I now have a better appreciation of Mark's experiment. Its not really
about Ohm's Law at all, its an experiment to integrate different topics
covered in class. Use what has been learned about resistivity vs
temperature, and power in electrical devices, in order to verify
Stefan's Law with something as simple as a light bulb and a couple of
meters. This has a lot of potential, though it could easily overwhelm
students and become just another 'follow the directions' experiment in
which they do little thinking themselves. I'm happy to give any benefit
of the doubt that he is in the first category rather than the latter,
however here are some ideas:
I would agree with Leigh that over this temperature range the linear
relation between resistivity and temperature is inadequate, however I
would worry about muddifying things by introducing a new device such as
a pyrometer. Assuming the filament to be tungsten one could use a table
of values, however I would prefer to keep as much as possible to things
measured in the lab itself and to not make assumptions where it can be
avoided. For a metal, one expects resistivity to be proportional to the
square root of temperature (in kelvin). Try that as your modeling
equation rather than a linear one and see where it gets you. In fact,
test it against the tabulated values you found for tungsten.
I would agree that a light bulb has a resistance (geometrical factor
times the resistivity) measured by V/I at any given filament
temperature, however the temperature itself changes with V&I so I see it
as confusing and of no value anyways to talk about this resistance. You
can get the power from IV, and what you are modeling to get the
temperature is the change in resistivity of the filament material. So
you have the resistance *at that temperature* is equal to the
resistivity *at that temperature* times an unknown geometrical factor
(simply becomes a shift in the log-log plot). I think the experiment is
clearer when framed using resistivity (using the resistance at each
temperature only as a passing factor in the calculation).
A final comment - I alluded earlier to the observation I've made on
light bulbs that if you retrace by going down in V you won't necessarily
follow the same I-V curve backwards. If this is the case for your bulbs
it should be possible to get a wildly scattered I-V plot by going up and
down in V from various starting points, however all such points should
follow the same smooth power vs temperature curve. This gives added
credibility to the power vs temperature curve being more
fundamental/consistent than your I-V plot.