the moral of the story
- From: "kell" <kellrobinson@xxxxxxxxxxxx>
- Date: 25 Oct 2006 12:51:04 -0700
I came into posession of an in-line oil heater sold for heating
vegetable oil.
Turns out it has a negative temperature coefficient. I measured the
resistance at several temperatures and did some curve-fitting just for
giggles.
32 F: R = 2.5 ohm
74 F: R = 1.85 ohm
212F: R = 1 ohm
First I though about quadratic regression, but you don't get asymptotes
with a quadratic. The actual resistance of the material would have an
asymptote for temperature increasing without limit (somthing less than
1 ohm, but obviously not a negative value).
So I decided to look at a kind of hyperboloid with three coefficients:
(R+a)(T+b)=c. After fussing around with the numbers some, I decided to
drop the a (making the resistance asymptote zero).
This only leaves two coefficients to fit three data points, but check
it out. I solved for b and c using the data points at 74 and 212
degrees; plugged in the third data point, and it fit. Thought whoa,
maybe I'm onto something here.
The equation: R(T+88.4)=300
Looking at it for physical significance, obviously R approaches 0 as
temperature increases without limit.
But what about that 88.4?
I decided to go ogle the internet.
Found mention that the R-T characteristic is supposed to be a
"negative, non-linear exponential function."
So I fitted the 74 and 212 degree data points, using Rankine values now
into an equation of the form
R = a exp(b/T) and got R = .0929 exp(10.76/T).
That predicts R = 2.39 at 32 degrees. Probably as good a fit as the
hyperbolic, considering
measurement error. And a better fit with physical reality, because the
hyperboloid
exhibits an anomaly at -88.4 F. Sort of like predicting absolute zero
is -88.4 degress F
instead of -459.
The hyperbolic was without any real physical significance.
But it points to a weakness we humans have in looking for theories to
fit the facts we have.
It was such a good fit, I thought it must mean something.
.
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