Gibbs and Maxwell's U-S-V surface

[WilliamL]

Hi all,

A few weeks ago I found http://www.sv.vt.edu/classes/ESM4714/methods/Gibbs.html" by Dr. Kriz of Virginia Tech. He describes how Gibbs envisioned a 3D U-S-V (energy-entropy-volume) surface, from which Maxwell created a sculpture.

Maxwell believed the surface was of great importance:

"Gibbs and Maxwell continued to use the graphical method to develop
the thermodynamic theory of state by asking the question:
What thermodynamic processes exist when moving from point A to point B on
the energy-entropy-volume diagram?" (Kriz)

I have been unable to find much information about this surface outside of the above website and the original papers of Gibbs/Maxwell.

I was hoping to discover thermodynamic relationships this surface may help visualize. I have created a 3D model of the surface (I can attach the .blend file when I get to the computer lab) that allows many different perspectives.

The relationships this graph provides:

• U-V-S, U-w-q
• Isotherms, Isobats, Isochores, Constant Entropy
• Phase changes
• Gibbs free energy (if you have a point below the surface, the Gibbs free energy is the vertical distance to the surface)
• Capacity for entropy (like above, only horizontal distance)
• and many more

Can anyone provide insight into this surface?

 

[rkriz]

perhaps this will be more insightful:
http://www.esm.vt.edu/~rkriz/classes/ESM4714/methods/free-energy.html

 

[netheril96]

Once you know the relations U=U(S,V) ,you will know everything,including G,F,H,T,C_V,C_p

But I don't know anything about the U-S-V surface
Don't you think it is hard for a human being to visualize an irregular 3D surface?

 

[rkriz]

Josiah W. Gibbs developed and described the U-S-V surface in his 1873 publications,
Graphical Methods in the Thermodynamics of Fluids and A Method of Geometrical
Representation of the Thermodynamic Properties of Substances by Means of Surfaces.
Gibbs preferred his graphical method over his analytic formulae, "It would, however,
be easy, starting from the first and second laws of thermodynamics as usually
enunciated, to arrive at the same results without the aid of analytical formulae, to
arrive, for example, at the conception of energy, of entropy, of absolute temperature,
in the construction of the diagram without the analytical definitions of these quantities,
and to obtain the various properties of the diagram without the analytical expression
of the thermodynamic properties which they involve", and so did James Clerk Maxwell.

James C. Maxwell created a 3D sculpture of Gibbs' surface in clay and plaster that
Gibbs described but never drew and published a 3D diagram showing how lines of
pressure and temperature map onto this surface in his textbook, Theory of Heat.

I don't think it is to hard for a human being to visualize an irregular 3D surface. We
teach our students in sophomore calculus, descriptive geometry, how to model and
visualize complex 3D structures. I believe what Gibbs developed and Maxwell further
developed graphical is no more complex than what we have asked our students to do.

And so i suggest that if anyone is interested read and study these original publications.
I believe that a superior understanding of the thermodynamic theory of state is
realized as recommended by Gibbs and endorsed by Maxwell. And they were human.