Benoit Paul Émile Clapeyron
Encyclopedia
Benoît Paul Émile Clapeyron (26 February 1799 – 28 January 1864) was a French
engineer
and physicist
, one of the founders of thermodynamics
.
, Clapeyron studied at the École polytechnique
and the École des Mines, before leaving for Saint Petersburg
in 1820 to teach at the École des Travaux Publics. He returned to Paris only after the Revolution of July 1830, supervising the construction of the first railway line connecting Paris to Versailles and Saint-Germain
. He married Mélanie Bazaine, daughter of Pierre-Dominique Bazaine
(mathematician and bridge and canal engineer), and older sister of Pierre-Dominique (Adolphe) Bazaine (railway engineer) and Francois Achille Bazaine
(Marshal of France).
, deceased two years before. Though Carnot had developed a compelling analysis of a generalised heat engine
, he had employed the clumsy and already unfashionable caloric theory
.
Clapeyron, in his memoire, presented Carnot's work in a more accessible and analytic graphical form, showing the Carnot cycle
as a closed curve
on an indicator diagram, a chart
of pressure
against volume
(named in his honor Clapeyron's graph).
In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot's principle, what is now known as the second law of thermodynamics
.
These foundations enabled him to make substantive extensions of Clausius'
work, including the formula, now known as the Clausius–Clapeyron relation, which characterises the phase transition
between two phase
s of matter
. He further considered questions of phase transitions in what later became known as Stefan problem
s.
es, the equilibrium of homogeneous solid
s, and calculations of the statics
of continuous beams
, notably the theorem of three moments
(Clapeyron's theorem
).
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
and physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
, one of the founders of thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
.
Life
Born in ParisParis
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
, Clapeyron studied at the École polytechnique
École Polytechnique
The École Polytechnique is a state-run institution of higher education and research in Palaiseau, Essonne, France, near Paris. Polytechnique is renowned for its four year undergraduate/graduate Master's program...
and the École des Mines, before leaving for Saint Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...
in 1820 to teach at the École des Travaux Publics. He returned to Paris only after the Revolution of July 1830, supervising the construction of the first railway line connecting Paris to Versailles and Saint-Germain
Saint-Germain-en-Laye
Saint-Germain-en-Laye is a commune in the Yvelines department in the Île-de-France in north-central France. It is located in the western suburbs of Paris from the centre.Inhabitants are called Saint-Germanois...
. He married Mélanie Bazaine, daughter of Pierre-Dominique Bazaine
Pierre-Dominique Bazaine
Pierre-Dominique Bazaine was a French scientist and engineer. He was educated at the École Polytechnique in Paris as an engineer...
(mathematician and bridge and canal engineer), and older sister of Pierre-Dominique (Adolphe) Bazaine (railway engineer) and Francois Achille Bazaine
François Achille Bazaine
François Achille Bazaine was a French General and from 1864, a Marshal of France, who surrendered the last organized French army to the Prussians during the Franco-Prussian war. He was the first Marshal who had started as a legionnaire and like the great Marshals of the First Empire, he had risen...
(Marshal of France).
Thermodynamics
In 1834, he made his first contribution to the creation of modern thermodynamics by publishing a report entitled the Driving force of the heat (Puissance motrice de la chaleur), in which it developed the work of the physicist Nicolas Léonard Sadi CarnotNicolas Léonard Sadi Carnot
Nicolas Léonard Sadi Carnot was a French military engineer who, in his 1824 Reflections on the Motive Power of Fire, gave the first successful theoretical account of heat engines, now known as the Carnot cycle, thereby laying the foundations of the second law of thermodynamics...
, deceased two years before. Though Carnot had developed a compelling analysis of a generalised heat engine
Heat engine
In thermodynamics, a heat engine is a system that performs the conversion of heat or thermal energy to mechanical work. It does this by bringing a working substance from a high temperature state to a lower temperature state. A heat "source" generates thermal energy that brings the working substance...
, he had employed the clumsy and already unfashionable caloric theory
Caloric theory
The caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids...
.
Clapeyron, in his memoire, presented Carnot's work in a more accessible and analytic graphical form, showing the Carnot cycle
Carnot cycle
The Carnot cycle is a theoretical thermodynamic cycle proposed by Nicolas Léonard Sadi Carnot in 1824 and expanded by Benoit Paul Émile Clapeyron in the 1830s and 40s. It can be shown that it is the most efficient cycle for converting a given amount of thermal energy into work, or conversely,...
as a closed curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
on an indicator diagram, a chart
Chart
A chart is a graphical representation of data, in which "the data is represented by symbols, such as bars in a bar chart, lines in a line chart, or slices in a pie chart"...
of pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
against volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
(named in his honor Clapeyron's graph).
In 1843, Clapeyron further developed the idea of a reversible process, already suggested by Carnot and made a definitive statement of Carnot's principle, what is now known as the second law of thermodynamics
Second law of thermodynamics
The second law of thermodynamics is an expression of the tendency that over time, differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system. From the state of thermodynamic equilibrium, the law deduced the principle of the increase of entropy and...
.
These foundations enabled him to make substantive extensions of Clausius'
Rudolf Clausius
Rudolf Julius Emanuel Clausius , was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. By his restatement of Sadi Carnot's principle known as the Carnot cycle, he put the theory of heat on a truer and sounder basis...
work, including the formula, now known as the Clausius–Clapeyron relation, which characterises the phase transition
Phase transition
A phase transition is the transformation of a thermodynamic system from one phase or state of matter to another.A phase of a thermodynamic system and the states of matter have uniform physical properties....
between two phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
s of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
. He further considered questions of phase transitions in what later became known as Stefan problem
Stefan problem
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a partial differential equation , adapted to the case in which a phase boundary can move with time...
s.
Other work
Clapeyron also worked on the characterisation of perfect gasPerfect gas
In physics, a perfect gas is a theoretical gas that differs from real gases in a way that makes certain calculations easier to handle. Its behavior is more simplified compared to an ideal gas...
es, the equilibrium of homogeneous solid
Solid
Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...
s, and calculations of the statics
Statics
Statics is the branch of mechanics concerned with the analysis of loads on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity...
of continuous beams
Beam (structure)
A beam is a horizontal structural element that is capable of withstanding load primarily by resisting bending. The bending force induced into the material of the beam as a result of the external loads, own weight, span and external reactions to these loads is called a bending moment.- Overview...
, notably the theorem of three moments
Theorem of three moments
In civil engineering and structural analysis Clapeyron's theorem of three moments is a relationship among the bending moments at three consecutive supports of a horizontal beam....
(Clapeyron's theorem
Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and previously accepted statements, such as axioms...
).
Publications
- Clapeyron E. (1834), Puissance motrice de la chaleur, Journal de l'École Royale Polytechnique, Vingt-troisième cahier, Tome XIV, 153–190.
Honors
- Member of the Académie des SciencesFrench Academy of SciencesThe French Academy of Sciences is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research...
, (1858). - The Rue Clapeyron in ParisParisParis is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
' 8th arrondissement (here) is named for him. - He is one of The 72 names on the Eiffel TowerThe 72 names on the Eiffel TowerOn the Eiffel Tower, seventy-two names of French scientists, engineers and some other notable people are engraved in recognition of their contributions. This is according to the design by Gustave Eiffel. The engravings are found on the sides of the tower under the first balcony...
.
See also
- Clapeyron's theorem (elasticity)Clapeyron's theorem (elasticity)In the linear theory of elasticity Clapeyron's theorem states that the potential energy of deformation of a body, which is in equilibrium under a given load, is equal to half the work done by the external forces computed assuming these forces had remained constant from the initial state to the...
- Ideal gas lawIdeal gas lawThe ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law...
- Clausius–Clapeyron Equation