IH Fnaboy I havent read what Ascoli65 have calculated, but you are in risk mixing two different things in your thinking. What comes to fitting stock price history on trying to predict future, does not work since opposite to early days of stock exchanges, number of variables has grown, sudden one time interference factors (9/11, wars sub prime crisis etc) simply cannot be predicted from history. Also robot traders (operating at ms speeds) are something that you cannot predict from history because they exaggerates even small interferences because of snowball effect caused by speed competition).
Curve fitting in physical processes instead is more predictable and is daily routine in process industry. You may do black box testing on unknown process (cause change on input and measure response curve on output). There can be multiple different serial time constants inside black box, which makes exact calculations more difficult.
But for this you don't need even that. It is enough to calculate how much mass at max. you could hide inside E-Cat and calculate its thermal capacity supposing it gets heated say 1000C. That is what Paradimonia above explains. Boiling water takes lot of energy compared to temp increase of same amount of metal mass. Air gap is just parameter to fit to make correct boiling speed, it has nothing to do with capacity.
I checked my earlier estimations:
- Heat capacity of steel is 0.466 J/g/K (=kJ/kg/K) half compared to aluminum but fits in smaller volume Source Wikipedia
- Heat of waporization of water is 2257 kj/kg (see Wikipedia)
So in other words, to boil each 1 l of water you need to add 4.8kg of steel losing 1000K of heat (so steel lump temp must be > 1100 to keep 1 l water boiling totally. End temp must be >100C )
That is only a safe calculation, in practise it has to overcome temp leaks and heating first incoming water ( 4.1813 kJ/kg/K) depending on test arrangements (which I have not read).
These calculations does not take account possible pressure tweaking (=suck vacuum and water boils even in room temp). But as I said in playground these old tests and sayings are not interesting because of so big other reasons in play.