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the moral of the story

Discussion in 'Electronic Basics' started by kell, Oct 25, 2006.

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  1. kell

    kell Guest

    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
    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
    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.
  2. Rich Grise

    Rich Grise Guest

    It's not an hyperbola - it's a log curve offset such that 0 is at 0.

    Hope This Helps!
  3. kell

    kell Guest

    Yeah. You skimmed over it, but it's there in my post. The equation
    with "exp" in it.
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