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Re: battery

A sl. emendation -- I was taught * electrons have such a high charge
density that they don't exist in an electrolyte, instead they attract
(are attracted to) water to produce OH-. This would, one thinks, result
in a rather low mobility (assuming mobility is a function of the size of
the ion). What happens is the electron is passed from one ion to
another. Same happens with hydronium.

* Doesn't necessarily mean it's true.

bc

John Denker wrote:

Ludwik Kowalski wrote:


The textbook I am using states:
"The real battery, however, always has some
internal resistance r. As a result, the terminal
voltage is not equal to the emf."

I do not like the "as a result" phrase.



I dislike several things about the quoted statement.

For starters, the thing they seem to be calling "emf"
has for the last jillion years or so been called the
"open-circuit voltage" or "Thevenin equivalent voltage"
or some combination of the two, such as "Thevenin
open-circuit voltage".

Also Ludwik is quite right to be suspicious of the alleged
origin of the observed Thevenin-equivalent impedance.
Batteries are remarkably tricky little creatures. The
I/V characteristic is nowhere near linear.
-- For small currents, the dominant effect has to do
with the chemical rate constants, and how much you shift
the rates by shifting the electrochemical potential.
-- For larger currents, the dominant effect is diffusion
through the electrolyte. Ionic mobility and all that.
-- I suspect that in any halfway-well-designed battery,
ohmic losses in the metal parts is a quite small effect.

> The change of resistivity


of wires (due to ohmic heating) is small



yes.

> and


the same is probably true for the electrolyte,
unless the number of free carriers drops
significantely.



I disagree. Ions move a lot slower than electrons.
The ionic conductivity of liquids is remarkably poor
compared to the electronic conductivity of ordinary
metals.