How long does the 2nd pot of water take to boil right after the 1st one finishes? Say I have a pot of water that boils in 20 minutes, at whatever temperature.
If I leave the fire on, take the pot off, pour the hot water into a container, refill the pot with tap water and put it back on the fire.
How long will the 2nd pot take to boil and why?
 A: Assuming the first was also tap water at the same temp and the pot was room temperature, then all that can be said given your question is "less than 20 minutes".  It depends on the thermal capacity of the pot.
Put another way, the first time you boil the water you have to do two things:


*

*Heat the pot to boiling temp

*Heat the water to boiling temp


The second time all you have to do is:


*

*Heat the water to boiling temp


What really happens when you put the tap water in the hot pot for the second time is that thermal energy from the pot flows into the cooler water and warms it up.  This lowers the temperature of the pot and raises the temp of the water until they are roughly equal temperatures (thermal equilibrium).  After this balancing the whole system starts out warmer than the first system did and less energy must be put into the system to heat it to the same boiling point.  If the first one took 20 minutes then the second one will take less time.  The actual amount of time saved depends on how much heat energy was stored in the pot and that depends on the size of the pot, what it's made out of, etc.
