The primary measure of MOAC’s performance is its overall measurement accuracy. When recently calibrated, MOAC can achieve the original design goal of +/- 0.1% relative accuracy. The table below shows a typical calibration regression result which provides the coefficients a and b for equation 3.

Regression Statistics
Multiple R 0.999999281
R Square 0.999998562
Adjusted R Square 0.999998431
Standard Error 0.005744603
Observations 13
Coefficients Standard Error
a 0.010942798 0.00372184
b 1.000451508 0.000361737
Heat Source Predicted Pin Residuals
10R1 10.8512 -0.0007
10R2 10.8603 -0.0105
10E 10.8561 -0.0056
5R1 5.8569 -0.0052
1.25E 2.1028 0.0020
1.25R1 2.1015 0.0037
3.5R1 4.3506 0.0039
7R1 7.8507 0.0032
10R1 10.8482 0.0048
10R1+5R2 15.8447 0.0073
5R1+5R2+5E 15.8437 0.0056
12E 12.8519 -0.0025
10E 10.8572 -0.0062

Note how close the value of b is to unity. This demonstrates the fundamental nature of this approach to calorimetry and also shows that MOAC’s thermal design is successful in removing heat from the chamber only via the flowing water.

Another important aspect of performance is specimen versatility. MOAC excels in this area by producing precisely the same reading on a wide variety of heat sources. The size, shape, temperature, and location within the chamber have very little effect on the measurement.

In the table above above, note how closely the various heat sources (R1, R2, and E – electrolysis power) fit the calibration line. This is a clear demonstration of MOAC’s excellent specimen versatility. We also conducted a location study in which a calibration heater was operated at 15 watts at several different locations within the CC. For all the reasonable locations, the difference between electrical input power and heat output power was 12 mW or less (i.e. within 0.1% relative). When the calibration heater was placed in one of the extreme corners of the chamber, the heat output power read 25 mW lower than the electrical input power (i.e. a 0.2% error).


MOAC exhibits both random and systematic errors. The random errors appear to be a combination of electrical noise and digital granularity in the temperature measurements. This conclusion is supported by the fact that fixed precision resistors located within the environmental enclosure report about the same jitter as the thermistors. Even with 100-reading averages comprising each observation, these errors produce a jitter in the temperature signals of about +/- 0.0005 °C. Given MOAC’s 10 W/°C sensitivity and the fact that inlet and outlet water temperatures are measured independently, this jitter corresponds to almost +/- 10 mW in the heat output power signal. Fortunately, MOAC’s thermal time constant is about one hour so it is permissible to apply additional averaging to the signals to reduce this jitter to negligible levels.

The systematic errors are more complex. When MOAC was first commissioned in the summer of 2004, it readily achieved 1% relative accuracy. However, numerous systematic errors prevented it from approaching the design goal of 0.1% accuracy. It took nearly 2 years of intensive testing and evaluation to find and eliminate these errors.

For the first few months of operation we observed mysterious perturbations in the heat output power reading. Usually the reading would slowly recover to the value before the disturbance. We finally determined that these perturbations were due to the sudden expulsion of an air bubble in the liquid-air heat exchanger in the CC. When the bubble departed, the wetted area of the heat exchanger was suddenly increased, which increased its efficiency and thus cooled the contents of the chamber slightly. We solved this problem by installing three air traps at strategic locations in the calorimetry water loop. The trap located just after the water is drawn from the stirred reservoir collects the most air and must be emptied every two or three months.

Another problem that caused noticeable short-term drift was instability in the water flow rate. We initially constructed MOAC with a pump system from FMI that was advertised to provide a highly stable flow rate. Once we identified pump speed variations as the problem we abandoned the FMI controller and tried a custom closed-loop speed control that employed a digital tachometer. That worked better but the brushes in the DC pump motor caused undesirable speed perturbations. After trying another type of DC motor with similar results we abandoned DC motors altogether and installed a synchronous AC motor powered by the 120VAC 60Hz mains. Small line frequency variations were clearly visible in the measured flow rate. Finally we conquered the flow rate stability problem by constructing a crystal-based 60Hz power supply for the synchronous motor. The result is a flow rate whose stability is typically +/- 0.02% relative.

For the first 6 months of operation, MOAC required a b calibration coefficient of approximately 1.01. In other words, we were losing 1% of the heat from the chamber. We tracked this loss down to the power and signal wires passing through the walls of the chamber. We initially thought that the active insulation system would eliminate losses in these wires because the temperature difference across the walls is forced to be zero. However, our wire bundles were not adequately thermally clamped at each wall so ambient air temperatures were having an unexpected influence. We solved this problem by instrumenting the wire bundles with temperature probes located at each wall of the CC. The measured temperature difference from these probes is used to calculate the wire loss term used in equation 3. After this correction was implemented, the b coefficient typically comes out between 0.999 and 1.001; in other words, within 0.1% of unity.

A number of other issues have been identified and addressed over MOAC’s four-year operating history. For example, we have struggled to find a suitable gasket for the calorimetry chamber door. Several designs were tried and some of them caused noticeable heat leaks. It must be remembered that a 0.5% loss is easily noticeable in a calorimeter that is expected to achieve 0.1% accuracy.

At the time of this writing, MOAC is quite reliable and readily achieves 0.1% accuracy when recently calibrated. The largest remaining source of error is the drift exhibited by the thermistors used for the critical inlet and outlet water temperature measurements. The observed drift is usually quite slow and is only a fraction of the manufacturer’s specification. That is, the thermistors are performing significantly better than the manufacturer’s guarantee but we can still see their drift. Because of this drift, MOAC typically requires recalibration, usually only a change in the a term, once every month or two.

<  Temperature Measurement   Interesting Results  >