One for thermodynamicists
Discussion
Firstly, I think we need to qualify the assumptions.
1. We don't care about total water usage, just the energy required to heat it.
2. The enery in the water that you run out of the tap before filling the pan is negligable. (We'll re-visit this assumption)
3. Pressure differences are negligable.
Then we need to define the problem.
Which is greater:
a) The energy required to boil a paan of water from room temperature.
or
b) The energy required to boil a pan of water that starts off warm, plus the energy required to heat the new water in the boiler so that the boiler returns to it's previous temperature.
Then we need to go away with a pen and paper and do some sums...
1. We don't care about total water usage, just the energy required to heat it.
2. The enery in the water that you run out of the tap before filling the pan is negligable. (We'll re-visit this assumption)
3. Pressure differences are negligable.
Then we need to define the problem.
Which is greater:
a) The energy required to boil a paan of water from room temperature.
or
b) The energy required to boil a pan of water that starts off warm, plus the energy required to heat the new water in the boiler so that the boiler returns to it's previous temperature.
Then we need to go away with a pen and paper and do some sums...

A guy i used to work with would fill several thermos flask with water he'd boiled at work and take them home to make his evening meal with (i kid you not). He also used to make about 10 cups of tea with a single tea bag etc etc, he wasn't even from Yorkshire (or Scotland for that matter!).
The water currently in the tap is already at room temperature. Only when you have used all the water in the plubing between the tap and the outside wall does it start getting colder. That is assuming the tap hasn't been used for a few hours beforehand.
Yet more assumptions, I obviously wasn't rigorous enough...
Yet more assumptions, I obviously wasn't rigorous enough...

Jinx said:
Is the pan upstairs or down - atmospheric pressure will effect the temperature the water boils at
Downstairs. The hot water comes from a tank one floor up.
I thought we should also allow for heat loss on the way down through the pipe - though that will decrease as the pipe warms up, reducing the heat loss from the water inside.
At first I thought this could be a neat GCSE Physics question, but it seems to be turning in to a PhD thesis
There's always the question of whether you need the hot water from the tank for anything else in the near future. If it's hot already and you don't need it then you are probably saving energy. If you doo need it, you might find that the hot tank is less efficienient that the hob.
Either way, I'd go for nestling a glass or metal container under the bonnet and going for an hour's drive. That'll warm it up. Not very efficiently, but who cares when you're in your car.
Either way, I'd go for nestling a glass or metal container under the bonnet and going for an hour's drive. That'll warm it up. Not very efficiently, but who cares when you're in your car.

scruffy said:
Microwave the fokker.
Gas has an efficiency of around 6%.
Electric(cookers) have an efficiency of around 14%.
Microwaves, around 55%.
I personally hate microwaves, but that's cause I'm a sandal wearing, lentilist.
I'd stick mine on my Child fuelled Aga.
So why don't we have microwave domestic boilers? Now that'd be a real "green" invention ....
Because a boiler is a lot more efficient than that - up to 90% odd for a condensing one. Also the figure of 55% for the microwave doesn't take into account the efficiency of turning fuel into electricity, which is probably around 30-40%, giving an overall efficiency of 17-22%.
Heating a pan of water from cold to boiling on a hob uses a lot more energy than if you heat the same amount of water part way with a boiler first. But there are other losses associated with the boiler system, like the amount of water you have to draw off first before it runs hot - which equates to a pipe full of wasted hot water afterwards - and the heat leaking out of the hot water tank; if you have a combi boiler, there's a fair bit of metal to heat up and cool down again just to heat a pan's worth of water. So it's a job to say which wins overall. Perhaps you could boil 20 pans of water a day, alternating each week between using the cold or hot tap to fill the pan, and keep daily records of the gas meter reading over a year or so, to see what you get. You'd have to make sure you only used gas for the boiler and the cooker, of course, no gas fires or anything.
Heating a pan of water from cold to boiling on a hob uses a lot more energy than if you heat the same amount of water part way with a boiler first. But there are other losses associated with the boiler system, like the amount of water you have to draw off first before it runs hot - which equates to a pipe full of wasted hot water afterwards - and the heat leaking out of the hot water tank; if you have a combi boiler, there's a fair bit of metal to heat up and cool down again just to heat a pan's worth of water. So it's a job to say which wins overall. Perhaps you could boil 20 pans of water a day, alternating each week between using the cold or hot tap to fill the pan, and keep daily records of the gas meter reading over a year or so, to see what you get. You'd have to make sure you only used gas for the boiler and the cooker, of course, no gas fires or anything.
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