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[Phys-L] Re: geometric interpretation of partial derivatives



JD wrote on his cited URL:
"What's worse, the conventional calculation provides little insight, so that
you are left wondering how anybody could possibly have discovered equation
14. If you ever forget the result, you'll have a hard time re-discovering
it, unless you have tremendous insight ... or unless you express the partial
derivatives in terms of wedge products"

Your Eq (14) is derived in standard texts ( Callen's, "Thermodynamics" or
Margenau & Murphy's "The Mathematics of Physics & Chemistry") The
derivation is identical to yours, but uses standard partial derivative
notation.


Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "John Denker" <jsd@AV8N.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Sunday, December 26, 2004 7:09 PM
Subject: Re: geometric interpretation of partial derivatives


|I added yet another section to my rant about partial derivatives and wedge
products,
| namely a discussion section, including a worked example. Specifically,
consider
| the case of free expansion (i.e. conditions of constant energy and
constant number
| of particles), and find an expression for
| the derivative of the entropy w.r.t volume
| in terms of
| pressure and temperature.
|
| There's an easy way to do it:
| http://www.av8n.com/physics/partial-derivative.htm#sec-freex
|
|