A water heater contains 57 gal of water. How many kilowatt-hours of energy are necessary to heat the water in the water heater by 25 ∘C? Express your answer using two significant figures.

Answer 1

Hello, Josyln,

Did the problem provide a specific heat of water in terms of kwh? It would have been helpful to have that.

The problem asks how much energy, in kwh, is required to raise 57 gallons of water by 25⁰C.

The relationship used for this is:

q = cmDt, where c is the specific heat

I know water's specific heat as 4.186 Joules/g⁰C. It would be helpful to have it in kwh/gal⁰C, but I'll covert everything we need as we go through the problem.

Convert 57 gallons into grams: (57 gal)(3.785 L/gal)(1000kg/Liter)(1000g/Liter)

This requires three conversions: from gallons to liters, then liters into kg, and finally g, so that we can use the specific heat value of 4.186 Joules/g⁰C.

Please check my calculations. I found 2.158x10⁵ grams.

The heat required to raise 57 gallons of water by 25⁰C:

q = (4.186 J/g⁰C)(2.158x10⁵ grams)(25⁰C) = 2.26x10⁷ J

We need kwh. I believe the conversion factor is 2.78x10^-7kwh/J, but please check.

(2.26x10⁷ J)/(2.78x10^-7kwh/J) = 6.3 kwh (2 sig figs)

This seems a little low, so please check the various conversions with your information.

I hope this helps,

Bob