From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 8 Mar 1996 21:04:05 GMT

In article <4hq03b$dan@guitar.ucr.edu>, baez@guitar.ucr.edu (john baez) says:

>In article <4hlv2o$dl7@geraldo.cc.utexas.edu> glhurst@onr.com (Gerald L.
>Hurst) writes:
>
>>In article <4hllf2$ch9@guitar.ucr.edu>, baez@guitar.ucr.edu (john baez) says:
>>>
>>>In article <31395391.4B3A@jhunix.hcf.jhu.edu> Michael Poon
>>><mpoon@jhunix.hcf.jhu.edu> writes:
>>>
>>>>the temperature (defined as the average kinetic energy of the molecule
>>>>(or atom?))...
>
>>>Temperature is not defined as the average kinetic energy of the
>>>molecules, or atoms, composing a substance.  Temperature is defined
>>>as the change in internal energy per change in entropy, divided by
>>>Boltzmann's constant.  
>
>>That may be true as a pronouncement of the latest committee, but
>>there still exists a sufficient relationships between the two,
>>at least in some special cases, to make it worthwhile to continue 
>>discussing those relationships.  The poster may have phrased his
>>question a little poorly from the standpoint of the strictest
>>rules of physical discourse, but his meaning was clear enough. 
>
>Sure.  I just wanted to remind him that ideal gases are not the last
>word on temperature.  Go ahead and discuss the relationships!  It's
>quite fun and worthwhile.
>
>The "latest committee" you refer to is apparently the one headed by
>Gibbs and Boltzmann in the late 1800s.

That's a clever mot, but not quite accurate. The boys back in 
the late 1800's did include the carnot principle in defining
their temperature scale, but they defined it in terms of 
a constant volume hydrogen gas thermometer. Other groups have
poked at that scale on a very regular basis up to and including
the 1990's.

BTW, I wish you would flesh out that definition you gave for 
temperature using delta E divided by delta S AND the Boltzman
constant. I am perpetually behind in thermo. The only relevancy
of the Boltzman constant that I am familiar with is in relating
temperature to the translational kinetic energy of molecules
in gases, i.e., T = 2*E/(3*k) and the Boltzmann distribution 
law.

I appreciate your helping me learn something new, and apologize
if I am missing something obvious to those more skilled in the
art.

Jerry (Ico)

From: ted@physics12.Berkeley.EDU (Emory F. Bunn)
Newsgroups: sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 8 Mar 1996 21:53:07 GMT

[Newsgroups severely trimmed.]

In article <4hq7c5$lkg@geraldo.cc.utexas.edu>,
Gerald L. Hurst <glhurst@onr.com> wrote:
>In article <4hq03b$dan@guitar.ucr.edu>, baez@guitar.ucr.edu (john baez) says:
>>The "latest committee" you refer to is apparently the one headed by
>>Gibbs and Boltzmann in the late 1800s.
>
>That's a clever mot, but not quite accurate. The boys back in 
>the late 1800's did include the carnot principle in defining
>their temperature scale, but they defined it in terms of 
>a constant volume hydrogen gas thermometer. Other groups have
>poked at that scale on a very regular basis up to and including
>the 1990's.

The annoying thing about Baez is that he tends to be right.  I'm not
sure I know what you mean here, but Gibbs et al. did indeed define
temperature in the way that he described, except that he blew the
factor of Boltzmann's constant.  Temperature is defined like this:

1/T = (dS/dU)_N,

where S is entropy, U is energy, and "_N" means "keeping the number
of particles constant."  

(John probably threw in the factor of Boltzmann's constant because
he's used to measuring temperature in energy units, and he knew that
he needed a Boltzmann's constant to convert to kelvins.  But he
probably forgot that entropy is conventionally measured with its own
factor of Boltzmann's constant, which cancels out the one in the
temperature.  It turns out that there's no Boltzmann's constant
in the definition of temperature, regardless of whether you use
conventional or "natural" units.)

This stuff is in the standard thermo textbooks.  For instance, it's
on pp. 41-42 of Kittel and Kroemer's "Thermal Physics."

For ideal gases, of course, this definition winds up coinciding with
the definition in terms of average kinetic energy of the atoms.

-Ted

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 9 Mar 1996 01:32:55 GMT

In article <4hqa83$64j@agate.berkeley.edu>, ted@physics12.Berkeley.EDU
(Emory F. Bunn) says:

>[Newsgroups severely trimmed.]
>
>In article <4hq7c5$lkg@geraldo.cc.utexas.edu>,
>Gerald L. Hurst <glhurst@onr.com> wrote:
>>In article <4hq03b$dan@guitar.ucr.edu>, baez@guitar.ucr.edu (john baez) says:
>>>The "latest committee" you refer to is apparently the one headed by
>>>Gibbs and Boltzmann in the late 1800s.
>>>
>>That's a clever mot, but not quite accurate. The boys back in 
>>the late 1800's did include the carnot principle in defining
>>their temperature scale, but they defined it in terms of 
>>a constant volume hydrogen gas thermometer. Other groups have
>>poked at that scale on a very regular basis up to and including
>>the 1990's.
>
>The annoying thing about Baez is that he tends to be right.  I'm not
>sure I know what you mean here, but Gibbs et al. did indeed define
>temperature in the way that he described, except that he blew the
>factor of Boltzmann's constant.

It will be easier to understand what I meant if you include
the paragraph you snipped, namely:

	BTW, I wish you would flesh out that definition you gave 
	for temperature using delta E divided by delta S AND the 
	Boltzman constant. I am perpetually behind in thermo. 
	The only relevancy of the Boltzman constant that I am 
	amiliar with is in relating temperature to the translational 
	kinetic energy of molecules in gases, i.e., T = 2*E/(3*k) 
	and the Boltzmann distribution law.

I'm sure John is usually right, but in the context of a definition
of temperature in the post in question it would appear he was in 
fact simply wrong in the specific area to which I called attention 
(Boltzmann constant).  This is not a reflection on John's 
intelligence or abilities - we all err from time to time, I more
than most.

More importantly this perfectly human error helps to underline the
original theme of my post, which was that esoteric definitions
are often of little use in educating people in the general 
principles of science. Note, for instance that no one but a passing
chemist of no particular merit apparently noticed the Boltzmann 
constant error.

If I had written PV = NRT^2 or made some other egregious error
even in the thompson definition definition based on the 
Carnot cycle, everybody would have noticed. John's typo went
unnoticed because of the understandable tendency of even well
educated physicists to rubber stamp esoteric ideas and assume
tha "John is usually right."

If the part you do not understand relates to my comments about
the constant volume hydrogen gas thermometer and its relationship
to the thermodynamic temperature scale adopted in 1887, then 
I suppose I need to emphasize that temperature is not merely 
a thermodynamic generalization relating to the Carnot cycle, but
also a term defined by that group in terms of the behaviour of
a real gas, albeit from properties extrapolated to ideality based 
on limiting values in that specific gas.

I agree that from the moment the equation G = H - TS was first
written we inherently had a definition of a linear temperature 
scale going from hot to absolute zero. Also from the moment
Carnot realized that efficiency could be expressed as a function
of such a temperature scale, we certainly had a reason for
adopting it. On the other hand, more than mere thermodynamics 
equations went into that early committee's definition and today
we still tweak that scale from time to time, especially in the very 
low and very high regions. The most notable recent tweak was in
establishing the triple point of water as 273.16 K by DEFINITION.

Now, I'd like to make an observation regarding the chicken and the 
egg. In many mainstream works on thermodynamics written in the
20th century you will find the following statement:

	The definition of the entropy increment is:
	dS = dq(rev)/T

What I am saying is that it is well established in the 20th century 
paradigm to define entropy in terms of temperature rather than the 
other way around. The point is that "committees" have obviously 
agreed to this concept just as other committees have done it the 
other way around, making entropy the independent variable in the 
definition. Don't mistake this for an argument over the relative 
merits of the two approaches. I am merely pointing out that the matter 
is not quite so simple as to say that a single acceptable viewpoint 
of the proper definition was settled by anybody in the nineteenth 
century except insofar as we choose to revise our 20th century history 
by pretending that the march of science and its paradigms was a 
steady, logical and temporally choreographed event.

Jerry (Ico)

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 11 Mar 1996 03:33:23 GMT

In article <4i0409$m1k@agate.berkeley.edu>, ted@physics12.Berkeley.EDU
(Emory F. Bunn) says:

>In article <4hvn1m$5tp@geraldo.cc.utexas.edu>,
>Gerald L. Hurst <glhurst@onr.com> wrote:
>>Ted, I don't believe that most of us plain vanilla people really
>>define temperature "as kinetic energy" per se. 
>
>If you go back and read the posting to which I was replying, you'll
>find that that's precisely the definition that was being espoused.

That won't be necessary (or possible). I remember the post well, 
and it was patently wrong.

>Baez's exact words were
>>>>>Temperature is not defined as the average kinetic energy of 
>>>>>the molecules, or atoms, composing a substance.  
>
>This is the definition that dcwhite was defending.

I suspect that he was perhaps less than articulate on this point but
probably really was only defending the limited relationship rather
than the simply wrong generalization. I'm assuming this, of course,
and could be dead wrong.

>I'm repeatedly jumping up on my soapbox on this subject because I
>think that this actually is what many people (vanilla or otherwise)
>think of when they think of temperature.  Indeed, I only just now
>realized that it's not the definition you were espousing.  (Maybe you
>made this clear in an earlier post, and I missed it; if so, I'm sorry
>for misinterpreting you.)
>
>Apparently your definition of temperature involves taking a small
>amount of ideal gas and letting it establish thermal equilibrium with
>the system whose temperature you want to know.  Then you use the ideal
>gas law to figure out the temperature of the gas, which is the same as
>the temperature of the other system.  Have I got that right?

Yes, precisely.

>If you want to define temperature that way, it's OK with me.  After
>all, it's equivalent to the definition that everyone else in the world
>uses.  My personal opinion is that it's way more cumbersome and
>confusing than the standard definition, and that it obscures rather
>than clarifying the beautiful and important relationships among
>thermodynamic quantities.  But that's mostly a matter of taste; if you
>like it better, then go right ahead.

Your point is quite reasonable.

>You seem to be claiming -- again, please correct me if I'm
>misinterpreting you -- that your definition is the one used
>historically by Gibbs, Boltzmann, and that crowd.  If that's true,
>then I'm grossly misremembering what I've read about the history of
>thermodynamics.  That's possible; I'll have to go read up on the
>subject again some time.

It's sort of like trying to figure out what the founding fathers
really meant by the right to keep and bear arms, but yes, I
believe that they were focussing on the Carnot cycle in conjunction
with the quite real hydrogen gas thermometer and its obvious
relationship to the kinetic theory.

Again, let me stress that I do not equate kinetic energy with
temperature, nor do I deny the validity of the relationship
between entropy and temperature. I merely suggest that there
are other VALID ways of looking at the definition of temperature,
which may more closely parallel 19th century thinking. I have
also suggested that we LOOK AT THE POSSIBILITY that our teaching
methods may be more esoteric than is desireable. The latter
suggestion, however, is not intended to imply that we should 
teach a less than valid definition merely because it is easier
to remember.

Jerry (Ico)

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 11 Mar 1996 02:21:03 GMT

In article <JMC.96Mar10155414@Steam.stanford.edu>, jmc@Steam.stanford.edu
(John McCarthy) says:

>1. Q is not energy, Q is heat which is only one form of energy.
>However, the heat content of a sample of material is not a well
>defined function of state.  The internal energy is a well-defined
>function of state.

I'm sure you were able to figure out my meaning. All energy may 
not be Q, but Q most certainly IS energy. The contex of my
question should have made it clear what form of energy was being 
referred to. We must, I see accept your word that a satisfactory 
definition for Q exists, but that does not exactly help define the 
quality of the definition of temperature as a function of entropy.

>2. I think that if you define temperature in terms of an ideal gas,
>where the gas is thermally ideal as well as ideal in terms of the gas
>law, you will get the same result as the standard definition.
>However, since ideal gases don't actually exist, a definition in terms
>of the ideal gas law doesn't lead to a means of actually measuring
>temperature.  using
>
>dS = (delta Q}/T
>
>does lead to ways of measuring temperature.

On the contrary, the kinetic theory of gases deals only with
translational energy, which can be measured either directly or
as a function of pressure for a wide variety of real gasses
at low pressures and/or temperatures. Even at ordinary pressures
the noble gases give superb correlation with the theoretical
values.

>By the way temperature isn't defined in terms of entropy.  T as a
>function of state is what makes (delta Q)/T exact.  Entropy is what
>you get when you integrate that exact differential.

If this is the case, then I certainly have no further questions. 
This sub thread began when John Baez stated that:

	Temperature is defined as the change in internal energy 
	per change in entropy.....".

and had his opinion supported by Emory Bunn who said:

	The annoying thing about Baez is that he tends to be right.  
	I'm not sure I know what you mean here, but Gibbs et al. 
	did indeed define temperature in the way that he described, 
	except that he blew the factor of Boltzmann's constant.  
	Temperature is defined like this:
		
		1/T = (dS/dU)_N,

	where S is entropy, U is energy, and "_N" means "keeping 
	the number of particles constant." 

Finally you added:

	The scientific formulation of thermodynamics defined 
	temperature as that which made 

		dS = (delta Q)/T

	an exact differential so that the entropy S became a 
	function of state.

These comments led some of us to question the idea that temperature
be prefferably defined in terms of entropy. Now that you tell us that 
"temperature isn't defined in terms of entropy," the unruly mob
can disperse and return to the saloon.

Thank you for taking the time to write your most interesting post.

Jerry (Ico)

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 13 Mar 1996 23:31:12 GMT

In article <4i6lj9$drj@pipe11.nyc.pipeline.com>, egreen@nyc.pipeline.com
(Edward Green) says:

>'baez@guitar.ucr.edu (john baez)' wrote: 
> 
>>Temperature is not defined as the average kinetic energy of the 
>>molecules, or atoms, composing a substance.  Temperature is defined 
>>as the change in internal energy per change in entropy, divided by 
>>Boltzmann's constant.   
> 
>I think part of the charm of this definition of temperature,  which just
>sends some practical minded people into ecstasies of appreciation,  is the
>fact that it turns the normal order of experimental determination on its
>ear! 
 
Ignoring the Boltzmann constant error, there are a couple of
problems with this so-called definition. First, it is not "the"
definition it is "a" definition.

The second problem is that the proposed definition is at best 
incomplete and at worst simply incorrect. Any process occurring 
spontaneously in an isolated system results in an increase in
entropy but no change in internal energy. Therefore, the "change
in internal energy per change in entropy" is zero, even though
the temperature is not zero. Yes, I know that "reversibility" is
a necessary limitation for such a definition, but that is not
what the paragraph says.

>In my ancient P-chem text  (the same one that allowed me to reminded me
>about the connection between pressure and the kinetic energy of gas
>molecules)  entropy makes its appearance,  by *definition*,  as 
> 
>                      dS  =  d(q_rev)/T 
> 
>In other words,  the reversible heat flow into a system,  divided by the
>absolute temperature.   So in this way of looking at things,  temperature
>is the primitive concept,  entropy the derived concept,  not the other way
>around.  This at least appeals to the historical order of things...  we had
>a number of (imperfect but roughly comensurate) temperature scales,  later
>we 'discovered' entropy.  
 
Not quite. Both theoretical thermodynamics and history begin with
the assumption of a concept of "temperature," expressed with a
little "t," which is nameless in the theory, but called "celcius"
or "reamur' or "fahrenheit" in practice. In both cases the initial 
definition of the scale is formless. History then discovers the 
concept of "absolute temperature" through two channels, the
ideal gas concept and the Carnot cycle. At about the same time
history also recognizes the value of Q(rev)/T based on the same
Carnot cycle, which uses reversible steps. 

Thus the absolute scale is accepted because it has PRACTICAL value 
in its applications to steam engine efficiency and the like. History 
accepts Q(rev)/T as a a fundamental concept and gives it a name 
("entropy"), because it is useful to do so considering the important 
and pivotal role the function plays in mathematically mapping real 
physical phenomena.

Theoretical thermodynamics, armed with the obvious practical
usefulness of "entropy" then proceeds to show that purely 
mathematical constructs can be shown to dictate that an absolute
form be assigned to the temperature (t) which has already been
assumed to thus form a new, non-specific absolute temperature (T). 
Thus the theoretical process mimics the historical process in which 
an empirical (e.g., celcius) scale (t) is first arbitrarily assumed 
and is subsequently formed into an absolute (e.g.,Kelvin) scale (T) 
based ultimately on the same initial seed of practicality of the 
Carnot cycle. Without the driving force of the practical process, 
the "pure" definition of T as a function of S would be just another
abstract mathematical construct, probably unknown by any of us.
 

It is worth noting that even in the purest form of abstract 
thermodinamics one begins with a little "t." 

Jerry (Ico)

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 17 Mar 1996 09:57:06 GMT

In article <314AFDAD.5E8A@hermes.bc.edu>, Keith Ramsay
<Ramsay-MT@hermes.bc.edu> says:

>Gerald L. Hurst wrote:
>>[I wrote:]
>> >You seem to be advocating using a certain sort of definition,
>> >*because* it conveniently gives an important (and idealized!)
>> >case "special" status, and you want to make sure people understand
>> >that special case, and so on. My point is, it would all be somewhat
>> >pointless if it didn't fit into a general scheme, applicable to systems
>> >which are not even made of molecules.
>>
>> If you were able to read this supposed advocacy into my posts, then
>> I must have failed to express myself adequately. 
>
>Oh? Note that I'm not imputing to you the claim that it should be 
>the only definition to use, ever. You have, however, advocated its 
>use rather strongly, unless somehow someone has been forging posts 
>from you.
>
>One rather key use of a definition is in communication.
>
>Earlier in the thread, you said:
>
>   The ideal gas temperature scale may now be "obsolete" for 
>   certain purposes, but it is a far better mechanism for teaching 
>   the uninitiated to develop some personal association in their 
>   minds with the interactions of material and energy at least 
>   from the macroscopic and moderately paced perspective of the 
>   older but not yet dead paradigms.
>
>Far better? Not just better, far better. I haven't seen you withdraw
>these claims.

You most certainly will not see me withdraw anything in the paragraph
you have quoted. The "uninitiated," who have never heard of Entropy
are hardly in a position to use a definition such as the one
recently presented by John Baez. John's definition was a humdinger,
but hardly suitable for the vast majority of students learning to
use science and mathematics as a map for the physical territory 
those students have trod but not understood to any degree.

If we were to adopt the simpler definition, which John first
suggested  T = dE/dS, a basic restatement of the second law at the
expense of teaching the historical ideal gas approach, we would
simply create even vaster hoards of semiliterate scientists and
engineers who could regurgitate but understand not at all.

Again you are in confusing an argument relating to to ORDER in which 
ideas are taught with an argument for the inherent quality of two 
definitions. The distinction is not subtle, but it appears difficult 
to grasp by many here.

Most of the arguments I have seen here which denigrate the 
importance of history are by people who have exhibited an 
astonishing ignorance of that same history.  So much is this the
case, that I now realize that most of the advocates of the
supremacy of newer definitions are abysmally ignorant of the 
fact that even those definitions rely on the dog-eared old methods
of the ideal gas law to calibrate the scales. "dE/dS" is only a
"conceptual definition." It cannot by itself produce a scale on
which you can assign a triple point to carbon dioxide unless one
uses that point as an arbitrary anchor for the system.

When I described the definition of "temperature" as it was first
proposed by Thompson and and later adopted international agreement,
I did not say "PV = nRT," but rather I described in many words
an entire scheme which takes one from the Carnot cycle, an 
expression of the second law through the theoretical ideal gas
law to the real gas thermometers which are still used today, again 
by international agreement. 

Even when one uses the most abstract of concept definitions as a 
starting point, it is the actual gas thermometer which acts as the 
basic standard for the international temperature scale (ITS) 
with its myriad of reference points. The ITS90 scale which came 
into force on January 1, 1990 is no different - it still relies
on the ideal gas law and its practical implementation in the
form of the real gas thermometer.  The gas thermometer is 
augmented by the acoustic thermometer, which again depends on
ideal gas relationships.

You were not listening when I pointed out that the entropy concept
is contained in the carnot cycle, from whose reversible processes 
the equality Q1/T1 = Q2/T2, i.e.,constant entropy, descends and
from which process Thompson PARTLY derived the definition. Thompson 
incorporated the real gas thermometer in the overall method two years 
later and the whole schema was adopted in 1887. There have been many 
adjustments to that scale since then, but the primary standard is
still the REAL gas thermometer, still interpreted by extrapolations
of the ideal gas law to extreme conditions to remove the vestiges
of nonideality.

Again I am not arguing "PV=nRT" vs "dE/dS = T"; "PV = nRT" is merely
part of a larger system that may start with Carnot or the entropy
concept (which is inherent in Carnot) derived from some more abstract 
definition.  When Thompson finally incorporated the ideal gas concept
into his already existing CONCEPTUAL definition, he had extensive
experience in the experimental investigation of the NONIDEALITY of 
real gases.  He and the international committee who later accepted
his system, nonideal warts and all, knew exactly what they were 
doing and why. Their example has been followed by all succeeding
international authorities for reasons which are still valid today. 

There seems to be some idea here that it is only in the recent
years that minds have expanded to the "modern" concepts which
were unknown to the generations of teachers who have taught
at least the elements of the way our latest international scales
have been defined. It is this group who have gotten swept up into
the odd notion that earlier generations were too ignorant to 
understand the finer points of good teaching methods. Perhaps this
is because you represent the first generation of college graduates
who were required only to learn their math and quantum mechanics
without any sense of either the history of their subject or the
actual mechanics of bridging from the theoretical to applications 
in the real world where measurements must actually be made.

Reread some of the posts of your supporters and note the pride they 
take in their ignorance of "ancient history."

Do you really think that Wolfgang Pauli was too ignorant to
understand modern approaches to physics when he used the classic
textbook definitions of temperature and entropy in his lectures
on thermodynamics in Switzerland? He obviously made a conscious
choice that thousands of other knowledgable scientists have made.
In so doing, he was not expressing an opinion on whether one 
definition is "better" than another, but he was definitely 
favoring one teaching approach - not for specialists but for
scientists in general and for those who would never make the grade
but would at least know from whence those numbers called "K"
originated.

Again, for those whose reading comprehension and historical
knowledge are not quite on par with their mathematical aptitude
and training, I do not have any opinion on which elementary
mathematical expression of either temperature or entropy is
"Better" or more "sophisticated." 

I do suggest that the long version of the definition of temperature,
as I have outlined it, is not only the best FIRST lesson, but should
be mandatory in addition to any other versions that are taught. If
you can succeed also in implanting more sophisticated notions, go
to it. One lesson is not learned at the expense of the other.

Our future generations will be better off if we make sure that the
current crop of scientists is the last to lack both historical
knowledge and hands-on experience. We will profit if the world's
scientists know how things are actually done and why.

When I said that I suggested that we at least look at the 
possibility that our teaching methods leave something to be desired,
I wasn't simply referring to some individual definition.

BTW, yes, William Thompson (Lord Kelvin) WAS an engineer, but he also
did a journeyman's job as a scientist.

>I also tend to think your calling the statement of another definition 
>"possibly true as a pronouncement of the latest committee" to be 
>intended to leave the impression that it is not so hot, at least from
>a longer-term point of view.

I did not call *another* definition "possibly true as as a 
pronouncement of the latest committee." I said that of *THE*
definition. My statement was too mild. The latest real 
international committees have not adopted any such definition. If
there is such a "committee" worth mentioning it is well hidden
from rank-and-file scientists. I made the mistake of assuming
that John knew something about some important formal resolution
that I did not. It appears that despite our having been told of
such a committee from the 1800's, the only real group consists
of a few current mathematicians with a proclivity for algebraic 
transposition.

The "sophisticated" definitions per se are ok until it comes to 
explaining to the students why the units of entropy in the handbooks 
are given as Joules/K, which is kind of like listing the second in 
units of joules, grams and centimeters.  This sort of thing works 
better in a mathematics book than in some pchem classes.

If I seem to be giving you folks less credit than before, it's 
because I've thought and read a bit more and looked into some
of the more far-out thermo systems without finding much 
support for your positions. In that same period I have noted that
the most vocal arguments against the classical approach come
from those who know the least about it. If I am perceived as
backsliding, chalk it up to the pull of the weight of the evidence 
that some (not all) of the arguments for more "sophisticated" 
definitions as general educational fare are the smoke of pipe 
dreams.

Jerry (Ico)


 
-----

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.physics
Subject: Re: Meaning of Thermodynamic Temperature
Date: 19 Mar 1996 07:41:21 GMT

In article <4il19g$cuv@pipe10.nyc.pipeline.com>, egreen@nyc.pipeline.com
(Edward Green) says:

>The modern definition of temperature for a simple physical system at
>equilibrium is:   The partial derivative of internal energy with respect to
>entropy,  holding volume (and of course mole number) fixed.  Correct? 
> 
>Can someone provide a physical motivation of this?  Presumably this would
>start from discussion of the 'exact differential' 
> 
>                             dS = dq_rev/T 
> 
>I am unable to free my thinking from that old bugbear that the temperature
>is a measure of the amount of energy available for partition,  if not
>precisely the 'average energy per mode'.   
 
It depends on what you mean by a "physical motivation."

If you mean a relation with practical physical phenomena then it
would be the appearance of constant Q/T in the reversible processes
of the Carnot cycle from which which the original concept of
Claussius' entropy stems.

If you mean a correlation with other physical and mathematical
concepts more inherently fundamental and quantifiable , you might 
look again at the most excellent recent post by Matthew J McIrvin 
entitled *Where does the Boltzmann factor come from?*. Matthew 
announced the coming of this post, which easily qualifies as a 
treatise, in an earlier message (*Re: Entropy of a Two State System*) 
in which he promised it would be "simple enough to be comprehensible 
to a particle physicist..." He is as good as his word, so I would
advise all of you who have been following the *Re: [Q] Energy of
atoms in molecules* to read matthew's work.

Although the article title emphasizes the derivation of the Boltzmann
constant, it deals equally well with the concepts of both entropy
and temperature. If you like to believe that dE/dS is *THE* 
definition of temperature, you can hone your arguing skills. If you 
have a "different strokes" attitude toward such matters, you should 
also read it for the perspective it brings to the overall subjects
of energy, entropy, and temperature.

Jerry (Ico)

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 19 Mar 1996 08:21:59 GMT

In article <1996Mar19.051115.8793@pmafire.inel.gov>,
russ@pmafire.inel.gov (Russ Brown) says:

>>There was no ideal gas law in the 18th century, no molecules no 
>>atoms, no absolute temperature scale.  Dalton and Avagadro and 
>>Gay-Lussac and Carnot and Thompson all developed the necessary 
>>intellectual ingredients in the 19th century.
>>

>Before dancing too far on thin ice, you might want to consider
>  
>  1) L. Boltzman, Populare Schriften (1905)
>  
>  2) L. Boltzman, Weitere Studien uber Warmegleichgewicht unter
>     Gasmoleculen, Sitzungberichte der K.Wiener Akademie, and
>     his Lectures of Gas Theory (Berkely, 1964).

Let me guess: 

1. You're testing me to see if I know that Ludwig spelled his name
   with 2 n's ?

2. You believe that since he was born in 1844 his work on "Further
   Studies of Thermal Equilibrium in Gas Molecules," published
   postumously, proves that the ideal gas law or the absolute 
   temperature scale was developed in the 18th century?

3. You believe that 1844 was in the 18th century?

4. You were wondering if I speak German?

5. You believe that Boltzmann published a paper in 1905 on the 
   problems of dancing on thin ice?

6. You had absolutely nothing to say, but you said it anyway?

Jerry (Ico) 

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 19 Mar 1996 22:26:05 GMT

In article <1996Mar19.135921.9793@pmafire.inel.gov>,
russ@pmafire.inel.gov (Russ Brown) says:

>No.  And you lose a point on "posthumously".  :)  
>You lose half a point for not catching the incorrect typing of "Berkeley".

You are quite right. I dropped the "h," which was  careless of me.
I really should take more time to proofread my postings. Ah, so you
were referring to the city in california.

>No.  The resolution of questions about scientific principles is not
>limited to historical niceties.  You seemed somewhat excited, too.

There is not and has not been any discussion of "scientific principles"
by me. This discussion deals with a matter of perspective and in 
particular with the question of whether there is only one acceptable
"definition" of the "temperature." The specific post to which you
made your less than relevant comments about Boltzmann had absolutely
zilch to do with the accuracy of my comments concerning the time
frame of the development of theories relating to ideal gases.  Once 
more we hear the endorsement of the banality of a group which actually 
takes pride in their lack of historical perspective.

In particular, references to Boltzmann and his work do not 
contribute much to the support of dogmatic argumments regarding
temperature definitions. Part of Boltzmann's fame rests on his
work on the kinetic theory of gases, which is a two-edged sword
in an argument advocating definitions based solely on his other
work on the relation of entropy to probability. Remember that 
Boltzmann's constant is also called the molecular ideal gas 
constant. How do you suppose the numerical value of his famous
constant was first determined, Bubele?

Here's are three bits of perspective from the *Encyclopedia of Physics*

	A precise distinction between kinetic theory and stastical
	mechanics cannot be made. The latter is usually more
	formalized but utilizes the same basic laws of mechanics
	and collisions. Statistical mechanics is generally regarded
	as the aspect of kinetic theory that deals with interpreting
	thermodynamic quantities like entropy and free energy by
	molecular collision analysis.

and, with regard to the derivation of the Maxwell-Boltzmann law:

	Finally recourse to Jopule's derivation is taken wherein the 
	mean molecular kinetic energy arises from

		(1/2)mc^2 = (3/2)(R/n)T = (3/2)kT

	The molal gas constant R, divided by Avagadro's number n,
	is called Boltamann's constant and is represented by k.

and, finally

	The Kelvin temperature of an ideal monatomic gas (thus of
	a real monatomic gas at sufficiently low density and
	pressure), for example, is given by T = (2/3k)E, where E is 
	the mean kinetic energy per atom and k is the universal 
	Boltzmann constant. More complicated relations hold for more 
	complicated systems; they all support the the generalization 
	that higher temperature is a macroscopic manifestation of 
	more energetic molecular and submolecular motion. This 
	generalization is for many scientists the essence of the 
	temperature concept.

>Never did.  But in 1906, he committed suicide, having become depressed
>about the scientific establishment's hostility to his work.  Buried in
>the Zentralfriehof in Vienna, his tombstone was engraved with the
>commendable (for all, even you) relationship, S = k ln(W).

Why did they bury his tombstone and if it is buried, how do you know
what is written on it?:)

Remember that k is R/N and is expressed in J/K. Wasn't it nice of
lord K to provide that K 

What conceit leads you to believe that simply because I deplore your
obvious ignorance of history and do not share your particular myopia,
that I am less capable of appreciating intellectual achievement than 
you? If they had not chisled it in stone, would the feat have been any
less admirable? Catchy epitaphs copied from the encyclopedia are not 
what I had in mind when I suggested learning a little history. 

>>6. You had absolutely nothing to say, but you said it anyway?
>
>"Nothing" seemed appropriate for a conversation that had degraded to
>personal exchanges.

It is sad that you admit being drawn into a discussion merely by
the attraction of "degraded personal exchanges" when you
had nothing of value say. I have tried to turn a sow's ear
into a silk purse by usuing your vacuous post as an excursion
point for some observations on perspective. 

I do not expect you to break your lockstep with the marching band 
of the sci.physics mafia, but consider the possibility that there 
might be other valid viewpoints.

Jerry (Ico) 

From: glhurst@onr.com (Gerald L. Hurst)
Newsgroups: sci.chem,sci.energy,sci.mech.fluids,sci.materials,sci.physics
Subject: Re: [Q] Energy of atoms in molecules
Date: 7 Mar 1996 20:59:26 GMT

In article <JMC.96Mar7075624@Steam.stanford.edu>, jmc@Steam.stanford.edu
(John McCarthy) says:

>Let me return to the topic of the thread - energy of atoms in
>molecules.
>
>I'm not entirely sure of this, so I hope someone will correctly if I
>am mistaken.
>
>Molecules have ground states and can absorb energy to go into excited
>states.  However, until a temperature considerably higher than room
>temperature is reached, molecules are almost all in the ground state.
>Hence the internal energy of molecules does not contribute to the
>specific heat of the substance below relatively high temperatures.
>
>Someone should tell us how high.

If you track the heat capacity of a simple gas such as hydrogen
as a function of temperature from well below room temperature
up to say a theoretically extrapolated temperature of say 6,000 deg,
you will find that there is a continuous increase in the value.

In my simple way, I assume that the major low-temperature contributions
to the value are first from rotational states as is consistent with
the relatively low frequency of infrared rotational spectra. More 
complex molecules show much higher heat capacities than simple diatomic 
molecules below room temperature, so at least a number their more 
numerous degrees of freedom must be active. For instance, C(v) for 
ethanol is nearly 5 times greater than for a monatomic gas at room T.

Presumably, the larger molecules have an easier time of it in reaching
numerous vibrational states because they do not necessarily require
intermolecular collisions to enable a new mode.

Anyhoo, it does appear that internal modes of one sort or another are
significantly active at normal temperatures albeit nowhere near as
active as at higher temps.

One incidental point is that at high pressure or low temperature
one may sometimes see increases in heat capacity on cooling, even
in the case of hydrogen or inert gases. At the other extreme, even
monatomic gasses may show increases in C(v) as a result, I assume,
of ionization.

Jerry (Ico)