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Re: Optical pyrometers, was R = V/I ?



These limitations are recognised... and there are others. We compensate for
the conductive/convective energy loss by extrapolating the vaguely linear
start of the power - T curve as a straight line, and then for several T
values we take the difference between the curve and the extrapolated line
below it as Pr, the radiated power. The glass envelope is kept immersed in
cold water to justify neglecting the energy radiated back to the filament
from the surroundings (I must check sometime to see just how much
difference this makes).

You are to be complimented for even thinking about the convective heat loss.
I have no idea how important it is, but the conductive and back-radiated
terms are surely negligible compared to the radiative loss. The fact that
convection occurs can be seen in old light bulbs that have burned in a
constant position for a long time. They develop a dark spot of deposited
tungsten at the top of the envelope. The tungsten got there by convection,
of course. I would skip the cold water bath. The difference, if any, will
be due to the convection process, not the radiative. The best way to check
this is to do the measurement with and without the bath.

Strangely, the result from the log(Pr) vs log(T) graph is very consistent:
it invariably comes out as a straight line with slope somewhere between 3.5
and 4.5. A serious error analysis is probably too hard at IB level.

It has to behave in some way, and radiation is the dominant process. What
value do you get for the Stefan Boltzmann constant? What is your highest
inferred temperature using your linear resistance model thermometer? What
is the melting point of tungsten?

I regard the lab as a valid exercise: it could be improved by trying to
quantify better the difficulties that we bridge with simplifying
assumptions. I do have the feeling that there may be bigger errors than we
think, which compensate for each other to give a result which is a bit too
good.

As with the light bulb demonstration I described last week, I think there
is much to discuss here, and the discussion will be valuable. I just don't
like to see students told something we know is untrue. In this case the
tungsten resistivity data are available. I haven't searched very hard to
find (in Kate & Laby) the values I did find. If you find values for the
complete range then you probably can use the resistivity of tungsten as a
thermometer with much greater confidence. You must still take a look at
the emitting area problem to get a value for the Stefan Boltzmann constant
but you may then have something to say about convective losses.

Leigh