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Mr Kilowatt
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Math: Relationship between Kwh and temperature of water in water heater

Mr Kilowatt does water heater math

Kilowatt hours of electricity needed to heat water ... the math formula:

 1.) Basic formula > it takes .0002931 Kwh to raise 1 pound of water 1°F

2.) Basic number >A gallon of water weighs 8.34 lbs (pounds)

3.) "A BTU is amount of heat needed to raise 1 pound of liquid water by 1° from 60° to 61° F at constant pressure of one atmosphere. Other definitions of BTU exist which are based on different water temperatures and cause the results to vary by .5%." (For analysis of water heaters, .5% is ignored. Variation in atmospheric pressure is also ignored. Water heater 'science' is an approximation since calcium carbonate in tank will vary electrical efficiency and tank capacity.)

4.) BTU formula > 1 BTU = 2.931 x 10–4 Kwh (kilowatt hours).
     BTU = 2.931 x .0001 = .0002931 Kwh
     Therefore it takes .000293 Kwh to raise 1 pound of water 1° F
 
5.) 30 Gallons of water x 8.34 = 250.2 lbs
     40 Gallons of water x 8.34 = 333.6 lbs

Calculation using 40 Gallon water heater:
> Ordinary 40 gallon water heater in attic. Temperature in attic = 50° F. Temperature of water in tank = 50° F.
> Water in tank weighs 333.6 lbs.
> How much electricity is needed to raise temperature of full tank to 120° F.
> 120° minus 50°  = 70° > so the temperature needs to go up 70°
> Multiply 333.6 x 70 x .0002931 = 6.84 Kwh

Calculation using 30 Gallon water heater:
> Same problem as above
> Water in tank weighs 220.2 lbs
> Multiply 250.2 x 70 x .0002931 = 5.13 Kwh

Temperature of water
 Cost if you use 40 Gallon per day Cost if you use 30 Gallon per day
Raise from 32° to 120° 8.60 Kwh x 14¢ = $1.20 6.45 Kwh x 14¢ = 90¢
Raise from 50° to 120° 6.84 Kwh x 14¢ = 96¢ 5.13 Kwh x 14¢ = 72¢
Raise from 70° to 120° 4.88 Kwh x 14¢ = 68¢ 3.66 Kwh x 14¢ = 51¢
Raise from 85° to 120° 3.42 Kwh x 14¢ = 48¢ 2.56 Kwh x 14¢ = 36¢

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