Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

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

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 Rauber, Ph.D 
Professor and Head of Physics
Department of Physics
South Dakota State University
Brookings, SD 57007
605.688.5428 (w)
605.688.5878 (fax)

-----Original Message-----
From: [mailto:phys-l-] 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