Yes, it takes 1 calorie of energy to raise 1 gram of water 1 degree Celsius. If the water is warmer it will take less energy to get it to boil. That being said you are heating the water that comes out your tap with your water heater instead of your stove.
Water boils at 212 F or 100 C at sea level. It takes energy to raise the temperature of water. So if your cold tap water is 40 degrees F and your hot water is 100 degrees F it would take more energy to raise the temperature from 40 degrees to 212 degrees than it would take to raise water from 100 degrees to 212 degrees. The easiest way to visualise this is fill a class of water 1/3 of the way and 2/3 of the way. The more water you have to add to reach to top of the cup, the more “energy” you add to the water.
Yes, heating colder water takes more energy than heating warmer water. The boiling point of water remains the same (100 degrees Celsius), but a larger amount of heating (from the cold water) requires more energy than a lesser amount of heating (from the warmer water).
No. It takes the same amount of total energy, it is just coming from two different sources. It does take 1 calorie to raise 1 gram of water by 1 degree Celsius, and it will take less energy from your stove top to boil warm tap water than cold tap water. But that warm tap water was at some point cold tap water that used the energy from your hot water heater to become warm.
I don’t think people are understanding your question. The real question is whether it is more efficient to raise the temperature of tap water to water heater temperature in a water heater or on the stove. In my house, the water heater is on the other end of the building. To get hot water from the heater to the faucet it probably takes a gallon of hot water to displace the cold water that is already in the pipes. So I am using a gallon and a half of hot water from the tap to fill a half gallon sauce pan with hot water. I think I’m better off heating cold tap water on the stove.
Yes. Boiling hot water is eliminating at least half of the work. If the water’s already closer to boiling, it’s like getting rid of an entire step to the process.
The difference between heating up the water in the tap and heating up the water on the stove is likely negligible in terms of energy. However, it will obviously be faster to bring water with a higher initial temperature to a boil.
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