If I have 2 pots of water of the identical size and identical volume of water contained within. If I boil both pots of water to the same temp. For example 100 degrees C. If I boil one pot using a lower flame and the other pot using a higher flame. Then I turn off the flames. Will the hot water contained in both pots cool down at the same rate or will one retain its heat longer than the other?
Will the hot water contained in both pots cool down at the same rate
or will one retain its heat longer than the other?
The cool down is really just a function of how much thermal energy is in water/pots and what the thermal resistance to the ambient temperatures. As long as that's the same for both pots they will cool down at the same rate.
The pot with the lower flame will take more time to get to boiling, but once both pots are boiling, they are at the same temperature and that's all that matters.