Historical research guide · 0509 · 2002
A systematic error in mass flow calorimetry demonstrated
Kirk L. Shanahan
In one minute
Kirk Shanahan, a chemist at the Savannah River site in South Carolina, wrote this short paper about how a mass flow calorimeter is calibrated. In that instrument a fluid flows past the cell and the temperature it picks up measures the heat released; the reading is turned into power by a straight line fitted to runs of known input, and the excess power reported afterwards is exactly the leftover of that fit. Shanahan’s point is arithmetic. If the true calibration drifts a little from run to run while one global line is applied to all of them, the leftover is not zero even when nothing new is making heat. He writes the size of it in a single equation: a three per cent difference in calibration slope gives about three per cent apparent excess, which at twenty watts input is six hundred milliwatts. He then recomputes ten current sweeps from a platinum-cathode experiment by Edmund Storms on that assumption.
Connection
Chapter 1 is the evidence ladder, and this paper is a rung of it: it names, in equation form, one specific way a calorimeter can report heat that is not there, and it says what data would settle the question. Chapter 12 is where that matters, because every excess-heat claim in lattice work is a calorimetry claim first.
From the source
In mass flow calorimetry the output power is obtained from a linear regression calibration, output power equals slope times heat capacity times flow rate times the inlet-to-outlet temperature difference, plus an intercept; the excess power is then defined as output minus input, which is exactly the statistical residual of that fit, so the practice of using linear regression guarantees a non-random excess power signal.Section 1, Equations 1 to 3
Solving the run-specific calibration under the assumption of no excess power and substituting it into the global calibration makes flow rate and inlet temperature drop out, leaving the apparent excess as a function of the two sets of constants alone: the ratio of global to run-specific slope, minus one, times the input power, plus the difference of the intercepts — so a three per cent calibration difference produces about three per cent apparent excess, which at 20 watts input is 600 milliwatts.Section 2, Equation 5
Reanalysing Edmund Storms’ platinum-cathode data, Shanahan divides the record into ten current sweeps and computes a calibration constant for each under the assumption that output equals input; the ten slopes scatter about the theoretical value for pure water with a mean deviation of 0.4 per cent and a standard deviation of 1.5 per cent, and the reported global constants sit among the largest deviations in that spread.Section 4, Table 1
Recomputing the excess power curve with sweep-specific rather than global calibrations leaves a curve statistically centred about zero, with the two sweeps that had shown anomalously low excess turning out to have run-specific constants closest to the global one; residual structure remains as transients near peak input power, which Shanahan reads as pointing to a further experimental effect or a calibration equation of a different form.Section 4, Fig. 2 and Fig. 3
The internal temperature profile differs between the two conditions being compared: during electrolysis the top-to-bottom thermistor difference runs from 0.1 degrees Celsius near zero input to about 1.8 degrees at the 26 watt peak, while during the resistive-heater calibration it reaches about 7 degrees at 12.5 watts, which scales to 14.5 degrees at 26 watts — a much stronger thermal gradient in the heater case, which Shanahan offers as a candidate cause of the calibration difference.Section 4, temperature-gradient paragraph
What Shanahan says the field should do next: determine and report the statistical variation in the calibration constants explicitly, since any variation is reflected through the residuals as non-random features, and record run-specific calibration data rather than inferring them, because none were collected in the experiment reanalysed here.Section 5, Conclusions
The way in
https://doi.org/10.1016/s0040-6031(01)00832-2How to cite it
Kirk L. Shanahan (2002) A systematic error in mass flow calorimetry demonstrated doi:10.1016/s0040-6031(01)00832-2