To determine the time taken for all the water to vaporize, we need to calculate the amount of energy required to vaporize the water and then divide it by the power of the electric kettle.
The energy required to vaporize the water can be calculated using the specific latent heat of vaporization formula:
Energy = mass × specific latent heat of vaporization
Given: Mass of water (m) = 0.4 kg Specific latent heat of vaporization (L) = 2 MJ/kg
Energy = 0.4 kg × 2 MJ/kg = 0.8 MJ
Now, let's calculate the time taken using the formula:
Time = Energy / Power
Power of the electric kettle (P) = 2 kW = 2 MJ/s
Time = 0.8 MJ / 2 MJ/s = 0.4 s
Therefore, it would take approximately 0.4 seconds for all the water to vaporize.