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Re: [Phys-L] heat content



On 02/10/2014 09:24 PM, Bob Sciamanda wrote:
Is it not possible, and useful, to distinguish that part of the
system energy which has been "thermalized" - that energy which
directly affects the system temperature and phase?

OK, here is a second answer to the same question. The answer
has two parts:

1) It is /sometimes/ possible and /sometimes/ useful to make
such a distinction.

2) It is not a particularly deep or clever way to think about
things. It is something you get away with, sometimes.

By way of counterexample, consider a pulsed NMR experiment.
Start with low spin temperature i.e. high polarization in
the Z direction. Apply a π/2 tipping pulse. At this stage
the system is far from equilibrium. After some time, the
spins will spread out in the XY plane. This is a τ2 process
i.e. spin/spin relaxation. We assume τ1 is huge compared
to τ2. The entropy increases /at constant energy/. On a
timescale τ2, the system comes into equilibrium with itself,
at a high temperature.

On a much longer timescale τ1, there will be spin/lattice
relaxation and the system will lose energy and come into
equilibrium with the environment. The temperature will
decrease. However, let's not worry about this. It is not
relevant to the point I want to make.

Here is the fundamental point: States are states. They are
not necessarily "energy" states. "Thermalization" aka
equilibration is not something that happens to the energy;
it is something that happens to the states, or rather to the
distribution over states. The distribution moves toward an
equilibrium distribution.

All fundamental questions about equilibrium, irreversibility,
and spontaneity should be formulated in terms of entropy, not
energy. Under /some/ special conditions you can get away with
speaking in terms of "thermal" energy or "thermalized" energy,
but I'm not at all convinced you are doing yourself any favors
by thinking in these terms.

Remember: The same rule applies in thermodynamics and (not
coincidentally) in quantum mechanics: States are states.
They are not necessarily energy states. There's a lot more
I could say about this.............

========================

True story: I once had a grad student tell me that he had been
assigned to give a talk that involved thermodynamics, and he
didn't know anything about entropy. He was up against a deadline.
He asked if I would please tell to him how to do thermodynamics
without entropy.

I swear this really happened. I have witnesses.