
HandsOnPhysics HEAT & TEMPERATURE

Physics Concepts

 Spreadsheets 

What to do With Curvy Data
Fitting to a straight line is fine when the data should be straight (linear).
But what about calibrating something like the thermistor that surely is
not linear?
Figure C10a
Nonlinear Calibration Curve
Is there an alternative to looking up values on a graph? Is there a mathematical
way of finding the best fit? The answer is yes, providing you know the equation
of the curve. For instance, physics predicts that the resistance of a thermistor
should obey the equation:
R = Ro * a / (T+To) Here, Ro and a are the calibration
constants like a and b in the straightline fit. To is the ice temperature
in the Kelvin scale, 273.2 °K. Once again, you don't have to understand
the mathematics to use this equation. Here is a AppleWorks spreadsheet
you can use with thermistor data. Just copy it into a AppleWorks spreadsheet
and use it. Enter your calibration data into cells A2...B8. Enter a resistance
reading in k in H1 and read the best fit temperature in °C in cell
H2. The other cells in column H are used to calculate parts of the bestfit
equation. The bestfit for temperatures for plotting the calibration curve
are calculated in cells G2...G8.
Figure C10b
Curvy Data Spreadsheet
The graph in figure C? shows the bestfit calculations lining up with
the experimental measurements. Suppose the resistance measurements were
not as carefully recorded and looked like this: 10, 7.5, 7.2, 6.1, 5.3,
5, and 3.67 K ohms. Then the calibration curve calculations would then be
quite different than the experimental data.
Figure C10c
Curve from Less Accurate Data
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