Re: Lowest energy level and increase in enthropy

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi all-
        Is Doug trying to say that if every "thing" is at the same
energy, then the entropy is maximized?  If so, I agree, and would so
advise the student in language that I  think that the student would
understand.
                                Regards,
                                        Jack
On Sun, 25 Feb 2001, Doug Craigen wrote:

> kostantinos alexakos wrote:
> > 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. How does this reconcile with the fact that entropy in the
> > universe is increasing? Am I missing something simple?
>
> These are the same law (though to be rigorous one needs to define what
> energy is decreasing and what is meant by "universe").  Basically the
> total energy of a system is given by:
> temperature*entropy - pressure*volume + other energy terms as
> appropriate
>
> Specifying how the system can interact with some outside reservoir
> dictates the appropriate quantity to minimize (in the case of energies -
> helmholtz, enthalpy...) or maximize (in the case of entropy) to find the
> condition for equilibrium.
>
> Perhaps the student's confusion is thinking that minimizing the energy
> of a system also decreases its entropy - so how can the universe's
> entropy be increasing.  First of all, yes entropy is very commonly
> decreased all around us in many situations.  (The belief that entropy
> always increases in every system has led to many erroneous
> conclusions.)  What the second law of thermodynamics tells us is that if
> you include everything relevant (not just the system which went down in
> energy, but also the surrounding reservoir which absorbed the lost
> energy) - in total there is more entropy.  The entropy increase in the
> surroundings is greater than the entropy decrease in the particular
> system - hence, the assertion that the entropy of the "universe" is
> increasing.  As for applying such arguments to the entire universe,
> hence begging the question of what could be the surrounding reservoir...
> I'll leave that to others.
>
> \_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\_/^\
>
> Doug Craigen
>           http://www.dctech.com/physics/about_dc.html

--
While [Jane] Austen's majestic use of language is surely diminished in its
translation to English, it is hoped that the following translation conveys
at least a sense of her exquisite command of her native tongue.
                        Greg Nagan from "Sense and Sensibility" in
                     <The 5-MINUTE ILIAD and Other Classics>