Re: Lowest energy level and increase in enthropy

[David Bowman <David_Bowman@GEORGETOWNCOLLEGE.EDU>]

Regarding the question of K Alexakos:

> While covering the 2nd law of thermodynamics one of my students asked
> the following question which I still can't answer properly in my mind:
> We learn that things have a tendency to go to their lowest energy
> levels.

But this is not necessarily the case.  The 'tendency' of 'things' in any
circumstance is to do what they tend to do in *that* circumstance.
Although this observation *is* quite tautological, it is often overlooked
by many who are confused by the 2nd law.

It is only true that a 'thing' tends to go to its lowest energy levels
when the 'thing''s surroundings are sufficiently cool so that if the
'thing' preferentially occupied those lowest levels, it would have the
same temperature as those surroundings.  If the 'thing''s surroundings
are hotter than the 'thing', then the 'tendency' is for the 'thing' to
go to *higher* energy levels than it currently tends to occupy.  The
'tendency' is *not* necessarily to go from high energy to low energy,
but rather, to go in such a way as to tend to equalize the temperature
of the 'thing' with that of the surroundings.

> How does this reconcile with the fact that entropy in the
> universe is increasing?

The correct 'tendency' is *quite* well reconciled with this principle.
When the energy of 'things' tends to be exchanged with their
environment in such a way as to bring about a reduction in the
temperature difference between the things and the environment, *that
does* 'tend' to increase the entropy of the universe.

> Am I missing something simple?

It appears that what is missing is an understanding of 'things' really
'tend' to do.  (I don't know if an understanding of the meaning of
the increase of entropy in the universe is missing or not because it
was not elaborated on in the question enough to find out.)

David Bowman