Re: Batteries

["John S. Denker" <jsd@MONMOUTH.COM>]

Ludwik Kowalski wrote:
> **** Start with a chunk of nickel. Make sure it is electrically
> neutral; if in doubt you can just count positive and negative
> charges and make sure they come out even.
>
> 1) It is easy for you to say this, teacher. How do we
>      count charges?

Answer #1:  With tweezers and a microscope.  It will take
you about 10^16 years.

Answer #2:  It's a joke.
  http://www.m-w.com/cgi-bin/dictionary?va=joke

When somebody suggests a totally preposterous experimental
technique, you should consider two hypotheses:
  a) He's an idiot.
  b) Maybe this is a Gedankenexperiment.  Maybe it
     doesn't matter _how_ we ensure neutrality, as
     long as it is possible in principle to do so.

> **** Now take a second chunk of nickel. It also starts out
> electrically neutral. Now imagine that using some powerful
> neutrino-ray or something, we cause an inverse-beta (electron
> capture) reaction that turns the nickel nuclei into iron nuclei.
> The crystal structure re-arranges itself accordingly. The chunk
> of iron remains, by construction, electrically neutral.
>
> 2) I have no idea what the "inverse-beta, electron
>     capture" is, teacher. How can I imagine a "neutrino-ray"
>     without knowing what it is? As far as I know, a piece of
>     metal is not a crystal, like salt or calcite.

#3) As for powerful neutrino rays, see answer to previous
question. (Answer #2 above.)

To prevent confusion among humor-impaired students, I have
removed the "counting" and "neutrino-ray" references, and
substituted an explicit mention of Gedankenexperiment.

#4) All metals are crystalline.  You can see the crystal structure
by cleaving the metal, etching it a bit to increase contrast,
and looking at it.  If it's microscrystalline you might need
a microscope, but not even a very powerful one.

For that matter, practically all solids are crystalline.
Sometimes microcrystalline.  Amorphous solids (e.g. glass)
exist but are really quite atypical.


> **** As we shall see, these two electrically-neutral pieces of
> metal attract electrons differently. They have different work
> functions.
>
> 3) What is the work function, teacher?

It's the topic of discussion.

> **** The work functions are different because of things
> like the Pauli exclusion principle.
>
> 4) Who was Pauli

http://www.m-w.com/cgi-bin/dictionary?va=pauli

>  and what principle are you talking about?

http://www.m-w.com/cgi-bin/dictionary?va=exclusion+principle

> **** You have a different number of fermions in a
> different-sized box, so the Fermi level will be different.
>
> 5) What are fermions teacher? And what are Fermi levels?
>     Why are you throwing at me words with which I am not
>     familiar? I did not skip classes and I read every assigned
>     textbook chapter. Nowhere did I see words you are using.

We have discussed this before, on the list.  I have incorporated
this into a new section of the web document:
 http://www.monmouth.com/~jsd/physics/battery.htm#sec-ball-and-stick

> **** The fact that different materials have different work
> functions is perfectly understandable also. Different
> materials have a different spacing between nuclei.
>
> 6) I did not know this, teacher.

Any decent periodic table will give something like
"lattice spacing" or "molar volume".  See e.g.
http://www.webelements.com/webelements/elements/text/Ni/phys.html

> **** So think of it as a particle-in-a-box problem: The smaller
> the box, the higher the kinetic energy the electrons must have.
>
> 7) What kind of a box are you referring to? And why should
>     the size of a box have an effect on the kinetic energies of
>     electrons. I have no idea what the Heizenberg?s uncertainty
>     principles are, in case that is what you expect me to know.
>
> **** You can even make a connection between the work
> function (a purely electrical property) and the elastic properties
> of the metal: when you squeeze the chunk of metal you squeeze
> the electron wavefunctions, and that raises their kinetic energy.
>
> 8) What is a wavefunction, teacher? How can a change in the
> 0.5*m*v^2 result from squeezing a function?

You wanted a microscopic explanation of what goes
on in a battery.  Why are you surprised that it
involves chemistry and atomic physics?

If you're allergic to bread, and allergic to tomatoes,
and allergic to cheese, don't order a pizza.

> 1) But do you agree that the existing sequence of topics,
> in a typical introductory physics course, is not consistent
> with your explanations?

Sequencing!  Ha!

I view knowledge in general, and science in particular,
and even physics more particularly, as a grand tangle
of interrelated ideas.  The cross-connections are very
high-dimensional.  There is a theorem that says you
cannot map things from one dimensionality to another
in a way that is one-to-one and continuous.

I consider it provably impossible to teach physics or
anything else worth knowing in a logical _sequential_
way.

> 2) Do you agree that EXPLAINING things to students
> today we must not lean on what some of them may later
> learn in more advanced courses?

Everybody has to lean on SOMETHING.

> The alternative is to
> describe experimental facts and relations and to say
> that "they can be explained" in advanced courses.

The possibilities are:

-- Do the experiments yourself.
-- Do the calculations yourself.
-- Take my word for it if I tell you I've done the
   calculations and/or experiments.
-- Read the literature and see if there is a consensus
   among a number of people who have done the calculations
   and/or experiments.

If the student can't or won't do any of the above, I
don't know how to proceed.  I don't even know how to
get started.