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



Hi John-
I started reading part 1 of your posting, but I need some help.
You start, as I understand it, byu postulating five "variables", RGVBY.
Fine, so I'm working in a 5 dimensional space. Later you talk about a
partial derivative, dG/dB. But this makes no sense to me, because you
have not postulated any functional relationships among the variables. Did
I miss something? Was I supposed to assume an equation of state that
related the variables?
The problem is of interest to me because I am in the process of
discussing an equation of state of a hot pion cloud which uneques free
expansion after its creation.
Regards,
Jack




On Sun, 26 Dec 2004, John Denker wrote:

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



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