On Dec 25, 2012, at 11:15, David Roberson <[email protected]> wrote:
> During the night Santa brought me a gift! A thought occurred to me that > there is a very good explanation for the 30 to 40 second time constant > exponential waveform that I have been seeking. In order to get the best > curve fit to the exact solution of the differential equation I have been > forced to modify the constant of integration slightly away from the ideal > value as determined by steady state measurements. Interesting discussion concerning the model you've been working on. Concerning the second-order equation, what you're describing sounds quite similar to the equation Ed Storms proposes in his Calorimetry 101 paper. I believe he is consciously ignoring radiative losses. Concerning the calculation of the error, there is the error of the fit of your curve with the MFMP data, and there is the error of the MFMP instrumentation (I assume). The error of the latter is related to the scatter in their calibration runs and is of two kinds -- stochastic and systematic. I believe that the instrumentation error could easily swamp out 1W purported XP. Concerning the 40 second constant you're adding, I wonder if this is related to the time the system requires to reach equilibrium; when you're calibrating the device, I think you need steps that last long enough for the cell to attain a new equilibrium after the change in input power. In a live cell, I suspect this same characteristic of the operation of the cell would manifest itself as a kind of momentum. Forty seconds might be too short to be this, however. Eric
