How long for water to boil? given change in temp. over time…?
Your electric tea kettle takes water from 20 degrees C to 100 degrees C in five minutes.
You want to know how long it will take to boil the water completely away. You need the
heat energy to vaporize water at 100 degrees C. You know that this is called the “latent
heat” of vaporization in Wikipedia. How long does it take to boil off?
use the first set of data to determine the heat output of your kettle
Q = m c delta T where m=mass (we can arbitrarily set it to 1 kg since we will have to evaporate the same amount of water)
c=specific heat of water = 4186J/kg/C
delta T = change in temp = 80C
so to heat 1 kg of water from 20 to 100 requires
Q = 1kg x 4186J/kg/C x 80C = 334,880 J
to do this in 5 mins means that the energy output/sec is 334,880J/300s = 1116J/s (a unit known as a Watt, or a power)
the heat of vaporization of water is 2257J/kg
so it takes 2257kJ = 2.257×10^6Jto evap this 1 kg of water, which takes a time of
2257×10^6J/1116J/s = 2022s