Optimizing Solar Water Heater Efficiency for Pool Heating

[tomot]

I thought Wolfram Alpha might be able to help me with this problem, however
so far I have had no luck, with the website nor their community:

I have a 1230 gal pool heated by the sun to 70 degrees F, If I remove 30 gal
and let the 30 gal be heated in my solar collector to 100 degree F, and then add it back to the pool.

What will my new pool temperature be?
Is this raise in temperature linear? meaning if continue to do this once every hour via a timer and a pump can I extrapolate how long it will take to raise the pool temperature to 80 degrees?

TIA!

 

[cesiumfrog]

Temperature is linear in average energy, so yes.
But, heat transfer [with the outside environment, rather than by direct mixing of enclosed fluids] is not linear. The solar heater will be more efficient if the water constantly pumps through it instead of overheating a smaller volume (and the pumping heats the water too). On the other hand, heat sinking pipes could reverse this. Also, the higher the pool temperature gets, the faster it will be cooling.

 

[tomot]

thanks for your reply! I presume then that I really need to look for is a generalized heat transfer formula for water, if there is such a thing?