Water heater contains 51 gal of water. part a how many kilowatt-hours of energy are necessary to heat the water in the water heater by 25 ∘c?

5.6 kilo-watt hours  
The specific heat of water is 4.1796 J/(K*cm^3) which means that in order to raise the temperature of 1 cubic centimeter of water 1 Kelvin, it takes 4.1796 Joules of energy. So let's start by converting 51 gallons into cubic centimeters: 
51 gal * 3.78541 L/gal * 1000 cm^3/L = 193055.91 cm^3  
Since the size of 1 Kelvin is the same as the size of 1 degree C, we don't need to worry about converting the temperature. 25 degree C increase is the same as a 25 K increase. So let's calculate how many joules we need. 
193055.91 cm^3 * 25 K * 4.1796 J/(K*cm^3) = 20172412.04 J 
20172412.04 J = 20172412.04 kg*m^2/s^2 
 20172412.04 kg*m^2/s^2 / 3600 s/h = 5603.447788 watt hours. 5603 / 1000 = 5.6 kilowatt-hours.

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