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Re: [Phys-l] The Abysmal Foundations of Thermodynamics



On 12/07/2010 12:32 AM, Derek McKenzie wrote:

To get to my point, can any of you please refer me to a text, or a
collection of journal articles, or even a website, that treats
Thermodynamics with the logical consistency and conceptual clarity
that is missing from virtually every resource I have ever
encountered?

On 12/07/2010 07:18 PM, John Mallinckrodt mentioned
Daniel V. Schroeder
_An Introduction to Thermal Physics_
as a "favorite text" that "may not satisfy Derek's apparent thirst
for extreme rigor".

=======

As I read it, Derek was not asking for "extreme rigor" ... just
clarity and consistency.

For my own account:
-- I vote for clarity and consistency.
-- I don't mind approximations, provided they are labeled as such.
-- Especially in an introductory text, I don't even mind crude and/or
naive approximations, provided they are labeled as such.
-- Indeed I rather enjoy collecting rules of thumb.
++ We should insist that rules of thumb not be passed off as fundamental
laws of nature!

=======

One conspicuously nice thing about the work of Schroeder -- and his mentor
Moore -- is that they have taken to heart the fact that there is no Q
such that dQ = T dS. More generally, I would say there are no inexact
differentials, in the sense that d(anything) is provably exact. T dS
exists as an inexact one-form, but it is not the gradient of any potential
(except in trivial cases).

This book is proof-by-construction that you can survey most of of thermo-
dynamics without ever writing dQ or dW. Schroeder calls dQ a «crime»,
which sounds about right to me.

ON THE OTHER HAND ... If the question is where to find a clear and
consistent discussion of the foundations of thermodynamics, this book
is not the answer. Mostly it avoids foundational issues; for example:
-- AFAICT there is no serious discussion of what we mean by "energy"
-- AFAICT there is on serious discussion of what we mean by "conservation"

This is quite a significant omission, given that the technical use
of these terms conflicts so strongly with the vernacular use, e.g.
in the expression "please conserve energy".

And when this book does address foundational issues head-on, the results
are not pretty.

-- There is no acceptable discussion of the second law; indeed on
page 59 it says «it’s not a a fundamental law at all». Wow.

-- On page 75 entropy is boldly defined as
S ≡ k log Ω [1]
... which is sad, because it would have cost nothing to define it
in terms of −∑ p log p and then derive equation [1] as an immediate
corollary. There is no reasonable reason (pedagogical, practical,
or otherwise) for using equation [1] as the definition.

-- The long discussion on «Free Energy as Available Work» is fundamentally
flawed.

For a somewhat more systematic discussion of the strengths and weaknesses
of this book, see
http://www.av8n.com/physics/schroeder-thermal.htm