Re: There's work, and then there's work

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Saturday, Jan 25, 2003, David Rutherford asked:

> Could someone please refer me to experimental evidence that
>  the total energy stored by a capacitor is 1/2 CV^2. Thanks.

(This question resulted in two suggestions for simple
student laboratory activities. I hope there will be more.
Meanwhile here is a problem prompted by the question.)

By how many degrees will the water temperature change
if a C=10 F capacitor is charged from a 3 volts battery and
then discharged through a resistor R immersed in 50 grams
of water?  Assume the procedure is repeated twenty times.
The mass of the resistor and the mass of the styrofoam cup
are negligible. Heat received by connecting wires can be
ignored because their resistance is much smaller than R.

(Answer dT=4.3 degrees C. A teacher may also add
a question for a short essay. Something like this:)

The answer does not depend on R. Does it mean that
a resistor of one hundred kilo-ohms can be used in the
 experiment? Justify your answer.

(Due to a very long discharging time, at least 3*R*C, heat
escaping through styrofoam would not be negligible.
Furthermore, too large R could cause self-discharging.
A sizable fraction of the discharge current would bypass
R resulting in heating of the capacitor instead of water.)
Ludwik Kowalski