Maxwell's thermodynamic surface
Encyclopedia
Maxwell’s thermodynamic surface is an 1874 sculpture made by Scottish physicist James Clerk Maxwell
(1831–1879). This model 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). It was based on the American scientist Josiah Willard Gibbs
’ graphical thermodynamics
papers of 1873. The model, in Maxwell's words, allowed "the principal features of known substances [to] be represented on a convenient scale."
techniques.
Maxwell sculpted the original model in clay and made three plaster cast
s of the clay model, sending one to Gibbs as a gift, keeping the other two in his laboratory at Cambridge University. Maxwell's copy is on display at the Cavendish Laboratory
of Cambridge University, while Gibbs' copy is on display at the Sloane Physics Laboratory of Yale University
, where Gibbs held a professorship. A number of historic photographs were taken of these plaster casts during the middle of the twentieth century – including one by James Pickands II, published in 1942 – and these photographs exposed a wider range of people to Maxwell's visualization approach.
of 15 July 1875 included sketches of these lines. Maxwell provided a more detailed explanation and a clearer drawing of the lines in the revised version of his book Theory of Heat, and a version of this drawing appeared on a 2005 US postage stamp in honour of Gibbs.
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, though not always with complete historical accuracy. For example, the thermodynamic surface represented by the sculpture is often reported to be that of water, contrary to Maxwell's own statement.
had constructed a plaster pressure
-volume
-temperature
plot, based on data for carbon dioxide
collected by Thomas Andrews
.
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. 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.
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
(1831–1879). This model provides a three-dimensional plot of the various states of a fictitious substance with water-like properties. This plot has coordinates volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
(x), entropy
Entropy
Entropy is a thermodynamic property that can be used to determine the energy available for useful work in a thermodynamic process, such as in energy conversion devices, engines, or machines. Such devices can only be driven by convertible energy, and have a theoretical maximum efficiency when...
(y), and energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
(z). It was based on the American scientist Josiah Willard Gibbs
Josiah Willard Gibbs
Josiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...
’ graphical thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
papers of 1873. The model, in Maxwell's words, allowed "the principal features of known substances [to] be represented on a convenient scale."
Construction of the model
Gibbs' papers defined what Gibbs called the "thermodynamic surface," which expressed the relationship between the volume, entropy, and energy of a substance at different temperatures and pressures. However, Gibbs did not include any diagrams of this surface. 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 the surface. This reflected Maxwell's talent as a strong visual thinker and prefigured modern scientific visualizationScientific visualization
Scientific visualization is an interdisciplinary branch of science according to Friendly "primarily concerned with the visualization of three-dimensional phenomena , where the emphasis is on realistic renderings of volumes, surfaces, illumination sources, and so forth, perhaps...
techniques.
Maxwell sculpted the original model in clay and made three plaster cast
Plaster cast
A plaster cast is a copy made in plaster of another 3-dimensional form. The original from which the cast is taken may be a sculpture, building, a face, a fossil or other remains such as fresh or fossilised footprints – particularly in palaeontology .Sometimes a...
s of the clay model, sending one to Gibbs as a gift, keeping the other two in his laboratory at Cambridge University. Maxwell's copy is on display at the Cavendish Laboratory
Cavendish Laboratory
The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the university's School of Physical Sciences. It was opened in 1874 as a teaching laboratory....
of Cambridge University, while Gibbs' copy is on display at the Sloane Physics Laboratory of Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...
, where Gibbs held a professorship. A number of historic photographs were taken of these plaster casts during the middle of the twentieth century – including one by James Pickands II, published in 1942 – and these photographs exposed a wider range of people to Maxwell's visualization approach.
Uses of the model
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." He sent sketches of these lines to a number of colleagues. For example, his letter to Thomas AndrewsThomas Andrews (scientist)
Thomas Andrews FRS was an Irish chemist and physicist who did important work on phase transitions between gases and liquids.-Life:Andrews was born in Belfast, Ireland where his father was a linen merchant...
of 15 July 1875 included sketches of these lines. Maxwell provided a more detailed explanation and a clearer drawing of the lines in the revised version of his book Theory of Heat, and a version of this drawing appeared on a 2005 US postage stamp in honour of Gibbs.
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, though not always with complete historical accuracy. For example, the thermodynamic surface represented by the sculpture is often reported to be that of water, contrary to Maxwell's own statement.
Related models
Maxwell's model was not the first plaster model of a thermodynamic surface: in 1871, even before Gibbs' papers, James ThomsonJames Thomson (engineer)
right|300px|James Thomson was an engineer and physicist whose reputation is substantial though it is overshadowed by that of his younger brother William Thomson .-Biography:Born in Belfast, he grew up mostly in Glasgow...
had constructed a plaster pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
-volume
Volume
Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....
-temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
plot, based on data for carbon dioxide
Carbon dioxide
Carbon dioxide is a naturally occurring chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom...
collected by Thomas Andrews
Thomas Andrews (scientist)
Thomas Andrews FRS was an Irish chemist and physicist who did important work on phase transitions between gases and liquids.-Life:Andrews was born in Belfast, Ireland where his father was a linen merchant...
.
Around 1900, the Dutch scientist Heike Kamerlingh Onnes
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He pioneered refrigeration techniques, and he explored how materials behaved when cooled to nearly absolute zero. He was the first to liquify helium...
, together with his student Johannes Petrus Kuenen
Johannes Petrus Kuenen
Johannes Petrus Kuenen was a Dutch physicist.-Biography:Kuenen was the son of the professor of theology Abraham Kuenen and his wife Wiepkje Muurling. His son Philip Henry Kuenen was professor of geology. From 1884 to 1889 he studied at the University of Leiden, where he graduated in 1892...
and his assistant Zaalberg van Zelst, continued Maxwell's work by constructing their own plaster thermodynamic surface models. 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.
External links
- Photograph of one of the two Cambridge copies in the Museum at the Cavendish LaboratoryCavendish LaboratoryThe Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the university's School of Physical Sciences. It was opened in 1874 as a teaching laboratory....
; for better readable legends to go with the axes, see here - Thermodynamic Case Study: Gibbs' Thermodynamic Graphical Method at Virginia Tech's Laboratory for Scientific Visual Analysis
- Maxwell’s thermodynamic surface at the "Encyclopedia of Human Thermodynamics"
