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Preamble

    1 BTU will raise the temperature of 1 lb of water 1 degree F.
    1 gallon of water weighs about 8.33 lbs.
    1 watt-hour of resistance heat yields 3.413 BTUs.
    4500 watts = 15,358.5 BTUs/hour
    

Calculations

10 Gallon System

BTUs = 83.3 * (Target Temperature - Start Temperature)

Duration = BTUs / BTU Rate

Cost of Heating = Duration * Watts * Price