How many gallons of boiling water would you have to add to a five hundred gallon tank to raise the temperature twenty degrees?

how hot is the boiling water? That makes a big difference? (is that a homework question?)

I'm just trying to apply logic here, bear in mind there may be some special properties that you may have to account for like the glass/plexiglas that the water is in will have to have its temp raised also. So here goes...

Raising 500 gallons of water 20 degrees would seem to require a combined value of 10,000 degrees (500 gallons times 20 degrees). So first you need to know the temperature difference between the existing water and boiling. Then devide the resulting difference into the 10,000 degrees for your simplistic answer.

However, it is a bit more complicated if the tank is full at 500 gallons because you have no room to add the boiling water. That is, it would roughly take 62 gallons of boiling water to raise 500 gallons of 50 degree water to 70 degrees and the tankwouyld obviously overflow. So if it was already full you would have had to remove 62 gallons first leaving 438 gallons and consequently reducing your degree needs to 8760 degrees which means if you add the 62 gallons of boiling water you would have ended up with 72.7 degree water.

So, I'd reduce the capacity to 445 gallons and add 55 gallons of boiling water and you should be pretty close.