Question

It takes an electric tea kettle with 20oC water 5 minutes to react the boiling point (100oC). How long will it take for all the water to boil away, assuming the same rate of heat addition?

Answer 1

The heat required for the water to reach a temperature of 100 degrees C from 20 degrees C is calculated through the equation,
H = mcpdT
where m is the mass, cp is the specific heat and dT is the temperature difference. cp for water is 1 cal/g°C. Thus, the heat applied is,
H = m(1)(80) = 80m
This heat was applied for 5 minutes.

Now, recall that the heat needed to boil off the water is calculated by the equation,
H = m(hv)
where m is still mass and hv is the heat of vaporization which is equal to 540 cal/g. Thus, the heat required is,
H = 540m
We use ratio and proportional to get the time required.
80m / 5 minutes = 540 m / x minutes
The value of x from the equation is 33.75 minutes.