Relationship between thermodynamics and differential geometry

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I am taking thermodynamics this semester as well as a course in differential geometry of surfaces, and I am seeing a lot of overlap.

For example, I can create a "state space" isomorphic to R3 of TxPxV I can then define a surface on this space of PV=NkT I can define quasi static state equations as curves restricted to the surface.

Is this an approach a useful approach to thermodynamics? Is this studied at all? I Googled "Thermodynamics differential geometry" and got results that were about much more advanced topics in thermodynamics. Is there a text, or paper, studying basic (I am taking an undergrad course) thermodynamics from this perspective?

 

[Andy Resnick]

Thermodynamic phase space has the structure of a 'contact manifold', in contrast to the symplectic manifold of classical mechanics phase space.

http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1142-13.pdf
http://www.math.rug.nl/arjan/DownloadPublicaties/eberard07.pdf