In
thermodynamics, Massieu function (sometimes called Massieu–Gibbs function, Massieu potential, or Gibbs function, or characteristic (state) function in its original terminology), symbol
(Psi), is defined by the following relation:
:
where for every
system with degree of freedom ''r'' one may choose r variables, e.g.
, to define a coordinate system, where ''X'' and ''Y'' are
extensive and
intensive variables, respectively, and where at least one extensive variable must be within this set in order to define the size of the system. The (''r'' + 1)-th variable,
, is then called the Massieu function.
[Inden, Gerhard. (2008). â]
Introduction to Thermodynamics
€, ''Materials Issues for Generation IV Systems'', pgs. 73–112. Springer
The Massieu function was introduced in the 1869 paper "On the Characteristic Functions of Various Fluids" by French engineer
François Massieu François Jacques Dominique Massieu (4 August 1832 – 5 February 1896) was a French thermodynamics engineer noted for his two 1869 characteristic functions, each of which known as a Massieu function (the first of which sometimes called free entrop ...
(1832-1896). The name "Gibbs function" is the eponym of American physicist
Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in ...
(1839-1903), who cited Massieu in his 1876 ''
On the Equilibrium of Heterogeneous Substances''. Massieu, as discussed in the first footnote to the abstract of Gibbs' ''Equilibrium'', “appears to have been the first to solve the problem of representing all the properties of a body of invariable composition which are concerned in reversible processes by means of a single function.†Massieu's 1869 paper seems to be the source for the generalized mathematical conception of the
energy
In physics, energy (from Ancient Greek: á¼Î½ÎÏγεια, ''enérgeia'', “activityâ€) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of hea ...
of a system being equal to summations of the products of pairs of
conjugate variables.
References
Further reading
*{{cite journal , last1=Massieu , first1=F. , title=Sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs , journal=Comptes rendus , date=1869 , volume=69 , pages=858–862 , url=https://babel.hathitrust.org/cgi/pt?id=uc1.31822009518986&view=1up&seq=864 , trans-title=On the characteristic functions of various fluids and on the theory of vapors , language=French
*Massieu, François. (1876). ''Thermodynamique : Mémoire sur les fonctions caractéristiques des divers fluides et sur la théorie des vapeurs''. 92 pgs. Académie des Sciences de L'Institut National de France.
Thermodynamics