To solve this problem we will apply the concept related to the heat transferred to a body to reach a certain temperature. This concept is shaped by the energy ratio of a body which is the product of the mass, its specific heat and the change in temperature. For the specific case, it will be the sum of the heat transferred to the Water, the Aluminum and the loss due to latency due to vaporization in the water. That is to say,

Here,
= Mass of Aluminum
= Specific Heat of Aluminum
= Specific Heat of Water
Mass of water
Latent of Vaporization
Replacing,

Converting,


Therefore is required 440.409kCal
Answer:

Explanation:
Given:
- thickness of the base of the kettle,

- radius of the base of the kettle,

- temperature of the top surface of the kettle base,

- rate of heat transfer through the kettle to boil water,

- We have the latent heat vaporization of water,

- and thermal conductivity of aluminium,

<u>So, the heat rate:</u>


<u>From the Fourier's law of conduction we have:</u>


where:
area of the surface through which conduction occurs
temperature of the bottom surface

is the temperature of the bottom of the base surface of the kettle.