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

[Mark Sylvester <msylvest@SPIN.IT>]

At 12.28 09/05/00 -0700, Leigh Palmer wrote:
> >At 11.21 08/05/00 -0700, Leigh Palmer wrote:
> >>At 10:17 AM -0700 5/8/00, Mark Sylvester wrote:
> >>
> >> >At 10.52 07/05/00 -0700, Leigh Palmer wrote:
> >> >
> >> > >Well, if one wishes to call the ratio V/I the resistance of a light
> >> > >bulb at a specific operating point one may certainly do so. It is a
> >> > >matter of some concern to me that this resistance can't be used to
> >> > >calculate anything else. It does not condense the information in a
> >> > >way that will simplify a later calculation - operating voltage or
> >> > >current must still be specified along with this resistance, so how
> >> > >is that an improvement over specifying two other numbers, say
> >> > >voltage and power?
> >> >
> >> >We do a lab where students measure I and V for a range of values, using a
> >> >12V bulb. They calculate R at each point in order to find the temperature
> >> >of the filament (and then go on to plot power vs temperature in
> pursuit of
> >> >the 4th power radiation law). I don't think this is a counter-example to
> >> >your comment, but it does show that the concept (of resistance) is useful
> >> >even when limited in the sense that you point out.
> >>
> >>You make my point; thank you. You have your students plot temperature
> >>vs. power (I assume). If the student has measured I and V, can he not
> >>calculate power without first calculating this questionable resistance
> >>parameter? Of what value, then, is V/I?
> >
> >It's used to determine the temperature of the filament, from R = Ro(1 +
> >alpha*theta). For Ro we use the smallest I and V that we can measure to 2
> >SD, using the best meters we have. We use the tcr of tungsten as found in
> >the data book.
>
> I will bet that this is a wildly inaccurate way to determine temperature.
> Why do you expect the resistance to vary linearly with temperature over
> a range of nearly a factor of ten when you already know its resistivity
> varies by more than factor of ten? You need a thermometer, and the optical
> pyrometer is the thermometer of choice for this purpose.
>
> On a related issue, how do your students determine the effective area of
> the radiating filament? You should examine a filament with a hand lens
> sometime, and you should recognize that its dimension will change
> significantly between cold and hot, though not nearly as much as the
> resistivity will change.

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).

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.

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.

Mark




_____________________________________
Mark Sylvester
United World College of the Adriatic,
34013 Duino TS, Italy.
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