About the tankless water heater:
5 gal/min is 1/3 liter/sec. Heating from 10 C to 45 C will require
4186 J/l-C * 1/3 liter/sec * 35 C
= 48000 Watt. = 200 Amp * 240 Volts
You can't wire for that.
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An electric tankless hot water heater is a device that can heat water without having to use a storage tank to do so. They may also be called instant hot water heaters, as the water is heated only as it is needed. In some cases, this can be a cost savings as unused heated water does not have to continually be reheated until use. The only time the heating elements work in an electric tankless hot water heater is when there is a need for them to do so.
In order to be used in a way that is comfortable for bathing, or effective for dish washing, and other types of cleaning, water must be heated. In the past, the only way to do that was to use a traditional hot water heater, with a large tank. The electric tankless hot water heater now offers a viable alternative. In cases where it may not be appropriate for all uses, it can still be used in certain situations in a home.
The keys to an electric tankless water heater are in the heating elements located inside the pipes. The elements are heated to a high degree and directly touch the water, so that heating happens nearly instantaneously. Most of the time there is no noticeable delay in the water coming out of a regular pipe, versus a pipe utilizing this type of heater. In fact, the hot water actually comes out much faster in the vast majority of cases, than with a traditional water heater. This is because there is no need to wait for the cold water to get flushed out of the pipes before the hot water starts to flow.
In most cases, an electric tankless hot water heater can provide hot water at a rate of between two and five gallons (7.5 to 19 liters) each minute. This should be adequate for nearly all types of conventional showers. It should also allow the filling of a bathtub without too much delay, though perhaps not quite as fast as a traditional hot water heater.
As with any electrical device, an electric tankless hot water heater will need to be installed properly, and in compliance with local codes. Due to the fact that these heaters deal with both electricity and water, it is especially important to make sure the installation is done properly. Ideally, a professional electrician should be hired for the job. Those who try to do the installation without the proper experience or knowledge may be putting themselves, or their homes, at risk.
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