 |
| An example 1939 symbol table, compiled by Ralph Fowler and Edward Guggenheim, for the main six thermodynamic functions found commonly in modern textbooks of the day; the latter of which μ (mu) being the chemical potential. [2] |
Symbol usage conflicts
The term "characteristic functions" is a term introduced in 1869 by French engineer Francois Massieu and for these functions, Massieu employed a Greek symbol notation scheme to represent the various thermodynamic functions characteristic of bodies. In 1873, this Greek symbol notation scheme was adopted by American engineer Willard Gibbs.
Prior to this, however, in 1865, the first two main thermodynamic functions, energy and entropy, were introduced using the English letter symbols U and S, respectively, by German physicist Rudolf Clausius. This was the start of a symbol use inconsistency that would last for at least a century, well into the early 21st century, with authors still inconsistent on their usage of the symbols A, short for arbeit (German for "work"), or F, short for frieie energie (German for "free energy"), to represent the Helmholtz free energy (U – TS).
Out of this conflict, into the 1930s, the symbol usage issue had become so chaotic and varied, that new thermodynamics textbooks were forced to compile notation tables and put this at the beginning of each book. The first of these notation tables seems to have been one compiled by Edward Guggenheim (1933), followed by a second made by Theophile de Donder (1936), and a third made by Ralph Fowler (1939).
In 1958, American geologist Hugh McKinstry, supposedly, wrote an extensive article on subject of the varieties of symbol use of the characteristic functions in thermodynamics; the article, supposedly, does not deal with thermodynamics directly, but is a commentary on the use of symbols. [4]
Function symbols table
An updated synthesis of these various notation tables (Guggenheim, de Donder, and Fowler) are regrouped together below, listed in chronological order:
| Energy U | Entropy S | Enthalpy U + PV | Helmholtz free energy U – TS | Gibbs free energy U + PV – TS | ||||
| ------------------------------------------------------------------ | ------------------------------------------------------------------------------- | ------------------------------------------------------------ | ------------------------------------------------ | |||||
| Heat content | Constant: V, P Free energy (Work function) | Constant: T, P Free energy (Available energy) (Useful energy) | ||||||
| Rudolf Clausius | 1865 | Mechanical Theory of Heat | U | S | ||||
| Francois Massieu | 1869 | “On the Various Functions Characteristic of Fluids” | U | U’ (U prime) | – tψ (name) | – tψ’ (name) | ||
| James Maxwell | 1871 | Theory of Heat | e | φ (phi) | ||||
| Willard Gibbs | 1876 | On the Equilibrium of Heterogeneous Substances | ε (epsilon) | η (eta) | χ (chi) | ψ (psi) | ζ (zeta) | |
| Hermann Helmholtz | 1882 | "On the Thermodynamics of Chemical Processes" | U | S |  , FGerman: ‘frieie energie’ | |||
| Walther Nernst | 1893 | Theoretical Chemistry from the Standpoint of Avogadro’s Rule and Thermodynamics | U | |||||
| Pierre Duhem | 1897 | Thermodynamique et Chimie | U | F | Φ (Phi) | |||
| Max Planck | 1897 | Treatise on Thermodynamics | U | Φ (Phi) | H | F | – Tψ (name) | |
| Fritz Haber | 1905 | Technical Thermodynamics of Gas Phase Reactions | U | S | A German: ‘arbeit’ (work) | |||
| Otto Sackur | 1912 | Thermochemistry and Thermodynamics | U | H | ψ (psi) | ζ (zeta) | ||
| Percy Bridgman | 1914 | "A Complete Collection of Thermodynamic Formulas" | E | S | H | ψ (psi) | Z | |
| Gilbert Lewis | 1923 | Thermodynamics | E | S | H | A | F | |
| James Partington | 1924 | Chemical Thermodynamics | U | S | H | F | Z | |
| Theophile de Donder | 1926 | L'Affinite | U | S | ψ (psi) | F | H | |
| John Butler | 1928 | The Fundamentals of Chemical Thermodynamics | E | S | H | F | ||
| Walter Schottky | 1929 | Thermodynamik | U | S | H | F | G | |
| Ralph Fowler | 1929 | Statistical Mechanics | E | S | H | – Tψ | – TΦ | |
| Hermann Ulich | 1930 | Chemische Thermodynamik | U | W | F | G | ||
| Georges Lerberghe | 1931 | Calcul des Affinites Physico-Chimiques | U | I | F | H | ||
| Edward Guggenheim | 1933 | Modern Thermodynamics | E | S | H | F | G | |
| Theophile de Donder | 1936 | Thermodynamic Theory of Affinity | E | S | H | F | F | |
| Mark Zemansky | 1937 | Heat and Thermodynamics | U | S | H | F | G | |
| Paul Epstein | 1937 | Textbook of Thermodynamics | U | S | χ (chi) | ψ (psi) | Φ (Phi) | |
| Johannes Bronsted | 1938 | Physical Chemistry | E | S | H | F | G | |
| Joseph Keenan | 1941 | Thermodynamics | E | S | H | ψ (psi) | Z | |
| Frederick Rossini | 1950 | Chemical Thermodynamics | E | S | H | F, u | ||
| Juliana Goates and Bevan Ott | 2000 | Chemical Thermodynamics | U | S | H | A | G | |
| IUPAC [3] | 2007 | Chemical Thermodynamics Symbol Table | U | S | H | A, F | G |
An important function not listed in this table, owing to its consistency is ‘bound energy’, symbol ‘B’, equal to the function ‘TS’, which is defined, according to Herman Helmholtz (1882), the coiner of this term, as “expressing the mechanical equivalent of that quantity of heat which must be conveyed into a body at temperature T in order to raise its entropy to the value S.” Hence, total energy (or total energy plus pressure-volume work energy) less bound energy is what is called ‘free energy’ (Helmholtz or Gibbs, respectively):
References
1. (a) Guggenheim, Eduard, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs (pg. 28). London: Methuen & Co.
(b) De Donder, Theophile. (1936). Thermodynamic Theory of Affinity: A Book of Principles (pg. xvi). Stanford University Press.
2. Fowler, Ralph and Guggenheim, Eduard A. (1939). Statistical Thermodynamics: a Version of Statistical Mechanics for Students of Physics and Chemistry (pg. x). Cambridge University Press.
3. Cohen, E. Richard, Cvitas, Tomislav. (2007). Quantities, Units and Symbols in Physical Chemistry, 3rd ed. (Chemical Thermodynamics Symbol Table, pg. 56). Royal Society of Chemistry.
4. (a) Vanserg, Nicolas. (1958). “Mathmanship”, The American Scientist, 46: 94A-98A; in: Essays on Thinking and Writing in Science, Engineering, and Business, (pgs. 110-), W.C. Brown, 1963.
(b) Nicolas Vanserg (pen name), supposedly, is Hugh McKinstry, a professor of geology at Harvard for many years.
(c) McSween, Harry Y, Richardson, Steven M., Uhle, Maria. (2003). Geochemistry: Pathways and Processes (pg. 45). Columbia University Press.
