Re: [Phys-L] circular definition of "success" .... was: standard DC circuits

[John Denker <jsd@av8n.com>]

On 12/01/2013 09:05 PM, Bruce Sherwood wrote:
> Even a real battery (which we deal with in some detail in chapter 20)
> maintains both a potential difference and a charge separation, with the
> sole exception of it being connected to a circuit of zero resistance, so I
> don't understand your point.

Well, let me try to explain it.

Let's start with an analogy.  In thermodynamics we are accustomed to
seeing things like
        dE = T dS - P dV - F dx .... et cetera           [1]

Let's focus on the F dx term.  The idea of force times distance is
standard fare in the introductory physics course.

An anvil in a uniform gravitational field exerts a constant weight,
i.e. a constant gravitational force, independent of height.  This
is considered an /ideal/ mechanism for exerting a force, for instance
if you wanted to apply a definite amount of tension to a rope, independent
of the length of the rope, to an excellent approximation.

Not all springs obey Hooke's law.  There exists such a thing as a
constant-force spring, where the force is independent of x.  Such
things are an article of commerce; see e.g.
  http://www.centuryspring.com/products/constantforce.php
This is another type of /ideal/ mechanism for exerting a force, e.g.
for applying a definite amount of tension.  In contrast, a Hooke's-law 
spring is less than ideal, because the force changes as a function of x.

The same concepts apply to the other terms on the RHS of equation [1].
An ideal heat bath maintains a constant temperature, independent of S.

Now ... an important term has been left out of equation [1].  It would
be better to write
     dE = T dS - P dV - F dx + (voltage) d(charge) .... etc.    [2]

The fourth term on the RHS can be taken as an implicit /definition/
of voltage, much as the first and second terms can be (and often are) 
taken as implicit definitions of temperature and pressure.

Again the same concepts apply.  An ideal battery, by definition, maintains
a constant voltage at its terminals, independent of how much charge goes
in or out.  It is profoundly analogous to an ideal anvil, and to an ideal 
heat bath.

Consider the following statements:
  "An ideal tensioner maintains a displacement and a force."
  "An ideal heat bath maintains a certain entropy and temperature."
  «A battery maintains a charge separation and a potential difference.»

The first time I see a statement like that I just assume it is a typo
and laugh it off.  However, when somebody makes a concerted effort to
defend such a statement, I say wow, we are dealing with some serious
misconceptions.

There are standard ways of visualizing what's going on.  The
operating curve (aka load line) for an ideal battery is shown here,
plotted in the (charge, voltage) plane:
  http://www.av8n.com/physics/img48/battery-operating-curve.png

If you're going to be talking about charge and voltage, you really
ought to draw the (charge, voltage) diagram.  This is profoundly 
analogous to the "indicator diagram" in (volume, pressure) space.
I think some guy named Watt developed the idea.

The operating curve is a contour of constant voltage, independent of
charge.  It crosses perpendicular to the charge=0 contour and to every 
other charge contour.  When talking about a battery, to suggest that 
charge and voltage play similar roles is to suggest that parallel is 
similar to perpendicular.

I am not some sort of "expert" obsessing over abstruse details; I am 
talking about the most basic zeroth-order concepts.

   Of course if you applied a constant voltage to a constant-sized 
   capacitor you would get a constant charge, but that's not even
   remotely what we are talking about.

> Even a real battery (which we deal with in some detail in chapter 20)
> maintains both a potential difference and a charge separation,

I quote from the beginning of section 20.4:

«We have been treating batteries as if they were ideal devices; that is, as if
they always managed to maintain the same charge separation regardless of 
what they are connected to.  Real batteries, however, don't quite succeed in
maintaining a potential difference equal to the battery emf, ....»

Chapters 19 and 20 are not lacking for detail;  the problem is, the details
are just not correct.  Charge separation is not a synonym for potential
difference, in the same way that volume is not a synonym for pressure, and 
entropy is not a synonym for temperature.

There's a lot more that could be said, but I'll stop here.