How many BTU's per 24 hour day to heat 17,000 gallons of water from 76 degrees to 86 degrees (10 degree rise)?

Question

I have a 17,000 gallon pool that stays around 76 degrees during the summer. I want to be able to circulate enough heated water (BTU's) to maintain an 86 degree temp. thru the summer months. This question has nothing to do with how I plan on heating the pool (black plastic solar panels btw) but how may BTU's I will need to raise 17,000 gallons from 76 to 86 degrees and maintain that 86 degree water temp 24 hours a day. The solar panels that I'm looking at produce 80,000 BTU's in a 24 hour period. I don't know how difficult this problem will be to solve but I'm sure some engineer is out there that can. Thanks.

Answer 1

1 BTU is the heat required to raise the temperature of 1 pound of water 1 °F.

You have 17,000 gallons. Using the approximation of 8 lbs per gallon, you have 17,000 gal x 8 lbs/gal = 136,000 lbs.

To raise the temperature 10 °F, you'll need:

136,000 lbs * 10 °F = 1,360,000 BTU's.

Keep in mind that once you've raised the temperature to 86 °F, you only have to maintain the temp by keeping up with the losses to the environment. This will be affected by the ambient temperature.

Your solar panels can produce 80,000 BTU's per day, but you've got 136,000 lbs of water. That means you can only make up for a temperature loss of .59 °F. (80,000 ÷ 136,000 = .59)

You can reduce this heat loss with a pool cover. I've seen some pool covers that look like giant bubble wrap. In the sun these solar convers actually helps heat the pool as well.

Answer 2

Won't we need some environment information, to factor in the rate of heat loss along the way?

Or are we assuming a perfectly-insulated system in this problem?