Math Geeks — What do you Think?

 Ok, here’s the situation:

Say you have a hot water tank (boiler here) that holds 80 liters of water.  You want to heat that water to 70 degrees C.  Assume the temp of the water in the tank (and the incoming water) is room temperature–20 deg celcius.  Also assume that during the day, electric costs 4 times what it does at night.

Now, is it better to heat all 80 liters of water at night (with cheap electric) or are you better off to heat it a bit at a time as it comes into the tank when you use it?  Assume 90% of the hot water usage is during the expensive time.

You’ll have to look up the formulas as I don’t have them handy right now (sorry).  My hypothesis is that it will be cheaper to heat the water at night all at once instead of during the day time as you use it.  Why?  Just because 1 cubic cm of water ALWAYS takes the same amount of energy to heat it up a given number of degrees.  But, I could be wrong.  What do you think?

Image from akirsa via flickr

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