Re: [Phys-L] spontaneity and irreversibility

[Matthew Heaney <matthewjheaney@gmail.com>]

On Thu, Aug 8, 2024 at 11:58 AM John Denker via Phys-l <
phys-l@mail.phys-l.org> wrote:

> On 8/7/24 8:23 PM, Matthew Heaney wrote:
> > Suppose I have a weight suspended a few feet above ground, attached
> > to a rope over a pulley.  In principle I could use this to weight and
> > pulley to do work, such as lifting something.  The system has the
> > capacity to do work, so it has "free energy" and thus low entropy.
> >
> > What's the entropy in this case?
>
> 1) If the weight and the payload are evenly balanced, there is
>   no spontaneity here. The weight might go down while the payload
>   goes up, or vice versa. There is no significant creation or even
>   transport of entropy.
>
> 2) If they are not quite evenly balanced, let's imagine that the
>   weight goes down, bounces off a cushion, and goes back up. The
>   system is a highly nonlinear oscillator. It goes up and down
>   forever. The weight spends half it's time moving in the direction
>   of the net force, and half moving the other way. Again entropy
>   plays no role.
>
> 3) If you want it to go down and *stay* down, let's imagine that
>   the weight smacks into a hydraulic shock absorber, like you have
>   on your car. Entropy is produced via viscosity in the fluid in
>   the shock absorber.

This is the case I had in mind.  The system will spontaneously lift the
smaller weight.  How does one quantify this spontaneity?  We do this all
the time for chemical reactions, but is there something analogous for
mechanical systems ?

There is available energy (or something -- not sure what is the correct
term here) in the system, and some of it is used to lift the smaller
weight, and some of it is lost as heat.  After the larger weight falls to
the ground, the system now has less potential energy (it is now the smaller
weight that is suspended) and the heat has increased the entropy.

Does one describe the change in system state in terms of a combination of
potential energy and entropy, or just entropy?

If a student asks why a ball drops to the ground when you release it, what
do you tell them?



> ================
>
> Defining energy in terms of "capacity to do work" is wrong
> physics.


Isn't that what "Gibbs free energy" is?  Is there a mechanical analog?


> It's also bad pedagogy, because of what we call
> "ignotum per ignotius". You can't explain the unknown in
> terms of the more unknown. Students don't have a usable
> intuition about "work". It's more ambiguous and hard to
> define than energy itself.
>
> It's wrong physics because you can easily have a system
> that has *more* energy but *less* capacity to do work.
> Details can be found here:
>
> https://av8n.com/physics/thermo/entropy-energy.html#sec-system-subsystem
>
>
> ////////////////////////
>
> Earlier:
>
> > My favorite site about entropy:
> >
> > https://franklambert.net/entropysite.com/
>
> I don't recommend that. Lambert was a crank IMHO. He crusaded
> against certain thermodynamic misconceptions ... by substituting
> new and different misconceptions. The following is particularly
> pernicious:
>
> > > Concisely, the second law is “Energy of all types changes from
> > > being localized to becoming more spread out, dispersed in space**
> > > if that energy is not constrained from doing so”.
>
> That's just wrong. If you have two rotating rings rubbing against
> each other, the energy is 100% spread out beforehand and 100% spread
> out afterwards, yet huge amounts of entropy are produced. Some
> discussion, with diagrams, can be found here:
>    https://av8n.com/physics/thermo/entropy-energy.html#sec-spreading
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