Re: [Phys-L] Entropy

[Daniel Schroeder <dschroeder@weber.edu>]

Fundamentally, entropy is a measure of the number of possible microscopic arrangements of an object's atoms and energy.

At a more practical level, entropy is the thing that increases by Q/T when heat Q flows into an object at temperature T.

In an algebra-based class I think students are fully able to understand both of these statements.  What I wouldn't attempt in an algebra-based class is quantifying the first statement (with a logarithm function) or connecting it to the second statement in a quantitative way.

To convey the idea of microscopic arrangements, I like to do simple counting exercises with a two-state system or an Einstein solid or a freely expanding gas.  I also like to use the molecular dynamics web app at https://physics.weber.edu/schroeder/md/ ;<https://physics.weber.edu/schroeder/md/> to show some irreversible processes (see the Presets menu) and talk/ask about how each of these processes increases the number of possible arrangements.

To convey the relation between entropy and heat, I start with the example on pages 95-96 of An Introduction to Thermal Physics:  two objects (perhaps "bricks") in thermal contact, one at 500 K and the other at 300 K, exchanging 1500 J of heat.  These numbers make it easy to calculate DeltaS for each brick and to see that the total DeltaS is positive.  Meanwhile, the MD simulation shows that during such a heat flow process there are more ways to arrange the energy afterwards than before.  So the two views of entropy are at least qualitatively consistent with each other, even without making the connection quantitative.

Good luck!

Dan


> From: Marc Reif <marc.pricereif@gmail.com>
> Subject: [Phys-L] Entropy
> Date: August 9, 2024 at 12:16:06 PM MDT
> To: phys-l@mail.phys-l.org
> Reply-To: marc.price.reif@gmail.com
>
>
> So it appears there is no way to explain entropy to students in their first
> algebra-based physics course that is both basically correct and
> understandable to students at that level.  Typically there are just a few
> days on this topic. I'm not going to get very far talking about probability
> spaces to kids who don't know anything about probability.
>
> Disorder doesn't quite get it, because some apparently disordered systems
> spontaneously order themselves (the salad dressing example) while
> increasing entropy.
>
> Energy dissipation doesn't get it, because it's possible to take energy in
> macroscopic systems and "dissipate it" into a smaller volume within the
> system as thermal energy.
>
> What about invoking "irreversibility"? Is that a tool that works to
> describe increasing entropy?