FP's experiments discussion

  • Just from the shape of the boiler? Huh.

    It is probably a heating surface area vs area exposed to the atmosphere thing, along with surface tension (related to the atmosphere “window” size). I read something about a long time ago.

    I’ll see if I can find a reference. I probably have a water boiling point folder someplace, on a drive. Apparently the experiments with “superheating” water can be quite dangerous. Spontaneous giant vapour bubbles (can throw all the other hot water out of, or break the container) and instant vaporization of all the water at once are potential hazards.

  • Quote: "Needless to say, the D in the lattice could not reach the surface in that time (the diffusional relaxation time is ~ 10^5 s) while the rate of diffusion of oxygen through the boundary layer could lead at most to a rate of generation of excess enthalpy of ~ 5mW."


    10^5 seconds = 27 hours. Sorry I was not more specific.


    Thank you for clarifying. In my estimation, this number is ludicrous unless one is talking about total unloading to 0.0 D/M. It is hard to get the last bit out. It is easy and fast to drop from D/M = 0.9+ to 0.7 (seconds to minutes), and somewhat slower to drop to the mid-plateau region (D/M~.3-.4) and below for the reasons F&P note, but it would only take minutes to a low number of hours at worst. Once the beta to alpha phase transition is complete, the desorption rate always increases again. The only modifying factor one needs to invoke is surface contamination. Some contaminants can poison the D+D->D2 recombination reaction, which would slow the unloading, but there is no information presented on this. What F&P is assert an unreferenced number, which is in disagreement with my experience with similar materials.


    Jed and other trolls won't accept this of course. I'm not going to argue with them.



    You don't believe Fleischmann?


    I believe F observed a deformation and jumped to the conclusion it was melting, and then got the melting temperature wrong.


    No, plugs do not get "deformed" for no reason in test tubes. Nothing was putting pressure on it. No one squeezed it with a pliers. The only reason it could change shape would be because it melted. There are no other widely variable conditions that could cause this.


    And you know this how? Your infinite scientific acumen?


    The rest of the post is just trolling....

  • It is probably a heating surface area vs area exposed to the atmosphere thing, along with surface tension (related to the atmosphere “window” size). I read something about a long time ago.

    I’ll see if I can find a reference. I probably have a water boiling point folder someplace, on a drive. Apparently the experiments with “superheating” water can be quite dangerous. Spontaneous giant vapour bubbles (can throw all the other hot water out of, or break the container) and instant vaporization of all the water at once are potential hazards.


    Simpler than that. At low boiling rates the shape of the vessel will determine how much mixing of atmosphere there is with vapour and hence partial water vapour pressure at surface. At high boiling rates the shape of the vessel will determine the total pressure increment at the surface due to dynamic effect of throttling the outgoing vapour.


    There is also, when turbulent boiling, as P says, total surface exposed but maybe this is not so much vessel shape dependent.


    Caveat - this is off the top of my head so maybe I've missed something?

  • [No, plugs do not get "deformed" for no reason in test tubes. Nothing was putting pressure on it. No one squeezed it with a pliers. The only reason it could change shape would be because it melted. There are no other widely variable conditions that could cause this.]


    And you know this how? Your infinite scientific acumen?

    This is practical knowledge. A plug that can be deformed several different ways in a test tube would be worse than useless. No one would manufacture such a plug, and no one would use it. It would be like putting bubble gum in the test tube.


    Furthermore, I am sure you cannot list any other reason why the plug would be deformed. You say it can be, just as you say a bucket of water will evaporate overnight in ordinary room temperature conditions, but this is nonsense, and you do not actually know of any mechanism that would make it happen.

  • You also might enjoy http://lenr-canr.org/acrobat/GoodsteinDwhateverha.pdf It describes the skewed reviewing that happens in the field. Goodstein wasn't aware of my 2002 publication in 2000 (even thought he original manuscript came out then, see http://lenr-canr.org/acrobat/ShanahanKapossiblec.pdf). I would guess he would be really interested to see the blatant use of a strawman argument in http://lenr-canr.org/acrobat/MarwanJanewlookat.pdf used to discredit my explanation of the FPHE. To see what I really said you have to look up J. Env. Monitor., 12, (2010), 1756-1764. The 'MarwanJane...' paper immediately followed mine.


    All these documents show that the controversy between the F&P supporters and their critics will never end. The fans of the two founders of CF will never stop affirming the competence and correctness of their heroes, as happens for the last eccentric Tesla, and as will eventually happen for Rossi.


    Another problem to prove the inconsistency of the F&P's claims is to dispel the criticisms into too many chemical-physical aspects. I think it is more appropriate and effective to focus on the excess heat, which is considered the real signature of the F&P effect, as stated at ICCF4 (1): "We conclude that there is an FPE and its signature is heat. Data existed in 1989 that could have lead to this conclusion. The source of the excess heat is still not understood. Scientific progress was not made through this debate, which was largely uninformed by appropriate experimentation, and patent considerations may have played a determining role in the scientific progress associated with the FPE."


    The prevalence of experimentation over theoretical debate, the affirmation of excess heat generation and patent management are the very empirical and concrete foundations that have guided the CF history since 1989 up to the Ecat. From F&P to Rossi, there is nothing in between them. Those who have had to set aside - at least temporarily - the "Rossi effect", have dusted off the old FPE, so that all the castle of cards of possible applications of hypothetical CF is back to rest on the calorimetric results claimed by F&P (2).


    Among the F&P's experiments, the most famous is the one presented in October 1992 at ICCF3 (3), in particular the DEMO9_2, whose transient is presented in fig.6B . These curves have accompanied the entire history of the CF until the advent of the Ecat. In 2009, Krivit and Marwan showed the same transient in Figs.4 and 5 of their paper "A new look at low-energy nuclear reaction research" (4), the document you criticized in the article you linked above.


    DEMO9_2 is so popular because it is the only one used by F&P to demonstrate the maintenance of heat generation even after the cessation of power supply. In December 1993 at ICCF4, the two scientists dedicated a specific paper to this alleged phenomenon (5), coining for the occasion the expression "Heat After Death", which will have great success in the CF field


    However, their paper does not mention that, during DEMO9_2, the voltage fluctuated around an average value of 5-6 V as long as the cell remained at high temperature. This unexplained behavior was very different from that of the other 3 cells, as shown in the following jpeg.


    PLTSh4A.jpg


    Now the big problem is that, in this single example of HAD documented by F&P, the input power has not ceased! So the cell was not "Death", and we can only talk of "Heat After Something", where the "Something" has not been highlighted and explained by the authors of the article.


    Kirk, you've been following the F & P experiments for many years, and you've done some tests. How would do you explain the residual voltage in Fig.6B?


    (1) http://www.lenr-canr.org/acrobat/MelichMEbacktothef.pdf

    (2) http://lenr-canr.org/acrobat/RothwellJcoldfusionb.pdf

    (3) http://www.lenr-canr.org/acrobat/Fleischmancalorimetra.pdf

    (4) http://newenergytimes.com/v2/l…ivit-S-ANewLookAtLENR.pdf

    (5) https://pdfs.semanticscholar.o…62833c812de0914674742.pdf

  • Kirk, you've been following the F & P experiments for many years, and you've done some tests. How would do you explain the residual voltage in Fig.6B?


    I wouldn't. It is an anomaly. There are a couple of things I could think of to explain it, but the explanations are just speculation. F&P (or someone) would need to replicate the effect and thereby demonstrate control over it. Then in principle they would be able to tell us what they did to reproduce it. So, today we not only have the Great F&P KelF Plug Anecdote, we have the Great F&P 'Heat After Death' Anecdote.

  • Now the big problem is that, in this single example of HAD documented by F&P, the input power has not ceased! So the cell was not "Death", and we can only talk of "Heat After Something", where the "Something" has not been highlighted and explained by the authors of the article.


    Kirk, you've been following the F & P experiments for many years, and you've done some tests. How would do you explain the residual voltage in Fig.6B?

    Do you have the current record? Obviously voltage is not power and a charged Pd cathode will maintain a potential difference with respect to a Pt electrode in the same electrolyte. There are quite a few other examples of "heat after death". The few that I saw absolutely had I=0 ... I disconnected the power leads myself.

  • Now the big problem is that, in this single example of HAD documented by F&P, the input power has not ceased! So the cell was not "Death", and we can only talk of "Heat After Something", where the "Something" has not been highlighted and explained by the authors of the article.


    I just skipped over the papers. As Mc Kubre already said a remaining voltage is to be expected! Decaying 4He from D-D fusion is strongly ordered due to magnetic momenta from excess flux. Thus the magnetic flux produces - expected by Maxwell source law - charge, what is equal to a certain voltage.


    Additionally I checked (F&P) the ramp-up time of the heat and the timing of the heat after death. Both are absolutely conform with the current D-D fusion model we use. It's sad he left us that early!

  • Hi mmckubre, very honored for your attention.


    Do you have the current record?


    No, of course. But I think F&P had it. So I wonder why they didn't show the curves of both the voltage and the current, at least for the DEMO9_2, which was the most discussed in their paper (1), and the only one to have shown a possible HAD event.


    Figure 8, in the same paper, shows the "Expansion of the temperature-time portion of Fig 6B during the final period of rapid boiling and evaporation". But Fig.6B also includes the cell voltage, it would have been natural to include also this quantity in the expansion in order to mark the exact time of the presumed ceasing of the power input. I see no reason why they excluded the cell voltage from Figure 8, unless they saw that it didn't go to zero, and had no explanation for this behavior.


    Quote

    Obviously voltage is not power and a charged Pd cathode will maintain a potential difference with respect to a Pt electrode in the same electrolyte.


    Yes, voltage is not power, obviously, and I don't know if a charged Pd cathode maintains a potential difference with respect to a Pt electrode in the same electrolyte, but in such a case I wonder why it happened only for 1 electrode out of 4.


    IMO, the voltage should have maintained the max possible value, the so called rail value (100 V for the experiments described in (1)), until the circuit was not open manually or by some automatic control. In the meanwhile the cell current should have progressively decreased, even if the galvanostat was set to a constant value of the current.


    So I would have expected that for all the four electrodes, the cell voltage should have stayed, at least for a while, at the rail value of 100 V even after the sharp drop of the corresponding cell temperatures. In the case of the prolonged high temperature registered during DEMO9_2, the cessation of the input power could have been marked in Figure 8 by adding the trend of the cell current.


    Quote

    There are quite a few other examples of "heat after death".


    I don't know which these other examples are and which experimental evidences are available on the web, but “From simplicity via complications back to simplicity” is still considered the major paper of Fleischmann (2), probably because it reports his best experimental results and the most convincing evidences.


    Quote

    The few that I saw absolutely had I=0 ... I disconnected the power leads myself.


    Very interesting.


    On this respect, I'd take the occasion to ask you some questions. Did you use the same power control strategy used by F&P? Did you use a galvanostat whose voltage was set at a certain rail value? Do you remember which was the cell voltage after disconnecting the wires: the maximum rail value, a null value, or a residual intermediate value as in Fig.6B (1)?


    Did you publish these results somewhere? Are they available on internet?


    Thanks in advance.


    (1) http://www.lenr-canr.org/acrobat/Fleischmancalorimetra.pdf

    (2) http://lenr-canr.org/acrobat/Fleischmanlettersfroa.pdf

  • So, today we not only have the Great F&P KelF Plug Anecdote, we have the Great F&P 'Heat After Death' Anecdote.


    I wonder if these anedocdotes have the same origin. Do you have some experience with this kind of cells powered by a galvanostat? What could happen if there is a short inside the cell, possibly caused by the intense boiling? Could the voltage decrease to a low value as in Fig. 6B?

  • I wonder if these anedocdotes have the same origin. Do you have some experience with this kind of cells powered by a galvanostat? What could happen if there is a short inside the cell, possibly caused by the intense boiling? Could the voltage decrease to a low value as in Fig. 6B?


    I don't know. The Kel-F deformation is likely due to a slightly elevated temperature combined with an applied stress. I could speculate on how that happens but it isn't worth the effort. The unusual residual voltage (only 1 out of 4 cases as you noted) could be from something else. That's the problem with anecdotes. No reproducibility to confirm/deny speculations (i.e. hypotheses).


    I personally have limited electrochemical experience and I'm not an expert in it. What I have routinely done is analyze the data as given and try to understand what it is saying, instead of forcing it to say what I want it to. A prime example is the first paper I published on the Storms Pt anode and cathode system. His first set of data had a strong negative feedback from the input power in it, which I reported to him. Scott Little of Earthtech also did that. Ed then redid his grounding setup and removed almost all of the feedback (which had caused baseline shifts) and reran the experiment. It was the second set that he and I separately analyzed (he presented his results at ICCF8 as an example of cold fusion).


    In any case for details like you are asking I am not an expert.

  • Ascoli65


    I should also add w.r.t. the Kel-F deformation that I think it reasonable that this is a manifestation of the so-called 'cigarette lighter' effect. (I know. Fleischmann thinks not...) It works like this...


    Once the electrolyte level drops enough to expose the electrode, that exposed metal now is exactly like the metal in a gas-loading cell. IOW, the electrochemical force holding the H (or D, or T for that matter) in is gone and all that is left is 'normal' gas pressure. Since the loading level obtained by electrochemical loading is much higher than achieved by gas loading, the electrode immediately starts to unload, reasonably rapidly I would expect, if the electrode surface has not been poisoned by stuff from the electrolyte. But the exposed region is still connected to the covered region, so H starts to flow from that area to the lower concentration area. Diffusion in Pd is quite fast, so thinking in terms of a step function change in H concentration at the boundary is unlikely to be true, but it may not 'instantaneously' reach equilibrium either. Further, there is significant H2 in the gas phase which means the exposed metal will equilibrate with that, leaving appreciable H in the metal, and not totally unload. The equlibrium H2 pressure for half-loaded Pd at 100C is around 250-300 Torr I think, D2 would be higher. One would have to calculate the ambient H2 pressure based on gas flow, but I'm guessing it would be ~2/3 of an atmosphere, with O2 making up the other third (IOW I am assuming the cell is filled with electrolysis gas). If the H2 pressure is 2/3 atm, the PdH will likely still be highly loaded (H/M~.5-.6 I would guess. The O2 will react with H2 to form water on the exposed electrode part, reducing the gaseous H2 content, which in turn will cause the metal to release more H2. Lots of things going on to make computing the Pd-H loading difficult.


    As well, in the F&P experiment, the electrolyte level is continuously dropping, so fresh, highly loaded Pd will become exposed over time, and it will rapidly unload to the equilibrium point. This continues until enough electrolyte is removed to break electrical contact, which is where the whole electrode becomes a participant in the gas unloading event and where electrolysis stops. Once the electrolysis stops due to loss of current flow, gas production in the cell is reduced. After a brief period to equilibrate the solid-gas H2-metal reaction, the only thing going on is H2+1/2 O2->H2O, which reduces the pressure. That does two things. It draws air into the cell from the vent line (more O2 to react), and it changes the equilibrium point of the hydride reaction which results in further unloading. Now the rate will be controlled primarily by the rate of the water formation reaction. So the question 'What is the H content of the Pd as a function of time?' is complicated as you can see.


    In any case, I am not surprised we see a slight increase in temperature after the current is supposedly turned off due to the onset of the water formation reaction (which was normally minimal while electrolysis was running and sweeping gases out of the cell through the vent) and due to the change in thermal characteristics of the cell from a) reduced electrolyte content, b) cessation of stirring in what electrolyte is left, c) reduction of gas flow out of the cell, and d) whatever else one might think of. And the temperature of the electrode is likely reasonably hot, above the current ambient, which would facilitate the Kel-F deformation.

  • As Mc Kubre already said a remaining voltage is to be expected! Decaying 4He from D-D fusion is strongly ordered due to magnetic momenta from excess flux. Thus the magnetic flux produces - expected by Maxwell source law - charge, what is equal to a certain voltage.


    I strongly doubt that McKubre was referring to this model of yours.


    Quote

    Additionally I checked (F&P) the ramp-up time of the heat and the timing of the heat after death. Both are absolutely conform with the current D-D fusion model we use. It's sad he left us that early!


    I don't know which model are you using, but I don't think it's a good publicity saying that it "absolutely conform" to the F&P results, if you are referring to those reported in their paper “Calorimetry of the PD-D2O System: From simplicity via complications back to simplicity” (1).


    This paper is one of the sloppiest I have ever read. After having presented a complicate calorimetric model made by long formulas with many variables, and having calculated the value of some experimental coefficients up to three significant digits, the paper ends with the baffling calculation of page 16. Most of the input data used in these calculations are not explained in the paper, and sometimes are even completely missed. In the first line - enthalpy input by electrolysis - the duration is omitted, and in the following lines a rounded off value of 600 s is used. This sloppiness clashes with the apparent precision exhibited in the first part of the paper.


    But the worst error is in the calculation of the enthalpy output in vapour, where it was assumed that all the water lost in the final boil-off phase – i.e. half of the initial inventory – left the cell as dry steam. This flaw speaks loud about the competence of anyone who believed those calorimetric results. Incredibly, this sloppy calculation ended with the estimation of a specific rate of the alleged excess heat of about 3700 W cm-3, giving rise to one of the most popular anecdote in the CF history: the mythical ability of the F&P cells to generate up to ~ 4 kW cm-3 of excess heat (2).


    To see a similarly sloppy document reach such a notoriety and influence in the CF/LENR field, it will have to wait nearly two decades, until the calorimetric report of the Ecat demo held in January 2011.


    IMO, a more suitable title for this F&P paper would have been "... From simplicity to sophistication, back to sloppiness".


    (1) http://lenr-canr.org/acrobat/Fleischmancalorimetra.pdf

    (2) http://lenr-canr.org/acrobat/PonsSheatafterd.pdf

  • In any case for details like you are asking I am not an expert.


    Thanks anyway for your exhaustive explanation of a possible electrochemical cause of the Kel-F deformation.


    In any case, I am not surprised we see a slight increase in temperature after the current is supposedly turned off due to the onset of the water formation reaction


    In the alleged HAD event shown in Fig.6B, the cell temperature remains at boiling level for a few hours, and drops only when the residual voltage goes to zero. So it seems very likely that the slight increase in temperature is somehow connected to this electrical anomaly. Let's see if McKubre will provide us some enlightenments on this issue.


  • Very interesting.


    On this respect, I'd take the occasion to ask you some questions. Did you use the same power control strategy used by F&P? Did you use a galvanostat whose voltage was set at a certain rail value? Do you remember which was the cell voltage after disconnecting the wires: the maximum rail value, a null value, or a residual intermediate value as in Fig.6B (1)?


    Did you publish these results somewhere? Are they available on internet?

    Happy to answer with the preface that all (only 3 or 4) incidents of HAD that I saw were with cells that remained full of electrolyte (all closed cells - some with external recombiner) so my experience has little direct relevance to the F&P cases.

    1) Our power supplies and strategy were a little different. We mostly used Kepco BOP power supplies in (slow) galvanostatic mode. But an (hypothetical) open circuit with a demand current > 0 would have driven the supply to the rail (typically 20V). As noted above these supplies were disconnected and various other strategies employed to check the reality of our I=0 and ∂T>0 assertions.

    2) I spoke about HAD (I called it heat after life) at ICCF4 ... not knowing that Martin was going to speak about it too. I wasn't really interested as the situation is uncontrolled. It is a good way to refute some calorimetric concerns in those not very experienced (hard to make an input power-measurement error if I*V=0).

    3) I do remember writing up one case in nauseating detail where the effect was small but certain. This was for DARPA so I doubt it is on the internet. My non-Google search of "Energetics/SRI replication" says it is mentioned in here http://lenr-canr.org/acrobat/McKubreMCHcoldfusiona.pdf - I did not see it on casual glance but the experimental set certainly is.

    4) The open cell potential is only a few hundred mV. This maintains for a surprisingly long time. Spontaneous deloading is slow for used cathodes. But this does not explain your "residual intermediate value". To understand this we would need to know I, and thus R, hence my inquiry. You might think about calculating the effect of a putative residual salt bridge (non-infinite impedance) between anode and cathode wires somewhere in the head of the calorimeter where the wires leave, but,

    5) I admire your zeal but do not see much to be gained from this line of inquiry. The HAD phenomenon is mysterious - but it is real. Fleischmann was not incompetent - until the final stages of Parkinson's. The only person who can help with direct personal information is Stan Pons - who might respond to a respectful, scientific inquiry.

  • Thank you for your detailed answer. It doesn't solve all my doubts, but provides some useful hints.


    Our power supplies and strategy were a little different. We mostly used Kepco BOP power supplies in (slow) galvanostatic mode.


    The galvanostatic mode was also used by F&P in their ICCF3 paper (1). In particular they wrote: "The current in the first cell was 0.500A. The initial current in each of the other 3 cells was 0.200A, which was increased to 0.500A at the beginning of days 3, 6, and 9, respectively."


    From the spikes in the voltage curves of their Figs.6, it appears that the current increases were sudden. I assume that the slow mode you used refers to the slow current increase shown on the diagram of Page 11 in your 2009 presentation at ICCF15, that you have addressed to me.


    Your diagram also shows that, contrary to what F&P did, you appropriately reported the curves of both voltage and current.


    Quote

    But an (hypothetical) open circuit with a demand current > 0 would have driven the supply to the rail (typically 20V). […] The open cell potential is only a few hundred mV.


    These two sentences confirm, as you also recognized, that the 5-6 V of residual voltage shown in Fig.6B of the F&P paper cannot be explained by any of these two possible conditions. IMO this reinforce the hypothesis of an accidental short, or some sort of electric bridge, between the cathode and anode circuitries.


    Quote

    I admire your zeal but do not see much to be gained from this line of inquiry. The HAD phenomenon is mysterious - but it is real.


    HAD is as mysterious as the whole CF/LENR phenomenon.


    For what I saw in this brief inquiry, the only publicly documented HAD event is the one reported in the F&P paper presented at ICCF3. This increases the HAD mysteriousness, as Fig.6B shows that the cell was indeed alive throughout the high temperature period. I'm sure you understand that this fact also increases the difficulty in accepting these phenomena as real.


    Quote

    Fleischmann was not incompetent - until the final stages of Parkinson's.


    I totally agree. I can't believe that an academic with his credentials could have ignored the enormous effect on the energy balance of his cells due to the liquid droplets entrained in the gas stream. But his recognized competence further increases the mystery around his claims and the whole CF/LENR history.


    Quote

    The only person who can help with direct personal information is Stan Pons - who might respond to a respectful, scientific inquiry.


    I'd like to, but FWIK he chose to stay away from the field.


    (1) http://lenr-canr.org/acrobat/Fleischmancalorimetra.pdf

  • I can't believe that an academic with his credentials could have ignored the enormous effect on the energy balance of his cells due to the liquid droplets entrained in the gas stream.

    He did not ignore that. He showed conclusively that no such droplets exist, with several methods, mainly by showing that all of the salt was left in the cell. Also, if that were the cause of apparent heat, it would happen with the control tests with platinum and ordinary water. It does not.


    No doubt, you will ignore what Fleischmann wrote and you will continue to repeat that nonsense, but you should be aware that anyone who reads the literature will see that you are wrong.


    There is much else that you cannot explain, such as: Why is it boiling at all, given that the input power is far lower than during the control tests? There are a whole series of questions I put to THH which he has ignored. No doubt you, too, will ignore them so I will not repeat them.


    THH has new theory that droplets of pure water can condense on the cell walls and then be driven up and out of the cell by steam. That's impossible, given the geometry of cell and the steam pressure which is only a tiny bit above 1 atm. THH should test this hypothesis with a test tube similar to the cell. Even if this could happen it would be orders of magnitude smaller than the excess heat effect, and it could not make the thing boil with far less input power than it normally takes. THH also applied this hand-waving droplet theory to the events before the boil off, when the water level was measured carefully and no water was lost unaccountably. Then he applied it to HAD when there is no water at all. So, clearly he is not bound by ordinary reality or facts.

  • Re. entrainment


    In S. Szpak, P.A. Mosier-Boss, M.H. Miles, M. Fleischmann; Thermochimica Acta 410 (2004) 101–107 (specifically p.105), the authors say: "In this experiment, the total consumption of D2O was 7.7 cm3 instead of 7.2 cm3, assuming 100% Faradaic efficiency, which is within experimental error." 7.7 cc is 106.9% of expected, or IOW, a 7% error. That is a little large to just blow off (pun intended) as undefined experimental error. In my reply to this paper I noted this and attributed it to entrained microdroplets in the exiting gas stream. As I recall however, the heat loss due to that wasn't all that significant in this system.


    The points are: A) Entrainment happens. B) The amount depends on a variety of factors, and C) That makes it difficult to know a priori whether it can be ignored or not.


    It is also true that the amount of entrainment would be larger if there was some 'in the cell' recombination, which was implied by the apparent excess heat signals they got. The amount is potentially calculable if more was known about the calibration equation and such, but as is typical when you 'get real', things get very complicated and to calculate reliable numbers you would need a good chemical process model with all the factors plugged in. (Note that the infamous F&F differential equation approach to calorimetry did not include an entrainment term.)