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Gibbs's thermodynamic surface is the expression of the thermodynamic relationship between the entropy, volume and energy of a substance at varied temperature and pressure. This thermodynamic expression is the basis of Maxwell's thermodynamic surface, a model that provides a three-dimensional plot of the various states of a fictitious substance with water-like properties. This plot has coordinates volume (x), entropy (y), and energy (z).

History

In 1873, Josiah Willard Gibbs, an American Scientist published the theory associated with thermodynamic state by designing a graphical method of expression of the relationship between energy, entropy, volume, temperature, and pressure. This historical publication was divided into part 1 and part 2. The part 1 involves a graphical methods in the thermodynamics of fluids while Part 2, deals with a method of geometrical representation of the thermodynamic properties of substances by means of surfaces. The graphical methods in the thermodynamics of fluids published by Gibbs provided an intuitive understanding of the thermodynamic property relationships governed by the 1st and second laws of thermodynamics.

The first paragraph of Gibbs's part 1 publication reads

“Although geometrical representations of propositions in the thermodynamics of fluids are in general use, and have done good service in disseminating clear notions in this science, yet they have by no means received the extension in respect to variety and generality of which they are capable. So far as regards a general graphical method, which can exhibit at once all the thermodynamic properties of a fluid concerned in reversible processes, and serve alike for the demonstration of general theorems and the numerical solution of particular problems, it is the general if not the universal practice to use diagrams in which the rectilinear co-ordinates represent volume and pressure. The object of this article is to call attention to certain diagrams of different construction, which afford graphical methods coextensive in their applications with that in ordinary use, and preferable to it in many cases in respect of distinctness or of convenience.”

Gibbs combined the first and the second laws of thermodynamics in what is known as fundamental thermodynamic relation before he actually developed this graphical method. This fundamental thermodynamic relation is generally expressed as an infinitesimal change in internal energy in terms of infinitesimal changes in entropy, and volume for a closed system in thermal equilibrium in the following way.

${\displaystyle \mathrm {d} U=T\,\mathrm {d} S-P\,\mathrm {d} V\,}$

Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume.

The graphical methods in the thermodynamics of fluids published by Gibbs in part 1 resulted in the development of a method of geometrical representation of the thermodynamic properties of substances by means of surfaces. This led to the establishment of the thermodynamic property relationship between the variables - energy, entropy, volume, temperature, and pressure. This was described comprehensively but without a diagram.

Maxwell’s plaster model

This model provides a three-dimensional plot of the thermodynamic variables based on Gibbs’ graphical thermodynamics publications of 1873. James Clerk Maxwell, a Scottish physicists received the reprinted paper of Josiah Willard Gibbs on thermodynamic surface and constructed the physical three-dimensional models of the surface known today as Maxwell’s thermodynamic surface. Maxwell sculpted the original model in clay and made three plaster casts of the clay model and sent one to Gibbs as a gift and kept the other two in his laboratory at Cambridge University. The two retained by Maxwell was copied on display at the Cavendish Laboratory of Cambridge University, while Gibbs' copy his own on display at the Sloane Physics Laboratory of Yale University, where Gibbs was professor of mathematical physics from 1871 until his death. Several historical photographs were taken of these plaster casts during the middle of the 20th century including one by James Pickands II, published in 1942. These photographs exposed a wider range of people to Maxwell's visualization approach.

See also

• List of things named after Josiah W. Gibbs

References

1. Cropper, William H (2004). Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. p. 118. ISBN 9780195173246.
2. ^ Thomas G.West (February 1999). "James Clerk Maxwell, Working in Wet Clay". SIGGRAPH Computer Graphics Newsletter. 33 (1): 15–17. doi:10.1145/563666.563671.
3. "J. Willard Gibbs -American scientist". Britannica.com. Retrieved January 9, 2015.
4. Maxwell, James Clerk (1995-01-01). Maxwell on Heat and Statistical Mechanics: On "Avoiding All Personal Enquiries" of Molecules. p. 248. ISBN 9780934223348. I think you know Prof. J. Willard Gibbs's (Yale College Connecticut) graphical methods in thermodynamics. Last winter I made several attempts to model the surface which he suggests, in which the three coordinates are volume, entropy and energy. The numerical data about entropy can only be obtained by integration from data which are for most bodies very insufficient, and besides it would require a very unwieldy model to get all the features, say of CO₂, well represented, so I made no attempt at accuracy, but modelled a fictitious substance, in which the volume is greater when solid than when liquid; and in which, as in water, the saturated vapour becomes superheated by compression. When I had at last got a plaster cast I drew on it lines of equal pressure and temperature, so as to get a rough motion of their forms. This I did by placing the model in sunlight, and tracing the curve when the rays just grazed the surface... I send you a sketch of these lines..." (letter to Thomas Andrews, 15 July 1875)
5. "Josiah Willard Gibbs Facts, information, pictures". Encyclopedia.com. Retrieved January 9, 2015.
6. "Thermodynamic Case Study-Gibbs' Thermodynamic Graphical Method". sv.vt.edu. Retrieved January 9, 2015.
7. Schmidt-Rohr, K. (2014). "Expansion Work without the External Pressure, and Thermodynamics in Terms of Quasistatic Irreversible Processes" J. Chem. Educ. 91: 402-409. http://dx.doi.org/10.1021/ed3008704
8. Erik Gregersen (January 2011). The Britannica Guide to Heat, Force, and Motion. The Rosen Publishing Group. pp. 317–. ISBN 978-1-61530-309-0.
9. Muriel Rukeyser (1942), Willard Gibbs American Genius (reprinted by Ox Bow Press, ISBN 0-918024-57-9), p. 203.
10. Maxwell, James Clerk (1990). The Scientific Letters and Papers of James Clerk Maxwell: 1874-1879. p. 148. ISBN 9780521256278. I have just finished a clay model of a fancy surface, showing the solid, liquid, and gaseous states, and the continuity of liquid and gaseous states." (letter to Thomas Andrews, November, 1874)
11. The Museum at the Cavendish Laboratory: Maxwell's Apparatus.
12. "J. Willard Gibbs". Physics History. American Physical Society. Retrieved 16 Jun 2012.
13. Kenneth R. Jolls (1990). "Gibbs and the art of thermodynamics". In D. G. Caldi and George D. Mostow (ed.). Proceedings of the Gibbs Symposium, Yale University, May 15–17, 1989. American Mathematical Society. p. 321. ISBN 978-0-8218-0157-4.
14. Maxwell, Garber, Brush, and Everitt, p. 49.

• Scientific modeling
• Thermodynamics