I am curious to know if a Jacob's Ladder would produce enough hot air to keep a hot air balloon afloat, or in other words, that it could be a substitute for a standard gas burner used for hot air balloons which carry humans. I am not actually planning to build one and use one for a real hot air balloon, it's just a scientific curiosity that I've had for a long time that I would now like to get an answer to from the Engineering community.
I am thinking that one could use several car batteries connected in series as the power source and a cable from these batteries would be connected to a high voltage transformer which would provide the high voltage for the Jacob's Ladder.
Not being an engineer, I have no idea how large the Jacob's Ladder would have to be in proportion to the hot air balloon, nor do I have any idea as far as how long the two rods would have be or what their thickness would have to be to handle the high voltage spark and heat from the plasma.
Also, I understand that the Jacob's Ladder could not inflate a hot air balloon by itself, one would still have to use a standard hot air balloon inflater/fan for doing that, yet once it's inflated, the Jacob's Ladder would then be turned on and would produce the hot air needed to make the balloon rise and keep it afloat.
Could a Jacob's Ladder produce enough hot air for a hot air balloon?
EDIT
Based on the comments and answer I've received about this idea, I am now thinking that instead of using car batteries, one could bring on board a small gas-powered electric generator and connect that to the high voltage transformer. A small, lightweight model like the one shown below may be an ideal model to use:
