ROBERTS
dynamics. Interscience Publishers, New York (1960).
22. J~~EIJHH. KEENAN. Thermodynamics. Wiley, NewYork (1941).
23. ERNSTSCHMIDT,VDZ- Wasserdampfiafein Mit einem
Mollier (i. s)-Diaaram bis 800°C. 4. AufIage. StxingerVerlag, geriin (11956).
24. SAUL FELDMAN,Hypersonic gas dynamic charts forequilibrium
air. Everett, Massachusetts:
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