Calculate time to heat my swimming pool

I have a swimming pool of 5300Liters. I have a heating element from a washing machine taking 1min17s to heat a bucket (10L) of water from 22 degrees to 30 degrees celcius.

the water in my pool is 19 degrees celcius.

how long would it take to warm my pool to 30 degrees? How long would it take to warm it to 25 degrees?

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migrated from math.stackexchange.comSep 3 '11 at 12:33

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I've asked a mod for physics.SE migration. –  user172 Sep 3 '11 at 12:23
I'm sorry I really had no idea what tag to give this one :) –  Stefanvds Sep 3 '11 at 12:26
A pool is such a huge and complex system, it will be near impossible to give an accurate theoretical answer to this. Your best bet is to do an experiment. –  Michael Sep 3 '11 at 14:18

It is a simple calculation. You need $77s$ to heat $10l$ water by $8$ degree so you need $0,9625s$ to heat $1l$ water by $1$ degree (noting that the relation is proportional, this is physics) and therefore $11 °\cdot5300 l \cdot 0,9625 \frac{s}{l \cdot °}= 56113,75s \approx 15,6 h$.

However I don't consider that your pool will cool itself down over time.

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If the pool ain't insulated, well... ;) –  user172 Sep 3 '11 at 12:27
Yea thats why I said I didn't consider that :-), but then it depends on many factors I think like the surface area of the water and the outside temperature. –  Listing Sep 3 '11 at 12:29
15 hours sounds long enough period so that the heat flux via the pool surface will be very significant. Actually for a "typical" pool I believe this effect will dominate. Perhaps you won't be able to heat the pool by 8 degrees at all (too bad for you). –  valdo Sep 4 '11 at 12:14