I calc it by considering the heat capacity of water and the energy density of fuel.
1. Heat capacity of water:
A material's "specific heat capacity" (or C) tells you how much heat is required to raise one unit mass by one unit temperature. The specific heat capacity of liquid water is ~4.184J/g/defC (this is where the energy unit "calorie" comes from).
That is 1 J will raise the temperature of 1g of water by 1degC.
So to increase the temperature of 455g of water by 125F (~69C, sorry to mix units)…you need ~69 X 455 X 4.184 = 131,000J = 131kJ of energy
2. Energy density of the fuel:
A fuel's "heat of combustion" tells you how much energy is release by buring a unit of that fuel. Typically this value will be given as either Higher Heating Value (HHV) or Lower Heating Value (LHV). LHV assumes that water resulting from combustion is in the vapor state, HHV assumes it is a liquid (for this reason I use LLV).
LHV for butane/protane/isobutane is ~46,000 J/g or 46kJ.
That is 1g of fuel burned will give of ~46kJ of energy
3: Fuel required
I calc minimum fuel required by: min fuel = (Energy required) / (energy density of fuel)…
=[131kJ]/[46(kJ/g)] = ~2.9g.
edited to add…
the above calc assumes that every bit of energy makes it to the water. The pot mass is negligible. All water stays in the liquid state. No combustion vapor condenses on the cookpot. It represents the very best you can do without breaking the law(s).

