History of thermodynamic surfaces

In science, history of thermodynamic surfaces refers to the historical development of the construction of two-dimensional thermodynamic data set plots or three-dimensional thermodynamic surfaces.

In 1869, Thomas Andrews, following ten years of research and data collection in his studies of the liquefaction of carbon dioxide, published the following diagram, a pressure-volume diagram (with the line of no volume to the right) upon which are drawn isothermal carbon dioxide curves for temperatures ranging from 13.1°C to 48.1°C, pressures ranging from 50 to 100 atmospheres: (Ѻ)

Andrews pressure-volume diagram

In 1871, James Thomson, using the based on data for carbon dioxide collected by Thomas Andrews, constructed a plaster pressure-volume-temperature surface, or P,V,θ surface as he labeled it, currently on display (Ѻ) at the Hunterian Museum and Art Gallery, University of Glasgow: [1]

Thomson’s thermodynamic surface

In 1873, American engineer Willard Gibbs published his first thermodynamics paper, “Graphical Methods in the Thermodynamics of Fluids”, in which Gibbs uses the two coordinates of the entropy and volume to represent the state of the body. [2] In his second follow-up paper, “A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces”, published later that year, Gibbs added in the third coordinate of the energy of the body, as shown in the following three diagrams, albeit mostly described via equations and verbally. [3]

Gibbs (figure 1)Gibbs (figure 2)Gibbs (figure 3)

Gibbs' figures 2 and 3, taken together yield the following three-dimensional figure:

Maxwell surface (cube)

In Nov 1874 to Jul 1875, Irish physicist James Maxwell, used descriptions of thermodynamics surfaces in American engineer Willard Gibbs' two 1873 papers on the graphical methods of thermodynamics, to make a plaster thermodynamic surface:

“I enclosed a rough sketch [adjacent] of the lines of Gibbs’ surface, co-ordinates volume [x], entropy [y], energy [z], in an imaginary substance in which the principle features of the substance can be represented on a convenient scale.”
— James Maxwell (1875), “Letter to James Thomson”, Jul 8 [4]
Maxwell surface (3D sketch 1875)

The following is the finished result (see: Maxwell's thermodynamic surface):

Maxwell thermodynamic surface 400px

In circa 1890, Dutch physical chemist Johannes van der Waals published a treatise on the Theory of Binary Solutions in the Archives Néerlandaises, wherein he related his equation of state (see: Van der waals equation) with the second law of thermodynamics, in the form first proposed by American engineer Willard Gibbs, and was able to arrive at a graphical representation of his mathematical formulations in the form of a surface which he called Ψ (Psi) surface following Gibbs, who used the Greek letter Ψ for the free energy of a system with different phases in equilibrium. Shown adjacent is his energy surface for carbon dioxide, shown at the Boerhaave Museum, Leiden. [5]

Energy surface for carbon dioxide

The following is some type of circa 1900 PVT surface model, for carbonic acid H2CO3, showing isotherms carved into a block of wood: (Ѻ)

PVT surface model (1900)

(add discussion)

1. (a) Sengers, Johanna L. (2002). How Fluids Unmix: Discoveries by the School of Van der Waals and Kamerlingh Onnes (GB) (abs) (pgs. 56, 104). Royal Netherlands Academy of Arts and Sciences.
(b) Model PV theta curve – Hunterian Museum & Art Gallery.
2. Gibbs, J. Willard. (1873). "Graphical Methods in the Thermodynamics of Fluids", Transactions of the Connecticut Academy, I. pp. 309-342, April-May.
3. Gibbs, J. Willard. (1873). "A Method of Geometrical Representation of the Thermodynamic Properties of Substances by Means of Surfaces", Transactions of the Connecticut Academy, II. pp.382-404, Dec.
4. Maxwell, James. (1875). “Letter to James Thomson”, July 8th; in The Scientific Letters and Papers of James Clerk Maxwell (pgs. 230-31). Volume 3; 1874-1879.
5. Museum Boerhaave – Wikipedia.

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