Maxwell's thermodynamic surface

[3][4] The model, in Maxwell's words, allowed "the principal features of known substances [to] be represented on a convenient scale.

As explained by Gibbs and appreciated by Maxwell, the advantage of a U-V-S (energy-volume-entropy) surface over the usual P-V-T (pressure-volume-temperature) surface was that it allowed to geometrically explain sharp, discontinuous phase transitions as emerging from a purely continuous and smooth state function

; Maxwell's surface demonstrated the generic behaviour for a substance that can exist in solid, liquid, and gaseous phases.

[6] As well as being on display in two countries, Maxwell's model lives on in the literature of thermodynamics, and books on the subject often mention it,[17] though not always with complete historical accuracy.

[18] Around 1900, the Dutch scientist Heike Kamerlingh Onnes, together with his student Johannes Petrus Kuenen and his assistant Zaalberg van Zelst, continued Maxwell's work by constructing their own plaster thermodynamic surface models.

[19] These models were based on accurate experimental data obtained in their laboratory, and were accompanied by specialised tools for drawing the lines of equal pressure.

Diagram of thermodynamic surface from Maxwell's book Theory of Heat . The diagram is drawn roughly from the same angle as the upper left photo above, and shows the 3D axes e (energy, increasing downwards), ϕ (entropy, increasing to the lower right and out-of-plane), and v (volume, increasing to the upper right and into-plane).