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*From*: "Rauber, Joel" <Joel.Rauber@SDSTATE.EDU>*Date*: Tue, 12 Jan 2010 07:44:04 -0600

John D. wrote in part:

We need to respond to this in a nuanced way:

-- On the one hand, we need to take this seriously.

We need to be careful. Thermodynamic state space

is different from ordinary XYZ space, different in

important ways. There are things you can get away

with in XYZ space that you cannot get away with in

thermodynamic state space. This includes dot products.

This includes any notion of the P direction being

perpendicular to the V direction. Students get

this wrong all the time, and it messes them up.

There is negative transference from XYZ space to

state space.

-- On the other hand, there are still lots of useful

things we can do in state space. Even though we

cannot identify any particular direction as the E

axis, we can identify contours of constant E, and

that's all we really need in order to do calculus,

up to and including Taylor series.

I have a question, asked in sincere ignorance:

If one can identify curves of constant E (or whatever coordinate), doesn't the idea of a tangent to the curve imply some sort of notion of directionality?

I suppose I could paraphrase by asking if tangent spaces exist for the Thermodynamic State Space?

Joel

_________________________

Joel Rauber, Ph.D

Professor and Head of Physics

Department of Physics

South Dakota State University

Brookings, SD 57007

Joel.Rauber@sdstate.edu

605.688.5428 (w)

605.688.5878 (fax)

-----Original Message-----

From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-

bounces@carnot.physics.buffalo.edu] On Behalf Of John Denker

Sent: Tuesday, January 12, 2010 6:44 AM

To: Forum for Physics Educators

Subject: [Phys-l] thermodynamic dot products, or not

**Follow-Ups**:**Re: [Phys-l] thermodynamic dot products, or not***From:*John Denker <jsd@av8n.com>

**References**:**[Phys-l] T dS versus dQ***From:*John Denker <jsd@av8n.com>

**[Phys-l] thermodynamics of dissipation***From:*John Denker <jsd@av8n.com>

**Re: [Phys-l] thermodynamics of dissipation***From:*Stefan Jeglinski <jeglin@4pi.com>

**[Phys-l] thermodynamic dot products, or not***From:*John Denker <jsd@av8n.com>

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