Maxwell's thermodynamic surface

Photographs of Maxwell's plaster model from different angles.

Maxwell’s thermodynamic surface is an 1874 sculpture^[1] made by Scottish physicist James Clerk Maxwell (1831–1879). This model provides a three-dimensional space of the various states of a fictitious substance with water-like properties.^[2] This plot has coordinates volume (x), entropy (y), and energy (z). It was based on the American scientist Josiah Willard Gibbs’ graphical thermodynamics papers of 1873.^[3]^[4] The model, in Maxwell's words, allowed "the principal features of known substances [to] be represented on a convenient scale."^[5]

^ Maxwell, James Clerk (1990). The Scientific Letters and Papers of James Clerk Maxwell: 1874-1879. Cambridge University Press. 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)
^ Maxwell, James Clerk (1 January 1995). Maxwell on Heat and Statistical Mechanics: On "Avoiding All Personal Enquiries" of Molecules. Lehigh University Press. 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)
^ Thomas G.West (February 1999). "Images and reversals: James Clerk Maxwell, working in wet clay". ACM SIGGRAPH Computer Graphics. 33 (1): 15–17. doi:10.1145/563666.563671. S2CID 13968486.
^ Cropper, William H (2004). Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. Oxford University Press. p. 118. ISBN 9780195173246.
^ Maxwell and Harman, pp. 230-231: "I enclose a rough sketch of the lines on Gibbs' surface, co-ordinates Volume Entropy Energy in an imaginary substance in which the principal features of known substances can be represented on a convenient scale." (letter to James Thomson, 8 July 1875)

[letters-1] Maxwell, James Clerk (1990). The Scientific Letters and Papers of James Clerk Maxwell: 1874-1879. Cambridge University Press. 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)

[onheat-2] Maxwell, James Clerk (1 January 1995). Maxwell on Heat and Statistical Mechanics: On "Avoiding All Personal Enquiries" of Molecules. Lehigh University Press. 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)

[siggraph-3] Thomas G.West (February 1999). "Images and reversals: James Clerk Maxwell, working in wet clay". ACM SIGGRAPH Computer Graphics. 33 (1): 15–17. doi:10.1145/563666.563671. S2CID 13968486.

[4] Cropper, William H (2004). Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. Oxford University Press. p. 118. ISBN 9780195173246.

[5] Maxwell and Harman, pp. 230-231: "I enclose a rough sketch of the lines on Gibbs' surface, co-ordinates Volume Entropy Energy in an imaginary substance in which the principal features of known substances can be represented on a convenient scale." (letter to James Thomson, 8 July 1875)

[1]

[2]

[3]

[4]

[5]