On the surface of lake when the atmospheric temperature is -15^∘ C, 1.5 cm thick layer of ice i

step 1 Here in this problem I can write the value of dm by d t multiplication l is equal to k a theta b

On the surface of lake when the atmospheric temperature is...

On the surface of lake when the atmospheric temperature is $-15^{\circ} \mathrm{C}, 1.5 \mathrm{~cm}$ thick layer of ice is formed in $20 \mathrm{~min}$, time taken to change its thickness from $1.5 \mathrm{~cm}$ to $3 \mathrm{~cm}$ will be (A) $20 \mathrm{~min}$ (B) less than $20 \mathrm{~min}$ (C) greater than $40 \mathrm{~min}$ (D) less than $40 \mathrm{~min}$ and greater than $20 \mathrm{~min}$

On the surface of lake when the atmospheric temperature is $-15^{\circ} \mathrm{C}, 1.5 \mathrm{~cm}$ thick layer of ice is formed in $20 \mathrm{~min}$, time taken to change its thickness from $1.5 \mathrm{~cm}$ to $3 \mathrm{~cm}$ will be
(A) $20 \mathrm{~min}$
(B) less than $20 \mathrm{~min}$
(C) greater than $40 \mathrm{~min}$
(D) less than $40 \mathrm{~min}$ and greater than $20 \mathrm{~min}$

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Key Concepts

Stefan's Law (or Stefan Problem)

Stefan's Law relates the thickness of the phase change layer (like ice) to the square root of the time elapsed. This law is crucial in predicting how the ice layer develops over time, considering the conduction of latent heat through the ice, and explains why the time required for growth increases non-linearly as the ice thickness increases.

Phase Change and Latent Heat

This concept covers the energy exchange involved when a substance changes from one state to another, such as water freezing into ice. The latent heat of fusion must be removed from the liquid for it to solidify, making the process depend on how quickly heat can be extracted from the system.

Thermal Conduction

Thermal conduction is the process by which heat flows through a material from regions of higher temperature to lower temperature. In the context of freezing water, heat must be conducted through the already-formed ice layer, which offers resistance to heat flow and affects the rate at which the ice layer can grow.

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