CHAPTER 8 PHASE TRANSITIONS AND EQUILIBRIA OF PURE SUBSTANCES
8.4 COEXISTENCECURVES 217
BIOGRAPHICAL SKETCH
Benoit PaulEmile Clapeyron (1799–1864) ́Clapeyron was a French civil and railroad en-
gineer who made important contributions to
thermodynamic theory. He was born in Paris,
the son of a merchant.
He graduated from theEcole Polytechnique ́
in 1818, four years after Sadi Carnot’s gradu-
ation from the same school, and then trained
as an engineer at theEcole de Mines. At this ́
time, the Russian czar asked the French gov-
ernment for engineers to help create a program
of civil and military engineering. Clapeyron
and his classmate Gabriel Lame were offered ́
this assignment. They lived in Russia for ten
years, teaching pure and applied mathematics
in Saint Petersburg and jointly publishing en-
gineering and mathematical papers. In 1831
they returned to France; their liberal political
views and the oppression of foreigners by the
new czar, Nicholas I, made it impossible for
them to remain in Russia.
Back in France, Clapeyron became involved
in the construction of the first French passen-
ger railroads and in the design of steam loco-
motives and metal bridges. He was married
with a daughter.
In a paper published in 1834 in the journal
of theEcole Polytechnique, Clapeyron brought ́
attention to the work of Sadi Carnot (page
106 ), who had died two years before:a
Among studies which have appeared on the the-
ory of heat I will mention finally a work by S.
Carnot, published in 1824, with the titleReflec-
tions on the Motive Power of Fire. The idea
which serves as a basis of his researches seems
to me to be both fertile and beyond question;
his demonstrations are founded onthe absur-dity of the possibility of creating motive power
[i.e., work]or heat out of nothing.... This new
method of demonstration seems to me worthy of
the attention of theoreticians; it seems to me to
be free of all objection...
Clapeyron’s paper used indicator diagrams
and calculus for a rigorous proof of Carnot’s
conclusion that the efficiency of a reversible
heat engine depends only on the temperatures
of the hot and cold heat reservoirs. However,
it retained the erroneous caloric theory of heat.
It was not until the appearance of English and
German translations of this paper that Clapey-
ron’s analysis enabled Kelvin to define a ther-
modynamic temperature scale and Clausius to
introduce entropy and write the mathematical
statement of the second law.
Clapeyron’s 1834 paper also derived an ex-
pression for the temperature dependence of the
vapor pressure of a liquid equivalent to what is
now called the Clapeyron equation (Eq.8.4.5).
The paper used a reversible cycle with vapor-
ization at one temperature followed by conden-
sation at an infinitesimally-lower temperature
and pressure, and equated the efficiency of this
cycle to that of a gas between the same two
temperatures. Although the thermodynamic
temperatureTdoes not appear as such, it is
represented by a temperature-dependent func-
tion whose relation to the Celsius scale had to
be determined experimentally.b
Beginning in 1844, Clapeyron taught the
course on steam engines at theEcole Nationale ́
des Ponts et Chaussees near Paris, the old- ́
est French engineering school. In this course,
surprisingly, he seldom mentioned his theory
of heat engines based on Carnot’s work.c He
eventually embraced the equivalence of heat
and work established by Joule’s experiments.d
At the time of Clapeyron’s death, the rail-
road entrepreneurEmile P ́ ereire wrote: ́ e
We were together since 1832. I’ve never done
important business without consulting him, I’ve
never found a judgment more reliable and more
honest. His modesty was so great and his char-
acter so good that I never knew him to have an
enemy.
aRef. [ 30 ]. bRef. [ 173 ]. cRef. [ 90 ]. dRef. [ 80 ]. eRef. [ 80 ].