# A Problem from my book 6

In cold regions, the temperature of the surrounding is $$-20^\circ C$$. The water of the lake starts freezing and freeze up to a maximum depth.Find the maximum depth of ice sheet in meters formed. If the height of lake before freezing was $$19 \text{ m}$$.

You are given that:

• $$\dfrac{\rho_{\text{ice}} }{\rho_{\text{water}}} = 0.9$$.

• $$\dfrac{K_{\text{water}} }{K_{\text{ice}}} = 5$$.

• Maximum density of water is at $$4^\circ C$$.

Where $$K$$ is the thermal conductivity of substance.

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