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

["Rauber, Joel" <Joel.Rauber@SDSTATE.EDU>]

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