i can help you with this. you don't give a lot of information, so i'll have to make some generic assumptions. but in general, yes it might boil, but it will take while. it also means you get a short thermodynamics lesson too. ;-)
if you want to take a water heating element and add it to your kettle, you should look up some fantastic instructions at
www.theelectricbrewery.com. easier is an immersion heater.
the immersion heaters that i've seen, just plug into an outlet at one end, and you stick the business end into the water (PLEASE MAKE SURE YOU USE AN ELEMENT DESIGNED SPECIFICALLY TO DO THIS!!!! - otherwise this is the brewing equivalent of bathing with your toaster). i'd do a quick google search for immersion heaters to find one. then i'd follow the instructions that come with it.
whether you buy an immersion heater, or follow kal's instructions for adapting a hot water heater element, it will take some time to make that water hot.
so how long will it take to heat your water?
here goes:
first let's discuss the element: heaters are rated in watts (the amount of power they use), electric heaters are nice since almost all of the energy going in gets turned to heat (so much so that its pretty safe to use 100%). a 120 vac socket usually has a max of 20 amps. to get the maximum watts on the circuit before the breaker blows you multiply the volts by the amps so your max is 2400 watts (this is not a smart move), it is safer to go at about 80% of this (1920W). i have no idea what's actually available.
7.5 gallons is a decent size pot, i used to use the same size, i would typically heat 6 gallons of water in that. the math is a lot simpler in metric, so we're switching.
6 gallons = 22.7 liters
to boil water you have to transfer energy into the water. the amount of energy needed to change the temperature of something is called the specific heat. specific heat is given in joules/gram times degrees c (sometimes written as J/gK), water is 1.46 J/gK
the amount of energy to raise one gram of water 1 degree c is one calorie, or 4.184 joules.
so you have 22700 grams of water that you want to raise from room temperature (20c) to boiling (100c). 22700*80=181600 or 7598144 joules.
oooooo kaaaaaay..... so what does this mean to you?
you need one more piece of information. watts are power, and joules are energy. power is energy over a period of time. lucky for us, 1 watt is equal to 1 joule per second. so your heater can deliver 1920 joules/second. therefore 7598144 joules/1920 joules/second = 3957.37 seconds, or about 66 minutes. in a perfect world.
as you know, this world ain't perfect. you will have heat loss through the sides of your kettle, and a huge amount of heat loss out the top. plus you have the energy of phase change to deal with as well. all that can be figured out too, but its a little more complicated. we would need to know the diameter and material of the pot, the air temperature, the barometric pressure at your altitude and so on. never the less, we can say that the time will be somewhere north of 65 minutes, and quite likely considerably higher.
hope that helps
prof warthog
