Excess heat is the result of mismeasurement of input power, caused by neglecting AC power.
McKubre expressly ignores AC noise power from fluctuations in the ohmic resistance. However, it’s not hard to add the missing term back into the energy budget model. If the ohmic resistance is fluctuating R±r, then PAC ≈ α²PDC, where α = r/R. V will be fluctuating V±v, with v = Ir = αV. In other words, α = v/V, so the peak-to-peak fluctuations in voltage suffice to obtain the value of α for a given amount of drive current, I.
Kort would be correct, if the AC has significant power at frequencies approaching or above the sampling rate. McKubre used a constant-current power supply with high bandwidth and slew rate. The source of AC noise is variations in resistance due to bubble formation. Bubble formation varies with conditions, but key in understanding McKubre’s work is understanding control experiments.
Bubble noise is low-frequency, because bubbles are gross physical phenomena that cannot move rapidly. The scientists working on these experiments use high-bandwidth oscilloscopes to examine the cell voltage. It will have substantial noise at audio frequencies. However, at high frequencies, it’s flat, very low noise.
Frequency is missing in Kort’s calculations. McKubre measures input power by sampling cell voltage at high frequency, and averaging the samples for a period, then multiplying the average by the constant current to give the power for that period. While there is a theoretical error introduced, if the frequency of the noise is low, the amount of power missed is negligible.
You can certainly add detail to the noise model by using something more sophisticated than a simple square wave model for the fluctuating resistance. A square wave model gives PAC = α²PDC, whereas a sine wave model gives PAC = ½α²PDC. It doesn’t really matter which model you use, for the purpose of demonstrating that AC noise will be present at a level ≈ α²PDC. Whether it’s measured directly or estimated from a simple model, it clearly needs to be included in the energy budget.
Instantaneous power will vary. But what is really being measured is input energy, which is the integral of power. Power is varying with the resistance noise. But how rapidly? There is AC power, all right, but it is at low frequency and does not affect the instantaneous power for short sampling times, when both current and voltage are close to constant. So the measure of net energy per sample time is easily as accurate as is needed.
My own cell kits, designed to measure neutrons (and not heat), were mentioned:
It’s easy to make your kits work. Just make sure that you have a whole lot of bubbling, and then pretend there is no AC noise power, and pretend the heat (from the AC noise) comes from some mysterious effect that no one has ever seen before. Then you can telephone up the press and speak over the phone using this same non-existent AC signal power. Recall that Arthur C. Clarke said, “Any technology, sufficiently advanced, is indistinguishable from magic.” Telephony, as you know, is a magical effect, since a voice signal somehow propagates over a line driven with a constant current
In hindsight, Kort was trolling, thinking up any possible argument, no matter how irrelevant. The kits I designed (and one was sold and run), did not measure heat at all. They were designed to detect neutrons. So Kort was, as it were, in a fog, not paying attention to fact, but only to whatever would seem to support his ideas. I was slow to react to the trolling, but eventually did. AC signal power is not “non-existent” in the McKubre approach, but is actually measured, by sampling at sufficiently high frequency.
But we can short-circuit all this argument:
Hypothesis: Input power is significantly mismeasured by using the McKubre method, due to bubble noise.
Prediction: Excess energy will appear based on the level of bubbling. [Kort actually predicts this, above]. It will appear regardless of cathode history, depending only on the current and loading relationship. For a fully loaded cathode, it will reliably appear.
Experimental results: In SRI P13/P14, P13 was a light water control cell in series with a heavy water experimental cell (P14). After reaching high loading, there were three current excursions following the same current profile. In the first two of these, no significant excess power appeared, in either cell. In the third, significant excess power appeared in the heavy water cell. An error due to bubble noise would have appeared in all three excursions.
Thus, mismeasurement of input power in the McKubre work, if it exists, cannot be explained by bubble noise.
(As I recall, somewhere, Kort asserted that deuterium bubbles would behave differently from hydrogen bubbles, hydrogen being much more buoyant, so bubbles would be smaller and thus cause less variation in resistance. That’s probably correct, but still irrelevant, because of the self-control, i.e., the same cell, same conditions, but different results. The obvious difference is cathode history, the material shifts in many ways.)
(As well, bubble noise would still affect the measurement of excess power in the light water cell, but all that is seen at higher current is increased noise in the power, not significant excess power.)
The bubble noise possibility was examined by Dieter Britz as a result of Kort’s writing about this on Knol. Electrolysis power calculation. Britz is a skeptical electrochemist, but careful and very knowledgeable.
The task he undertook:
We have, some years ago, investigated the effect on power calculation of cell current and
voltage fluctuations in galvanostat configurations that were close to instability , as in fact
used in published work [3, 4] and concluded that there was no significant effect, even if there
were current fluctuations, as long as these are uncorrelated with the cell voltage fluctuations –
as they were found to be. However, the recent claims invoke a factor not taken into account
in the earlier work, that is, the finite reaction time of the current control circuit, or its finite
slewing rate. It is true that this means that whenever the cell resistance changes, there is a
current transient away from its controlled value, and it takes a finite time for this to relax back
to the nominal value. This might in principle lead to a computed mean power different from
that obtained from the mean cell voltage multiplied by the (assumed) constant current, or even
multiplied by a fluctuating current’s mean. This will be examined in this report.
Britz first does the math, and then runs similations, summarizing the result in graphs. His label has:
Figs. 2, 3 and 4 show the various time functions. Clearly there are perturbations to all
quantities, but these relax again to close to what is expected at the end of the resistance changes.
Some very small errors in the mean power remain after the resistance changes, however, but
only for rather unrealistically large τ .
And he had defined τ
We assume a constant current generator, which however responds with a certain time constant τ to a step change in load resistance.
Then he goes on:
Although the above already seems to lay the charge of wrong power calculation to rest, it might
be of some interest to look at a better model of cell resistance. In a previous paper , we
recorded cell voltage against time at constant current over 6.5 s, and got the trace seen in Fig. 5.
Sampling was at 10 kHz, and the paper shows a power spectrum of the signal, from which we
note that it flattens out at about 3 kHz, so there are no significant components above that
And then he looks at this in detail. His conclusion:
For realistic cell resistance fluctuations and current control circuits, the long-term running mean
power calculation is correct within small error bounds. The time constant of the control circuit
(or its slewing rate) will not, in practice, lead to false power calculations, and therefore not to
significant excess power artifacts.
Kort was very aware of this paper, but has continued, years later, promoting his delusions.
(He wrote a document where he argues for this in detail, I will review that separately.)