File:Maxwell's letters plate IV.jpg

Maxwell's sketch of the isothermals and isopiestics on his surface (Plate IV of his collected letters).

Maxwell’s thermodynamic surface is an 1874 sculpture[1] made by Scottish physicist James Clerk Maxwell showing the various states of a fictitious water-like substance[2] on a three-dimensional volume-energy-entropy plot, based on the American scientist Willard Gibbs’ graphical thermodynamics papers of the early 1870s.[3]

Gibbs' papers defined what Gibbs called "the thermodynamic surface" in term of the triple volume-energy-entropy. After receiving reprints of Gibbs' papers, Maxwell recognized the insight afforded by Gibbs' new point of view and set about to construct physical three-dimensional models of this surface.[4]

Maxwell sculpted the original model in clay and made three plaster casts of the clay model, sending one to Gibbs as a gift, keeping the other two in his laboratory at Cambridge University.[3] Maxwell's copy is on display at the Cavendish Laboratory of Cambridge University,[3] while Gibbs' copy is on display at the Sloane Physics Laboratory of Yale University,[5] where Gibbs held a professorship.

Maxwell drew lines of equal pressure (isopiestics) and of equal temperature (isothermals) on his plaster cast by placing it in the sunlight, and "tracing the curve when the rays just grazed the surface."[2] One of his letters reports sending sketches of these lines to Thomas Andrews.[2]


  1. James Clerk Maxwell and P. M. Harman (2002), The Scientific Letters and Papers of James Clerk Maxwell, Volume 3; 1874-1879, Cambridge University Press, ISBN 0521256275, p. 148.
  2. 2.0 2.1 2.2 James Clerk Maxwell, Elizabeth Garber, Stephen G. Brush, and C. W. Francis Everitt (1995), Maxwell on heat and statistical mechanics: on "avoiding all personal enquiries" of molecules, Lehigh University Press, ISBN 093422334, p. 248: "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"
  3. 3.0 3.1 3.2 Thomas G.West (February 1999). "James Clerk Maxwell, Working in Wet Clay". SIGGRAPH Computer Graphics Newsletter 33 (1): 15–17. 
  4. Maxwell, Garber, Brush, and Everitt, p. 49.
  5. Kenneth R. Jolls (1990). "Gibbs and the art of thermodynamics". In D. G. Caldi and George D. Mostow. Proceedings of the Gibbs Symposium, Yale University, May 15–17, 1989. American Mathematical Society. p. 321. ISBN 978-0-8218-0157-4. 

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