Re: [ATM] Entropy OT -- But, What the hell?

[Mark Holm <mdholm@telerama.com>]

Entropy is a slippery subject. It is most easily understood in the

context of classical thermodynamics, and even there it is a bit of a 
mind bender.  There are some chemical and thermal phenomena that are 
impossible, or at least pretty difficult, to explain without entropy.

For instance, if you have room temperature ammonium nitrate and room 
temperature water, and you dissolve the ammonium nitrate in the water, 
the solution becomes cold.  In other words, it has less thermal energy 
than it had before you mixed the two together.  How the heck did that 
happen, and where did the energy go?  It takes entropy to explain it.  
Josiah Willard Gibbs, a Connecticut Yankee, described it with the equation

delta G = delta H  -  T delta S

G is Gibbs free energy,  H is heat energy or enthalpy,  T is temperature 
and S is entropy.  Delta means the change from before an event to 
after.  For anything (macroscopic) to happen, the net change in G has to 
be negative.  Now, for a firecracker going off, it is easy to see that 
delta H is negative.  A Whole bunch of heat comes out.  Delta S also 
happens to be negative, so delta G is negative, and we observe that the 
firecracker does explode.

For dissolving ammonium nitrate in water, delta H is positive.  The 
solution gets cold.  Without the T delta S term, Delta G would be 
positive and the ammonium nitrate would just fall to the bottom of the 
beaker and not dissolve.  Dissolving one substance in another creates 
entropy or disorder, thus delta S is positive  and
 - T delta S is negative.  In the case of ammonium nitrate and water, 
sufficiently negative to overpower the positive delta H, so it 
dissolves.  At high temperature, the T delta S term is greater, so more 
dissolves.  At low temperature the term is smaller, so less dissolves.

If you dissolve sulfuric acid in water, or sodium hydroxide in water, 
the solution gets hot, so heat and entropy change both drive the 
dissolution.  If you dissolve sodium chloride or table sugar in water, 
there is little heat change, so the process is really driven mostly by 
entropy, but is isn't so obvious to us because there isn't a 
counterintuitive thing like the solution getting cold to catch our 
attention.

Entropy shows up in a lot of common affairs.  Refrigerators and air 
conditioners are my next favorite examples, salt melting ice is another 
good one, but I won't do them here.  Already have a lot of bandwidth on 
an OT subject.

I think I have heard the connection between entropy and number of 
dimensions too.  I am sure this only applies directly, if at all, to 
very large systems, like the universe, and/or to very small ones like 
quarks.

Any theories beyond 4-d are still in the speculative realm, so far as I 
know.  One group of theoretical physicists think they can tie things up 
if they go to about 10 dimensions, but, so far as I know, they still 
have a lot of convincing to do.

By 4-d I mean the familiar 3 spatial ones and time, which for us 
macroscopic beings appears to run only in one direction without 
stopping.  Feinman relates, in "QED: the Strange Theory of Matter and 
Light", that a number of things on the subatomic scale are best 
understood by things going backwards in time.

Mark Holm
mdholm@telerama.com



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