Water is boiled at 1 atm pressure in a coffeemaker equipped...

Water is boiled at 1 atm pressure in a coffeemaker equipped with an immersion-type electric heating element. The coffeemaker initially contains $1 \mathrm{~kg}$ of water. Once boiling has begun, it is observed that half of the water in the coffeemaker evaporates in $10 \mathrm{~min}$. If the heat loss from the coffeemaker is negligible, the power rating of the heating element is (a) $3.8 \mathrm{~kW}$ (b) $2.2 \mathrm{~kW}$ (c) $1.9 \mathrm{~kW}$ (d) $1.6 \mathrm{~kW}$ (e) $0.8 \mathrm{~kW}$

Water is boiled at 1 atm pressure in a coffeemaker equipped with an immersion-type electric heating element. The coffeemaker initially contains $1 \mathrm{~kg}$ of water. Once boiling has begun, it is observed that half of the water in the coffeemaker evaporates in $10 \mathrm{~min}$. If the heat loss from the coffeemaker is negligible, the power rating of the heating element is
(a) $3.8 \mathrm{~kW}$
(b) $2.2 \mathrm{~kW}$
(c) $1.9 \mathrm{~kW}$
(d) $1.6 \mathrm{~kW}$
(e) $0.8 \mathrm{~kW}$

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Key Concepts

Latent Heat of Vaporization

This concept refers to the amount of energy needed to change a substance from a liquid to a gas at its boiling point, without a change in temperature. It is expressed in joules per kilogram and is key to understanding how much energy is required to evaporate a given mass of a substance, such as water, during boiling.

Energy Transfer in Phase Change

This concept involves calculating the total energy required to vaporize a portion of a substance using its latent heat of vaporization. In processes like boiling, the energy supplied goes into changing the state of the material rather than increasing its temperature. This calculation is essential for determining the energy demand in operations where phase changes occur.

Power and Rate of Energy Transfer

Power is defined as the rate at which energy is transferred or converted, typically measured in watts. In the context of heating and boiling, determining the power rating of an appliance involves dividing the total energy required to induce a phase change by the time period over which the energy is supplied, reflecting the device’s energy delivery capability.

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