Re: batteries

[John Denker <jsd@MONMOUTH.COM>]

> Brian referred to a situation in which a lower V battery is a
> load for a higher V battery. Is the resistance presented by a
> battery when it is used as a load the same as when it is used
> as a source? I suspect it is very different. But I am not sure.

To first order it is the same.  To first order, it's linear.
Indeed, as the saying goes, to first order, everything is linear :-).
[Extra credit:  Explain why this saying is not strictly true.]
The Thevenin equivalent is, by construction, "the" linear
model.

> 2) I am always puzzled by battery cells. Most introductory
> physics texts describe their electrical properties. Chemical
> reactions taking place in some cells are also described,
> occasionally. But all this seems to be a description of what
> happens rather than an explanation of why it happens.
> I suspect that many on this list would appreciate if
> somebody could post a short essay about batteries for an
> elementary physics course.

I thought somebody already had posted such an essay.
  http://mailgate.nau.edu/cgi-bin/wa?A2=ind0007&L=phys-l&P=R27156

> My impression is that electochemical cells can not be explained
> at the elementary level;

How elementary?  Elementary-school level?  Obviously this subject is not
suitable for fourth grade.  But it would be within the scope of an
ordinary modern-physics course.

> they are what they are; period.

That seems like cop-out.  It's just physics, after all.

> [Using big words, like Gibbs
> potential, QM or double layer, does not contribute to clarity
> at the level of my teaching.]

Well, if you want to explain batteries in terms of 18th-century physics,
you're going to be disappointed.  There is no ball-and-stick model that
explains why different metals have different work functions.

If you want to explain electrochemistry you're going to have to use the
methods (or at least the results) of modern physics in some form.
Battery voltages are on the order of a fraction of a Rydberg, and that's
not a coincidence.  If you insist on no quantum mechanics, there will be
no atoms, no molecules, no metals, no work functions, no batteries, and
no humans to ask questions about the lack thereof.

Once you come to terms with the idea that nature does not require
materials to be electrically neutral in equilibrium, the rest of the
battery explanation requires little more than high-school physics.