Re: Entropy for the unenlightened

In article <1hjp288.1nrpck91jdb88sN@xxxxxxxxxxxxxxxxx>,
nospam@xxxxxxxxxxxxxxxx (J. J. Lodder) wrote:

Denis Loubet <dloubet@xxxxxx> wrote:

"J. J. Lodder" <nospam@xxxxxxxxxxxxxxxx> wrote in message
news:1hjmcl7.17s9g3oysfm77N@xxxxxxxxxxxxxxxxxxxx
Denis Loubet <dloubet@xxxxxx> wrote:

"J. J. Lodder" <nospam@xxxxxxxxxxxxxxxx> wrote in message
news:1hjlelf.7rvzun13aelb1N@xxxxxxxxxxxxxxxxxxxx
Denis Loubet <dloubet@xxxxxx> wrote:

Why do you call those things ordered? Would it be less or more ordered
if
everything was ground up and spread homogeniously throughout the
universe?

Can you describe what a disordered universe should look like?

It is called 'the heat death'.
All you may want to know on
<http://math.ucr.edu/home/baez/end.html>

Neat. But why should that be considered more disordered than what we have
now? To a layman, the heat death looks MORE ordered. The universe seems
to
be left with black holes and mostly iron spread out more or less
uniformly
at a constant temperature. This seems simpler and more ordered than the
energetic and chaotic universe we have now.

'Entropy' explains 'disorder',
not the other way round,

You're still not addressing that "layman" thing.

There is no solution to the 'layman' thing.
Entropy is a -very- non-intuitive subject.

Anything for the layman about it is at least half-wrong,
and will create more confusion than that it clarifies.

Sorry,

Jan

"When someone says 'entropy' there are three possibilities.
A) He means \int dQ/T (macroscopical)
B) He means constant*\Tr(rho\log(\rho)) (microscopical)
C) He makes empty noises and doesn't know what he is talking about."

*
Well said, Jan!

The microscopic entropy was defined (by Ludwig Boltzmann):

S = k ln W.

That admittedly won't tell the reader much without some background.
Boltzmann's entropy equation talks about a specific kind of
system--an isolated system with a specified constant total energy E
(although the constant E does not explicitly appear in the equation,
it is implied and crucial), in a state of equilibrium. It tells how
to calculate the entropy S of that system in terms only of the
microscopic particles (molecules) which make it up. On the right
hand side, k is a universal constant now known as Boltzmann's
constant. The function "ln" is the natural logarithm, and the
argument of the logarithm function is the quantity W. W is a pure
number that connects the microscopic with the macroscopic.

Suppose the system we are looking at is a volume of gas inside
an insulated container. The gas is specified to have total energy
E, which is constant because the container is insulated so that
no heat can transfer in or out of it, and it is rigid so that no
work can be done on the gas by compression. There are roughly
10^22 molecules of gas in a wine-bottle-sized container if the
gas is at atmospheric pressure and room temperature. At any
particular moment, each molecule is at a particular position
inside the container, and has a particular velocity. The position
and velocity of a particle constitute its state, for Boltzmann's
and our purposes. The collection of the states of all the molecules
at any moment is called a "microstate" of the whole volume of
gas. A microstate of the gas system is constrained by two
requirements: first, the positions of the molecules are constrained
to lie within the container (which has volume V); and second, each
molecule's velocity determines its energy, and the sum of the
energies of all the molecules must equal E, the total energy of the
gas. An interesting question is, how many different microstates are
there that satisfy these requirements at energy E and volume V? The
answer to that question, provided we can calculate it, is the
number W, which is the number sometimes referred to as the measure
of "disorder".

Credit for the above to John Pieper jbp34@xxxxxxxxx

As a matter of interest, the next time you are in Vienna visit the
Zentral Friedhof (Central Cemetery) and ask for directions to the
grave of Ludwig Boltzmann. Engraved on his tombstone is:

S = k ln W

earle
*

.

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