Watts is final power applied at the coil, or amount of work that is being done.
Joules is similar in a
sense but when applied to heating and cooling like British Thermal Units (BTU), Joules measures how much heating is being done over a period of time best I can simplify it down, 10 Watts per second is about equivalent to 10 Joules of watts per second something to that effect. Watts and Joules shake hands so closely in our application or in the application of say heating your home during the winter its kind of hard to sepperate the line between them.
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You are not the only one confused as many have arisen the same question of which is better suited to measure what our atomizers are doing, watts or joules, myself I am leaning toward the Joules side of the camp.