Replication of Mills Light Water Calorimetry Experiment - Run 3 - 29JAN01
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An introduction to this experiment and the report on Run 1 should be reviewed before reading this report.

During the course of Run 2, which was a control run using Na₂CO₃ electrolyte, we discovered that the gas flow rate measurements made in Run 1 were substantially in error.  We experimented with various alternative flow rate measurement methods during Run 2 but it wasn't until Run 3 began that a reliable method was validated and put into practice.  We therefore demote both Run 1 and Run 2 (no report) to the status of practice runs and direct your attention to the subject of this report, Run 3.

Run 3 was conducted with a new Ni wire cathode and fresh 0.57M K₂CO₃ electrolyte.  All materials were cleaned and assembled as described in our earlier reports.

This  photo shows the essential elements of the gas flow rate measurement we are presently employing.  A 1 cc syringe, graduated in 0.01 cc increments, is connected via a tee fitting into the gas plumbing that leads into the head space inside the active cell.  Just above that tee is a second tee that leads to a sensitive differential pressure transducer (OMEGA PX74-0.3DV) which can resolve pressure differences as small as 0.005 mmHg.  The output of this sensor is zero when the pressure difference across it is zero and can swing both positive and negative to indicate the magnitude and direction of a pressure difference.  Beyond the pressure sensor (just above the edge of this photo) is a valve that can be used to close off the gas vent path.

To make a gas flow rate measurement with this apparatus, the syringe plunger is first pushed all the way into the barrel.  Simultaneously, the valve is closed and a stopwatch is started.  Because the electrolysis process is continuously producing gas,  pressure begins to build up in the now-closed head space making the pressure sensor signal go positive.  The syringe plunger is withdrawn precisely to the 1cc mark, thus increasing the volume of the closed head space by 1 cc.  This increase in volume lowers the pressure in the head space (which is about 200 cc) making the pressure sensor signal go negative.  The stopwatch is stopped precisely when the pressure sensor signal crosses zero, indicating that the pressure in the head space has returned to its original value before the 1cc volume increase.

Concerned about the effects of heat flow in/out of the system during the volume change, we compared two methods of withdrawing the syringe plunger, (1) gradual withdrawal keeping the delta-pressure within 0.25 mmHg of zero at all times, and (2) sudden withdrawal about halfway through the time period (which changes the pressure in the system by about 4 mmHg.  There was no discernible difference in the results obtained with these two methods.

Our gas flow rate measurements for Run 3 were rather consistent.  In the first half of the run, the observed gas flow rate was about 56% of the theoretical value computed from the cell current (corrected for ambient temperature and local atmospheric pressure).  In the latter half of the run, that declined to about 53%.  Throughout the entire run we never obtained a reading outside the range 52-57%.

The large photo below shows the entire setup for Run 3.  The two Dewars are in the background on the right. In the foreground is the gas sampling system used to deliver the electrolysis gases to our RGA (long gray box) for analysis.  The RGA (which stands for residual gas analyzer) is a quadrupole mass spectrometer with 1 AMU resolution.  It was designed to provide continuous monitoring of residual gases in a high vacuum system, primarily for vacuum diagnostic purposes.  However, by metering a gas stream into the vacuum system it can be used for qualitative and semi-quantitative analysis as we have done here.

This plot of pressure vs mass shows a typical RGA spectrum obtained from the gas produced in Run 3.  The hydrogen (H₂) peak at mass 2 goes off-scale vertically.  The next highest peak is oxygen (O₂) at 32.  Water vapor shows up mainly at 18 but also reports at 17 due to splitting of the H₂O molecule into HO by the ionizer in the RGA.   CO₂ appears at 44, and nitrogen (N₂) at 28.   Also shown (in green) is a background spectrum taken after the cell gas had been completely pumped out.  As you can see, most of the water vapor, nitrogen, and CO₂ signals are still present in the background spectrum.  The small peak at 16 that is absent in the background spectrum is due to monatomic oxygen produced by the ionizer.  Obtaining a representative background for the water vapor is problematic because water adheres to the walls of the vacuum system so tenaciously.  Despite the fact that the background spectrum shows the same level of water vapor as the cell gas spectrum, there can be no doubt that the cell gas does contain some water vapor.  It also contains a small amount of CO₂ and some nitrogen, apparently left over from the start of the experiment when the cell was initially full of air.  However, the vast majority of the cell gas is H₂ and O₂ as expected from the electrolysis process.

This plot shows the entire calorimetric record for Run 3.  The horizontal axis is time (0-400 hours) with 20 hr/div.  The color-coded power traces Pout and Pin are plotted on a vertical scale that runs from -100 mW to +400 mW (50 mW/div) with 0 mW marked by the horizontal grey line two divisions up from the bottom.  

The other traces are temperatures and are all plotted on a scale that runs from 10°C to 60°C (5°C/div).  The temperature of the electrolyte in the active cell is Tcell.  The temperature of the water in the reference cell is Tref.  Room air temperature is Troom.

Per Mills, the run necessarily starts with electrolysis power on.  His protocol calls for immersing the Ni cathode into the electrolyte with electrolysis power applied.  A constant-current power supply was employed and, for this run, was set to drive 0.083 amps through the cell.   That current persisted for the entire 380 hour duration of the run.   The system reached thermal equilibrium after ~70 hours.  At the 90 hour mark, precisely 100 mW of power was applied to the teflon-encased calibration resistor submerged in the active cell's electrolyte.   This "standard addition" persisted for another 90+ hours, again with thermal equilibrium occurring in the last 20-30 hours.  At the 185 hour mark, power was removed from the calibration resistor in the active cell and a manually adjustable power was applied to the calibration resistor in the reference cell.   By 240 hours, this power had been adjusted so the temperature of the water in the reference cell closely matched that of the electrolyte in the active cell, thus achieving a null balance.  Evidence of this last condition is marked by the Tcell and Tref traces merging together and the Pout trace going to zero.

This table summarizes the calorimetric results from this run.  All values are in watts.  Column A represents the results obtained from the first equilibrium (i.e. 70-90 hrs) employing a calibration based upon the 100 mW standard addition.  Column B represents the same data as Column A but interpreted with a calibration based upon the calibration resistor only (i.e. without electrolysis going on in the cell).  Column C represents the results obtained from the latter part of this run, when the null balance method was employed.  The bottom row in this table, labelled "difference", represents the observed amount of excess heat in Run 3.  As you can see it is less than 10% of the electrical input power and varies from positive to negative depending upon the calibration method.

Although the variations among these different calibration methods are interesting and possibly significant, we must first focus on the dramatic difference between our results and those obtained by Mills in the experiment we are trying to replicate.

This table shows selected parameters of Mills' experiment (Randall Mills, "The Grand Unified Theory of Classical Quantum Mechanics", 1996 edition, Table 1,  p 479) side-by-side with the same parameters (averaged) observed in our Run 3.  Everything tracks reasonably well until you get to the heat output power.  Mills' value exceeds his total electrical input power while ours is substantially less.

We can think of only 3 reasonable explanations for this vital difference between our experiments:

1.  A fundamental difference in the chemistry/physics of the two experiments  -  Possibly it is not sufficient simply to use nearly identical materials and prepare them in nearly identical ways.  One indication of a possible problem is the cell voltage.  Ours is noticeably lower than Mills.  Also, Mills found reason (see discussion on p. 474 in the above referenced book) to believe that there was no recombination of the electrolysis gases occurring in his cell.  Measurements on our cell indicate approximately half of the gases produced recombine within the cell.   

2.  A significant error in our calorimetry -  We have demonstrated 3 different methods of calibrating this style of calorimetry.  Although they differ noticeably, they are all essentially in agreement when compared to the very different result that Mills obtained.  We cannot imagine a still-hidden error in our calorimetry, affecting all three of these methods more-or-less equally, that would be large enough to explain the difference between our result and Mills' result.

3.  A significant error in Mills' calorimetry  -   According to discussion on p. 469 and 470 of the above referenced book, Mills' primary calibration technique was very similar to our standard addition method.   From the information he presents, we cannot identify any errors in his calorimetry.

At this point we are stuck.  We need assistance and cooperation from Mills to make any real headway.  There is one thing that can be done and that is presently underway.  Run 4 is a control run in which the K₂CO₃ electrolyte used in Run 3 has been replaced with Na₂CO₃.  The results of this run should be quite interesting and we will report them ASAP.

Regarding the difference between our standard addition calibration and the one derived from the calibration resistor alone (columns A and B in the table above), Mills also observed this difference (p. 469 in the book) and said of the latter method, "This method over-estimates the cell constant (°C/watt) because there is no gas flow (which adds to the heat losses)."  We concur with his observation that the calibration resistor method produces a higher cell constant but his reasoning does not appear to be correct.  With an input power of 0.25 watts and a nominal cell constant of 40 °C/watt, the cell interior runs 10°C above ambient.  At 0.083 amps, the cell is producing 0.86 nanograms/sec of H₂ and 6.9 nanograms/sec of O₂.  If all of this gas escapes at 10°C above ambient, it carries off a purely thermal power of only 0.2 milliwatts.   A more likely reason appears to be the fact that, with electrolysis underway, the surfacing bubbles create a fine mist in the head space that continuously wets the upper portions of the Dewar walls with warm electrolyte.  This raises the temperature of those walls above what it would be without the electrolysis and thus increases the heat lost via radiation.   Perhaps surprisingly, radiation losses are indeed significant in this apparatus and amount to about 2/3's of the total heat loss from the Dewar.  The rest is conducted through the insulated lid.

Regarding the difference between the null balance method (column C above) and the others, it is possibly due to intrinsic differences between the insulating properties of the two Dewars.  Eventually we may investigate this issue further but it is not of primary importance right now.

Comments and suggestions are welcome:  little@earthtech.org