### Re: Is not a hurricane an example of entropy reversal?

Date: Fri Oct 30 11:29:57 1998
Posted By: Radu Grigore, Undergraduate, Electronics and Telecommunications, Politehnica University of Bucharest
Area of science: Physics
ID: 907687350.Ph
Message:

If you want information on hurricanes I would recommend:
www.aoml.noaa.gov/hrd/tcfaq/tcfaqHED.html

```Think of a gas composed of two identical particles for which only two
states are availble. This would be a very special gas because the
probability of having the two particles in the same state is 1/2:

--X--X--   --X-----   --------   -----X--
--------   -----X--   --X--X--   --X-----
or
--X--X--   --X-----   --------
--------   -----X--   --X--X--
(1)        (2)        (1)

But for three possible states and three particles we have:

--X--X--X--   -----------   -----------   -----------   --------X-- 2
-----------   --X--X--X--   -----------   --------X--   ----------- 1
-----------   -----------   --X--X--X--   --X--X-----   --X--X----- 0
(1)-a         (1)-b         (1)-c        (3)-d          (3)-e

-----------   --------X--   --X--X-----   --X--X-----   --------X-- 2
--X--X-----   --X--X-----   -----------   --------X--   -----X----- 1
--------X--   -----------   --------X--   -----------   --X-------- 0
(3)-f         (3)-g         (3)-h         (3)-i         (6)-j

Now we have this probabilities:
1/9 - all in the same state
6/9 - two in one state and one in another state
2/9 - each in other state

Let-s say we consider only those states which have a state-labels sum
of 3. We speak of the "same macroscopic parameter". Then we have:
1/7 - state b
6/7 - state j

We say state j is more probable than state b. State b is more ordered
state (particles are aligned). So the more ordered state is less
probable than the one less ordered. This is the second law. If we let
a system in state b, after some time we will find it in state j. Of
course this does not mean that the system can't jump from state j to
state b. But this will happen very infrequent. We can say the same
thing about the hurricane: it happens infrequently (it is by far more
probable that you are not now in a hurricane) but it can happen.

We can say this for any other sum. You can try other numbers (0,1,..6)
to see what pops up. And if you take more than three particles the
difference in probabilities will be even more obvious (for two it
wasn't -obvious- at all).

But you can say: "Are you sure THIS is the second law of
thermodynamics? I know it simply states that dS>0, it does not leave
room for dS<0 (j->b) in any case, as you did!" Well, the second law
actually says what I said above plus the fact that if dS<0 for a system
then there must be a bigger system for which dS>0. It is like another
law: if for a system the total energy is not a constant there there
must be a bigger system (in which the first one is included) for which
the energy IS a constant.

In our case for a portion of atmosphere where a hurricane appears dS<0,
but for the whole atmosphere dS>0.

The second law of thermodynamics gave rise to the hypothesis of the
thermic death of the universe. The universe being the bigest
thermodynamical system one can find we must always have dS>0 (entropy
raises). This suggests that eventualy the whole universe will have
the same temperature and there will be no more energy flow (movement).
We say that energy will be perfectly dispersed.
```

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