Using Google Sheets to Check the Fit

    Since I was limited to the use my mobile phone I installed Google Sheets to do some simple calculations. Below is a check on the fit for the cooling temperature data and constants given in the last two blogs. Just below constants are three lines that show the formulas for the indicated cells.
This fit shows a slight improvement over the original fit due to a change in the interval used to fit the thermistor temperature curve as indicated by the cell containing the rms error. The rounded values for the temperatures may have also affected the fit.

Missing Cooling Experiment Rate Constants

  I inadvertantly failed to include the two rate constants, λ1 and λ2, for the fit of the cooling data in the last blog. One can now use the constants given here to check the fit.

The fit was rather difficult to do since the formula for the fit function has a nonlinear set of undetermined constants so one cannot use linear least squares. The solution required a search for the values of the rate constants along with a linear fit of the constants A, B and C that would minimize the rms error of the fit. In addition, the problem was ill-conditioned.