Gordon-Loomberah wrote:depending on the coefficient of performance, they would be ahead by a reasonable factor. However, unless they are using a different gas than what's in a heat pump hot water system, they wont bring the water to a boil... or are there heat pumps for boiling water in the kitchen available now

The problem with the heat-pump, is that it would be possibly wasteful, in that it would create COLD within the environment (the kitchen), that would then need to be heated, during winter.
It's the reverse of a refrigerator, where in SUMMER, the created heat becomes a nuisance.
From my findings with the HW-Heat Pump, it is clear that in winter, I use significantly more power (60%) to heat the same volume of water.
I admit that my first response to the first question of "Which is the most efficient"? would have been ÏNDUCTION"..
Not having played with them, I suppose the issue is the heat generated by the electronics.
I am aware that an installation requirement is that they have plenty of ventilation to move the waste heat.
The only other consideration in the "COST" of heating that water, is the actualy COST of the energy.
ie. the cost of the GAS used , rather than the WATTS equivalent of the energy. I'll try and calculate that from your maths
A most interesting experiment.!
I still ponder why any form of "Resistive Heating" differs in watts/cost, to another.
ie. I would have guessed that the Immersion-Heater and the "Resistive-Element-Jug" would have used the same WATTS.
I could have imagined that one of those "Conduction" jugs ( The two separated plates ), might be inefficient because some energy could be lost to other energies being created.
Could the immersion-heater be more efficient, because it's a gentle heater, with minimal energy lost to violent water aggitation.
Was the old-electric-jug, a wire-wound bobbin or an enclosed element. ?
I would still think that a quality jug with an enclosed element (replicating an immersion heater) would then be the same as the immersion heater.
PS -- There are such devices as Refrigerated (Heat-Pump) water heaters.
They tend to have two outlets.. One with boiling water and one with refirgerated water, so they do make the maximum use of the available energy.
I too, wonder how they could use a normal refrigeration gas to BOIL water. I think that the maximum temp you can get from a normal heat-pump is about 70DegC
Perhaps, they pre-heat, a tank of water, which then feeds (upon usage) another tank containing a resistive heater to boost the final temp to boiling.
PPS -- OT -- Last night in Sydney , the temp got down to 5DegC.
Last night I smelt burning coal. We have noticed burning wood smells for some time.
God help us if we end up like it was back in the 60's with the heavy smell of burning coal and smogs that blanketed the sun until mid mornings..
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