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*From*: Stefan Jeglinski <jeglin@4pi.com>*Date*: Mon, 11 Jan 2010 15:04:30 -0500

The good news is that we all understand what is going

on here. We understand it physically, conceptually,

qualitatively, quantitatively, et cetera. You stir

the paint with a paddle. Your arm gets a little bit

tired and the paint gets a little bit warm. We can

quantify the energy as it goes in via

dE = F dot dx

This to me is, or I want it to be (grin), the great unifying concept, but I'm not sure how to word the concept succinctly or also determine whether I can always sleuth it in a physics problem. We are all familiar with F dot dx from mechanics, and using it to explicitly write down the mechanical potential or kinetic energy. But it seems also to be highly general, a way to tie thermo and mechanics together, dE being a sum of as many terms "as you can think of that apply to the problem." The dot notation reinforces the gradient notion JD brought up. Eschewing signs, we have terms such as T dot dS (entropy), P dot dV (mechanical, just another form of mechanics' F dot dx?), mu dot dN (particle exchange), and the aforementioned V dot dQ (charge transfer). To be conservative, the general term "F" must itself be the gradient of a potential, no? So we have 2 gradient in what I have called a sum of generalized F dot dx terms?

Haven't read JD's new discussion yet, but I can't find a good general discussion, including the pitfalls, of what I think I'm trying to say above.

Stefan Jeglinski

**Follow-Ups**:**[Phys-l] Boiling Point of water - a mystery?***From:*"Fakhruddin, Hasan" <hfakhrud@bsu.edu>

**[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>

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