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Re: cold resistors



[wherein I burble at length about some data fits. Quite possible
to bypass this post without great loss...]

At 21:57 1/2/00 -0800, John M. wrote:

At 08:37 PM 1/2/00 -0600, brian whatcott wrote:

Temp (K) Res (ohms)
0.3 10^6
1 10^2
3 3
10 1
30 0.7
100 0.3 (from a graph of Rose-Innes's)
...
[John D]
log(R) = 0.1136/sqrt(T) + 0.327

[John M]
I was using log(R) = a - b*sqrt(T)


...I get quite different results, specifically
log(R) = 8.6/sqrt(T) - 2.7

with a *lot* of uncertainty in those coefficients and
pretty ugly looking residuals.

A least squares fit of that function, expressed as
Res = exp(a + b*(Temp)**-0.5)

gave me values of a = -6.5, b = 11.2 with t values of 244, 759
respectively, and a sky-high F for the regression.
This probably highlights the difference to be expected when
fitting the raw data vs. a transformed version.

[John M continues]
I get a far better fit to all but the 100 degree point with
log(R) = 4.36/T - 0.5
...
John Mallinckrodt

Relaxing the constraint on the power of T in the following function
Res = exp(-0.3834 + b*(Temp)**-c
leads me to a least squares estimate of the parameters as
b = 5 c = 0.87 ( Student's t = 569, 595 resp)

Compare this with John Ds revised function:
log(R) = 5.2392 T^(-0.85) - 0.7491

..which is quite comparable - the principal difference being
in the value of the exponential's non-thermal offset.
I admit that providing a 4 digit value here
is in fact over fitting the data (and the package was not slow
in letting me know).

Evidently, all parties favor a power of temperature closer to
one than to one half. J.M = 1, J.D = 0.85 B.W = 0.87

I checked how far the data had to be forged to minimize the
residuals and have them normally distributed, following a
hint in Brian McInnes's note.

This data set was manipulated to cultivate the results:
Before After
Temp K Res Ohms
0.3 1 000 000
1 100
3 3 5
10 1
30 0.7
100 0.3 0.5

This data was 'optimal' for the function
Res = -0.7 + exp(4.6*(Temp)**-0.9)

So the fitting parameters are highly variable with suspect data.


Carl Mungan offered two fits from the literature
and an approximation as follows:
T = E*Z/(Z - F)^2
where Z = ln(Temp)

which leads to a least squares fit with rather modest statistics
of t = 9 and 32 for the two parameters, using the sample dataset.


Ruby with some chrome is mentioned as a paramagnetic thermometer
but the most cool (in my view) is the cobalt 60 crystal's
gamma radiation anisotropy at low temperature below 50 mK
measured at room temperature, outside the enclosure.

Reminds me of the hooha about a thermal effect on nuclear radiation
nearer room temperature.....
(One of those other effects that were said to be impossible?)
:-)























brian whatcott <inet@intellisys.net>
Altus OK