^^-- the power is turned into heat.
Total heat. Do not confuse with heat flux, which is heat divided by surface area.
So that other day I had someone tell me that if you were to take a .5 ohm, 1ohm, and 2ohm coil made with the same type of wire and at the same gauge they would all vape the same at 20 Watts.
Perhaps the point he was trying to make is: most "2 ohm" coils, for example, may be 2 ohm because they're made to draw low amounts of power from a normal battery. So people confuse this with
all 2 ohm coils, because they don't really understand it anyway. You can make a high power 2 ohm and a low power .5 ohm, in fact his statement is an example of exactly that, not coils with equal power. To use the same wire one must use a longer coil for more resistance, so the 2 ohm coil would be 4 times as large as the .5 and therefore require 4 times the power to work properly (and 4 times the voltage to make that power flow). The correct way to set up this example would be use different materials of wire, with differing resistivities, and otherwise make the coils exactly the same. It would then be very close to true (the mass and thermal conductivity of the coils would be a bit different). The closest practical example would be coils made of different wire, thinner wire made longer, for the same surface area, driven at differing voltages to achieve the same power.
All the power from the battery is converted into heat. The only forms of inefficiency relate to stuff being heated but not vaporized. Some power is lost between the battery and atomizer. The coil wire may be clamped in a post that absorbs heat. Parts of the wick containing fluid that isn't vaporized (yet) get heated. The coil has some heat left over which escapes if not used again rapidly. The whole atomizer may become hot. I'd say these losses are higher for high power devices, but still the majority of the power goes into vaporizing fluid.
Ribbon wire is misunderstood. The amount of heat required to come out of the coil is related to its surface area. Since its surface area is large, it needs a lot of power, compared to round wire of the same resistance. Therefore the coil needs fewer turns, to keep resistance low to draw more power, and to avoid the surface area from being too much larger. The only real advantage is the result has less mass than round wire and heats up a little more quickly. A little less energy is lost in cooling off.
At the highest power levels, increasing voltage does significantly increase efficiency. For low power levels, high voltages result in wires too small to handle.
