Physics Help - Energy / Efficiency Problem?

I don't even know how to go about starting this problem. I am so lost...

1. Compute the cost (to the nearest penny) of warming the water in a Swimming Pool by 9 degrees F (5 degrees C) using a gas pool heater having 80% efficiency.

2. Repeat the computation if the pool uses an electric heater having 80% efficiency.

Pool characteristics:
diamater: 18 feet, round
height: 4 feet, but average water depth is 3.5 feet

Use current gas and electric rates from Nationalgrid utility bill:
gas charge equals $1.01 per therm
electricity rate is 16 cents per kilowatt-hour

1 therm = 105480.4 kiloJoules
1 kwh = 3600 kiloJoules
1 cu ft = 28.317 liters
1 liter = 1 kg of water
1 cal = 4.187 J
1 btu = 1.0548 kJ

We obviously need the mass of the water, so let's do this first:

The area of the pool is r²π, so it is 9²π ft² ≈ 81*3.14 ft² ≈ 254 ft².
The volume of water is 3.5*254 ft³ ≈ 890 ft³.
In liters, this is ≈ 890*28.317 ≈ 25200 L.

Heating one liter (or 1kg ... almost the same) by 1 Kelvin uses up 4187 J of energy. So we need

5 * 25200L * 4.187 kJ ≈ 528000 kJ

of net energy to heat up that pool by 5 K (or 5 deg C).

With 80% efficiency, you need 528000/0.8 kJ = 660000 kJ of energy you'll pay for.

1. 660000 kJ / 105480 kJ/therm ≈ 6.26 therms, so you pay $6.30 or so when using gas.

2. 660000 kJ / 3600 kJ/kWh ≈ 183 kWh, so you pay 183*$0.16 = $29.30 or so when using an electric heater.

Why is that difference so large? Electric energy is much more versatile because it can be used for many different purposes - e.g. running motors, running computers and TVs, lighting etc. Gas, on the other hand, can only be used for heating. So you pay dearly if you use that versatile energy of electricity for simply producing primitive heat.

For More Information on Btu Swimming Follow The Links Below-

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Propane Pool Heater

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As you already understand choosing a swimming pool heather is a pretty serious task. To learn more on this issue you can check for pool heaters and pool supplies at http://haywardpoolheater.net

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