I love this kind of stuff. I know, I’m a geek.
First off, let’s spout some thermo chemistry.
[li]Water is water.[/li][li]The specific heat of water is based on WATER, not the amount thereof.[/li][li]Twice as many Joules of energy are required to heat twice as much water over the same temperature change.[/li]
Using the equation:
Joules of energy requires = Mass water * Temp change * Specific heat of water.
If I recall from the teaching days, the specific heat of water is 8.14 Joules/gram*degree Celsius.
Thus, to raise the temperature of 100 g of water from 0 to boiling (100 C) requires:
Joules = (100g)(100 C - 0 C)(8.14 J/g*C) = 81,400 Joules
As can be seen, twice the water (200 g) would require twice the energy.
So you’re thinking, “Spritle, does this mean the 1/2 means 1/3 thing is crap?” Not exactly. Certainly heating only the water you need (and no more) is important, but we have to bring in efficiencies of heating into the mix.
Lab burners and other open flame methods are incredibly inefficient at heating stuff. For every 100 Joules of energy released, 10 to 25 Joules actually go into heating the water (in this case). Element heaters are more efficient, in terms of less heat loss, but tend to be less efficient if one considers how the electricity is converted to heat in the element. Submerged elements are more efficient than contact elements (like the burner on an electric stove). Back to flames…
Why the range of efficiency in flames? Composition of the pot (e.g.; aluminum vs iron) and surface area (interface between flame and pot) have an effect. It is faster to heat water in a skillet over a large flame than in a tall thin pot (soup can). Faster means more efficiency and less fuel is spent. However, heating water in a skillet with a candle won’t work if you are losing heat from the surface of the water at the same rate as it enters.
So… Bunk? probably not. Heating faster is more efficient and therefore requires less fuel. Heating faster can be accomplished by heating smaller volumes of water.
Are you using 1/3 the fuel to heat 1/2 the amount of water? Not sure. There are many other factors involved; pan shape, composition, etc. There’s also the issue if the same pan is used over and over without cooling. This would increase efficiency in that you wouldn’t have to heat the pan each time.
It just seems unlikely the 1/2 means 1/3 thing. Eventually, if you heated enough very small volumes of water would you be adding fuel to the tank?