Water at -10^∘ C is present in a thermally insulated...

Water at $-10^{\circ} \mathrm{C}$ is present in a thermally insulated container. The ratio of mass of ice formed and initial mass of water, if a small crystal of ice is thrown into it, will be :
(a) $1 / 15$
(b) $1 / 17$
(c) $2 / 15$
(d) $1 / 8$

Key Concepts

Supercooling and Nucleation

Supercooling refers to the state of a liquid being cooled below its standard freezing point without solidification. When a small crystal (nucleation site) is introduced into supercooled water, it initiates the rapid formation of ice. This concept is crucial in scenarios where water is below 0°C yet remains liquid until a disturbance prompts freezing.

Thermal Equilibrium in Isolated Systems

In a thermally insulated (isolated) system, no heat is exchanged with the surroundings, meaning that all changes in temperature and phase occur solely due to internal energy transfers. The system ultimately reaches thermal equilibrium when all parts attain the same temperature, and the energy exchange between cooling water and the freezing process (latent heat release) is balanced.

Specific Heat Capacity

Specific heat capacity is the measure of the amount of heat needed to raise the temperature of a unit mass of a substance by one degree Celsius. In the scenario of water cooling from an initial subzero temperature, the specific heat capacity of water determines how much energy is released as it cools, which then contributes to the phase change.

Latent Heat of Fusion

Latent heat of fusion is the amount of energy required to change a substance from its liquid phase to its solid phase (or vice versa) at constant temperature. For water, as it freezes, it releases a specific quantity of latent heat, and this released energy is what facilitates the phase change from water to ice.

Conservation of Energy

This principle states that in an isolated system, the total energy remains constant; energy can be transferred from one form to another but is neither created nor destroyed. In the context of water freezing in a thermally insulated container, the energy lost by the water as it cools is exactly equal to the energy used to convert some of the water into ice via the release of latent heat.

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