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A layer of ice of thickness y is on the ...

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.

Text Solution

Verified by Experts

The correct Answer is:
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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