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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?

Perhaps at a more introductory level than you want, but a splendid antidote for Fear of S and Entropy Envy:

*Brewer’s Introduction to a Measure of Entropy*

*http://www.jick.net/~jess/hr/skept/Therm/node5.html <http://www.jick.net/%7Ejess/hr/skept/Therm/node5.html>*

*Entropy *

/"If we wish to find in rational mechanics an a priori foundation for the principles of thermodynamics, we must seek mechanical definitions of temperature and entropy."/-- J.W. Gibbs

The function Omega(n,N)is called theMULTIPLICITY FUNCTIONfor the partially specified system. If /N/ and /n/ get to be large numbers (which is usually the case when we are talking about things like the numbers of electrons in a crystal), Omega(n,N)can get/really huge. /<http://www.jick.net/%7Ejess/hr/skept/Therm/footnode.html>It is so huge, in fact, that it becomes very difficult to cope with, and we do what one usually does with ungainly huge numbers to make them manageable: we take its/logarithm/. We define the [natural] logarithm of Omega to be theENTROPYs:

s = ln Omega(15.3)

Let's say that again: theENTROPYs is the/natural logarithm/of theMULTIPLICITY FUNCTIONOmega --/i.e./of the/number of different ways we can get the partially specified conditions/in this case defined by /n/.

Is this all there is to the most fearsome, the most arcane, the most incomprehensible quantity ofTHERMODYNAMICS? Yep. Sorry to disappoint. That's it. Of course, we haven't played around with s yet to see what it might be good for - this can get very interesting - nor have I told this story in an historically accurate sequence; the concept ofENTROPYpreceded this definition in terms of "statistical mechanics" by many years, during which all of its properties were elucidated and armies of thermal physicists and engineers built the machines that powered the Industrial Revolution. But understandingTHERMODYNAMICSthe old-fashioned way is/hard/! So we are taking the easy route - sort of like riding a helicopter to the top of Mt. Everest.

from A Skeptic's Guide: Jess H Brewer 1998

per Brian W