From: mshute@cs.man.ac.uk (Malcolm Shute)
Newsgroups: bionet.info-theory
Subject: Re: Question on entropy at 0K
Keywords: entropy of Cu
Date: 12 Nov 92 12:41:58 GMT
Organization: Dept Computer Science, University of Manchester, U.K.

What have I done!?!
'Sorry folks for igniting this sudden flurry of discussion in this newsgroup!
Actually, I'm not sorry!
I've found the resulting discussion extremely interesting.
I've also found it surprising.
And confusing.

Where has it got us?

>In article I wrote:
>>I said that I was therefore confused as to what it was that you had consulted
>>in your tables on entropy of copper.

In article <BxIJ2v.67w@ncifcrf.gov> toms@fcs260c2.ncifcrf.gov (Tom Schneider) writes:
>Pull out your CRC and look up entropy entries.  You'll see the data there.
Ah... now, Tom, you've forgotten that I'm only a visitor to this group...
a mere mortal computer architect who thinks that CRCs are cyclic redundancy codes :-)

>Other folks posted answers to the other parts of your question.
That's as maybe, but I'm still no clearer what they've told me.

If you'd asked me a couple of weeks ago, I would have told you that I was
happy with the explanation that (using my own simile... so correct me if it's
wrong) "Entropy is a bit like potential energy... you can't work with it as
an absolute static measure (this object has this number of joule so potential
energy, or this number of units of entropy), but you can work with it as a
absolute dynamic measure (this object has just lost/gained this amount
of potential energy, or this amount of entropy)".

I was happy with this... but then you mentioned these CRC tables, and I was
confused... they seem to be tables of absolute static entropy for Copper at
various temperatures.  I don't understand!

How can you say: "This 63.5g lump of copper at 1K has 'x' units of entropy"?
Is this what your CRC tables would be saying?
Surely the amount of entropy in a substance (like the potential energy) depends
on how deep you are prepared to look into it...
This particular lump has 6.024e23 atoms to arrange in an imperfect lattice,
so there's one source of entropy... the amount of information needed to specify
that arrangement.
But... 63.5g of Cu can also be thought of as being a lump of (29+29+34.5)*6.023e23
(i.e. 5.57e25) atomic particles... and they require somewhat more information
to specify as a structure.
But... 63.5g of Cu can also be viewed as 1.67e26 quarks...
But... 63.5g of Cu can also be viewed as n*1.67e26 sub-quark particles which we
haven't even discoved the existance of yet...!

So... really, my initial question was "What are these CRC tables able to state"?


Now... since then, this sudden flurry of discussion has occurred, and confused
me more!
First someone says that all substances have zero entropy at 0K
[BTW... yes, it was *my* fault for erroneously thinking that your tables were
for 0K]
and that it doesn't matter how many undiscovered levels of sub-atomic particle
there are, because the entropy of each of them is 0 at 0K.
Fine.

Then, someone says that the entropy of a substance is only 0 at 0K if it
is a perfect crystal.
But I am then lead to ask, what about NaCl?  If it has 0 entropy, then it
ceases to have structure (?), and hence ceases to be NaCl, surely?
A 58.4g lump of NaCl at 0K would then be indistinguishable from a 23g lump
of Na lieing beside a 35.4g lump of Cl.  Is this correct?

Then, someone else says that some substances (H2O and CO2... interesting, they
are both compounds, like NaCl) have >0 entropy at 0K.  In which case, my
question about "how do you know how many sub-sub-sub-atomic particles there
are in the structure?" rears its head again.


As I say... thanks everyone... the discussion so far has been extremely
interesting.  Please, please, please keep going... you haven't convinced me
yet of what is going on here!
--

Malcolm SHUTE.         (The AM Mollusc:   v_@_ )        Disclaimer: all
Newsgroups: bionet.info-theory