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# Re: Lowest energy level and increase in enthropy

• From: Doug Craigen <dcc@ESCAPE.CA>
• Date: Sun, 25 Feb 2001 21:02:43 -0600

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