Answer:
22.6 minutes
Explanation:
The energy that must be supplied to the water, in order to completely boil it, is given by:
[tex]Q= m \lambda[/tex]
where
m = 1.5 kg is the mass of the water at boiling temperature
[tex]\lambda=2.26\cdot 10^6 J/kg[/tex] is the specific latent heat of vaportization of water
Substituting into the equation, we find
[tex]Q=(1.5)(2.26\cdot 10^6)=3.39\cdot 10^6 J[/tex]
The power supplied by the kettle is
[tex]P=2.5 kW = 2500 W[/tex]
We also know that power is defined as the ratio between energy supplied and time:
[tex]P=\frac{Q}{t}[/tex]
Therefore, the shortest time the kettle must be left on in order to completely boil the water can be found by re-arranging the previous equation:
[tex]t=\frac{E}{P}=\frac{3.39\cdot 10^6}{2500}=1356 s= 22.6 min[/tex]
