Has anyone ever made a battery-powered kettle with significantly higher power than can be pulled from a wall outlet? Modern lithium batteries can deliver many kilowatts of power, and given that the total energy needed to boil the water is basically fixed, the battery size requirements might be pretty reasonable. I wouldn't be surprised if boiling water in 15s is possible even on a 120v American outlet.
At 3.6V and 45A, each battery should output 162 watts. Rounding to 150 watts, we'd need 20 of them to make 3 kilowatts. So $100 worth of batteries.
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Question #2: How long will they last? Long enough to boil water?
At the 45-amp discharge rate and with 4.2 amp-hour capacity, it should take 4.2/45 hours = 6 or 7 minutes to discharge them.
By my math, it takes 335 kilojoules to heat a liter of water from 20°C to 100°C. A 3 kilowatt kettle should be able to do it in 335/3 = 112 seconds.
So the batteries should be able to boil water around 3 times before discharged.
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Those calculations are for running on battery alone. Since you can get 1500W out of an American 120V outlet, you could make a kettle that draws 1500W from the wall and boosts it with 1500W of battery power. (I'd use two heating elements.) Then you only need $50 of batteries.
The kettle is going to be a bit heavy, though. The batteries are 70g each, so 20 of them is 1.4 kg. Also, I don't know much batteries heat up when cranking out 45 amps, but I bet the answer is a lot, and you may need active cooling and/or thermal shutoff.
Put the batteries and controller in the base, have the jug lift off from the electrical connectors to the heating elements, the jug is therefore light and convenient.
It would be better to have a box that converts 2 NEMA 5-15 120v plugs to one 6-15 240V plug.
I've seen such a box for sale, I think for the RV market. You plug into both phases of the 120/240V split phase and get a dryer plug at a lower amperage.
Now I realize that what I really want to build is a kettle with two 3kW heating elements. On a UK ring main, I can plug the two elements into two neighbouring sockets and still have headroom before I blow the breaker. I can cut my time-to-tea from 45 seconds to 22 seconds!
It's certainly possible; whether it makes any economic sense at all is a different matter. I can't imagine much of a market for a device like this. Basically you're proposing a relatively complicated device (compared to a simple tea kettle, though modern ones have a handy auto-shut-off feature) for the sole purpose of boiling water a little faster. Americans aren't big tea drinkers in the first place, so it's hard to imagine many would pay 5x-10x as much (guessing) for a fancy battery-boosted tea kettle just to boil water a little faster. I suppose it's possible though; Li-ion batteries are pretty commonplace these days.
I think it's certainly possible. FWIW car batteries can often support 1000A especially those for large diesel engines. They aren't meant for continuously loads or deep cycles though. Marine batteries may be able to overcome this.