Breakeven for "hot" fusion is simple to understand and often mentioned (though the figure is a tad useless in practical terms). But I've been wondering about "breakeven" for a cold-fusion electrolysis cell.
I tried this for a definition: "Breakeven" is the amount of excess heat the cell must generate such that it would be possible (in principle!) to generate an amount of electricity from the cell equal to the amount being used by the cell. For this to mean anything we need to make some assumptions. Here's a picture (which isn't really necessary to the argument): http://www.physicsinsights.org/images/naive-cf-wet-electrolysis-cell.png And here are the assumptions: a) We have a closed electrolysis cell with an internal recombiner, so heat of dissociation is recaptured. (This would surely NOT be how a "real" commercial cell would work -- you'd most likely want to reclaim the dissociation "free energy" by running the evolved D2 gas through an external fuel cell. But for a first cut I just assumed passive catalytic recombination.) Total electrical power into the cell is "P_in". b) Coolant from the water jacket drives a heat engine which generates electricity. Coolant temperature to the heat engine is "T_high". Electrical power out from the heat engine is "P_out". c) There's some kind of cold reservoir available. Its temperature is "T_low". d) The cell is perfectly insulated and no heat is lost -- it all goes into the heat engine and thence into the cold reservoir. The heat engine is perfect, too, of course (we're looking for hypothetical "breakeven" here, not practical estimates!). e) Excess heat = "Excess" = percent over 100% of the input heat which we get out, divided by 100. From these assumptions we can find the output power immediately: P_out = P_in * (1 + Excess) * (T_high - T_low)/T_high At breakeven, P_out = P_in, and we must have 1 = (1 + Excess) * (T_high - T_low) / T_high or Excess = T_low / (T_high - T_low) or Excess = 1 / ((T_high/T_low) - 1) Note well that the excess heat at breakeven depends on the _ratio_ of T_high to T_low. If the device is to operate in a normal room environment with air cooling, T_low is likely to be ~ 20 degrees C. If the cell is operated in the usual range, between room temperature and boiling, we're pretty tightly constrained here. Now, whipping out a trusty old slide rule, we can immediately write down the breakeven values for a handful of ratios of T_high/T_low, along with the cell temperatures these represent given a couple plausible values for T_low. (Unit width font, please!) Breakeven T_high, assuming T_high, if T_high/T_low Excess T_low = 293K = 20C T_low = 273K = 0C ------------ --------- ------------------ ------------- 1 Infinity 293K (20C) 273K (0C) 1.1 10 322K (49C) 300K (27C) 1.2 5 352K (79C) 328K (55C) 1.3 3.3 381K (108C) 355K (82C) 1.4 2.5 410K (133C) 382K (109C) 1.5 2 440K (167C) 410K (137C) A couple comments are in order. First, we see immediately that we'd want to run such a cell as hot as possible; well over boiling. (This is still trivial stuff compared to the boiling lithium reactors which are on the drawing boards for _hot_ fusion! Man, if a pipe bursts on one of THOSE babies you head for the county line, I think!) At the highest temp I ran the table up to, 167C, breakeven is 200%. Even that it out of reach of most CF cells I can recall reading about. However, there was mention in ICCF-12 of someone achieving 600% excess heat. Depending on the cell temperature used, that might _already_ be above breakeven! Second, if the evolved D2 and O2 were run out to a fuel cell to be recombined, the "Excess heat" needed for breakeven would be a lot lower. Using a passive catalyst just discards most of the "free energy" pumped into the cell, which you certainly wouldn't want to do. But it would take some additional rather complex assumptions to determine "breakeven" for a CF cell with an external fuel cell recombiner.
