A layer of ice of thickness y is on the surface of a lake. The air is at a constant temperature `-theta^@C` and the ice water interface is at `0^@C`. Show that the rate at which the thickness increases is given by ` (dy)/(dt) = (Ktheta)/(Lrhoy)` where, K is the thermal conductivity of the ice, L the latent heat of fusion and `rho` is the density of the ice.

A layer of ice of thickness y is on the surface of a lake. The air is

1.	A layer of ice of thickness y is on the surface of a lake. The air is at a constant temperature `-theta^@C` and the ice water interface is at `0^@C`. Show that the rate at which the thickness increases is given by ` (dy)/(dt) = (Ktheta)/(Lrhoy)` where, K is the thermal conductivity of the ice, L the latent heat of fusion and `rho` is the density of the ice.
Answer» Correct Answer - A See the extra points just before solved examples. Growth of ice on ponds. We have already derived that `t = 1/2 (rhoL)/(Ktheta) y^2` `:. (dt)/(dy) = (rhoLy)/(Ktheta)` `:. (dy)/(dt) = (Ktheta)/(Lrhoy)` .

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