Need formula -> How long will it take water to boil if :?

Question

m = 1 l
delta t = 90°C
P = 500W

need to find time

some one help me with the formula

Also the formula for the time needed to vaporize that 1 l of water please :)

Answer 1

The energy (Q) it takes to raise the temperature of water:

Q = mCΔT

m = 1 kg
C = 4186 J/kg°C
ΔT = 90°C

Q = (1 kg)(4196 J/kg°C)(90°)
Q = 376740 J

If you have a 500 W heater, it puts out 500 J of heat every second.

So 376740 J / 500 J/s = 753 s

That will get the water to the point that it's able to boil. You have to continue to add energy to continue to vaporize (boil) the water.

If you wanted to vaporize the entire kg of water, you'd need an additional 2260000 J of heat which would take the 500 W heater 4520 s.

Answer 2

The actual time to boil a pot of water depends on several factors, such as barometric pressure, wind velicity (convective heat transfer loss), if there are bubble initiatation sites (impurities) in the water, etc. But in general,

Q(dot)= m*Cp*(delta T)/(delta t)
where Q(dot) is the power (heat rate) going into the water;
Cp is the heat capacitance of the water;
delta T is the temperature difference of the water at start to the boiling point (212F);
delta t is the for the water to boil.

Just plug in your numbers, making sure of the correct units.