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?

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. 

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